TARGET IIT JEE 2013 XIII MODERN PHYSICS C O N T E N T S. KEY CONCEPT...Page 2. EXERCISE I...Page 6. EXERCISE II...Page 7. EXERCISE III...

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1 PHYSICS TARGET IIT JEE 013 XIII MODERN PHYSICS C O N T E N T S KEY CONCEPT...Page EXERCISE I...Page 6 EXERCISE II...Page 7 EXERCISE III...Page 8 OBJECTIVE QUESTION BANK... Page 13 ANSWER KEY...Page

2 KEY CONCEPTS 1. CATHODE RAYS : (a) Generated in a discharge tube in which a high vaccum is maintained. (b) They are electrons accelerated by high potential difference ( 10 to 15 Kilo Volt) (c) K.E. of C.R. particle accelerated by a p.d. V is ev = (d) Can be deflected by Electric & magnetic fields.. ELECTROMAGNETIC SPECTRUM : Ordered arrangement of the big family of electro magnetic waves (EMW) either in ascending order of frequencies or of wave lengths Speed of E.M.W. in vacuum C = m/s = 3. PLANK'S QUANTUM THEORY : A beam of EMW is a stream of discrete packets of energy called PHOTONS, each photon having a frequency and energy = E = h. h = plank 's constant = Js. 1 P mv. m 4. PHOTO ELECTRIC EFFECT : The phenomenon of the emission of electrons, when metals are exposed to light (of a certain minimum frequency) is called photo electric effect. Results : (i) Can be explained only on the basis of the quantum theory (concept of photon). (ii) Electrons are emitted if the incident light has frequency 0 (threshold frequency) emission of electrons is independent of intensity. The wave length corresponding to 0 is called threshold wave length 0. (iii) 0 is different for different metals. (iv) Number of electrons emitted per second depends on the intensity of the incident light. (v) EINSTEINS PHOTO ELECTRIC EQUATION : Photon energy = K. E. of electron + work function. h = 1 mv = Work function = energy needed by the electron in freeing itself from the atoms of the metal. = h 0 (vi) STOPPING POTENTIAL OR CUT OFF POTENTIAL : The minimum value of the retarding potential to prevent electron emission is : ev cut off = (KE) max Note : The number of photons incident on a surface per unit time is called photon flux. 5. WAVE NATURE OF MATTER : Beams of electrons and other forms of matter exhibit wave properties including interference and diffraction with a de Broglie wave length given by = h p (wave length of a praticle).

3 6. ATOMIC MODELS : (a) THOMSON MODEL : (PLUM PUDDING MODEL) (i) (b) Most of the mass and all the positive charge of an atom is uniformly distributed over the full size of atom (10-10 m). (ii) Electrons are studded in this uniform distribution. (iii) Failed to explain the large angle scattering - particle scattered by thin foils of matter. RUTHERFORD MODEL : ( Nuclear Model) (i) The most of the mass and all the positive charge is concentrated within a size of m inside the atom. This concentration is called the atomic nucleus. (ii) The electron revolves around the nucleus under electric interaction between them in circular orbits. (iii) An accelerating charge radiates the nucleus spiralling inward and finally fall into the nucleus, which does not happen in an atom. This could not be explained by this model. (c) BOHR ATOMIC MODEL : Bohr adopted Rutherford model of the atom & added some arbitrary conditions. These conditions are known as his postulates : (i) (ii) (iii) (iv) The electron in a stable orbit does not radiate energy. i.e. mv k ze r r A stable orbit is that in which the angular momentum of the electron about nucleus h h is an integral (n) multiple of. i.e. mvr = n ; n = 1,, 3,...(n 0). The electron can absorb or radiate energy only if the electron jumps from a lower to a higher orbit or falls from a higher to a lower orbit. The energy emitted or absorbed is a light photon of frequency and of energy. E = h FOR HYDROGEN ATOM : (Z = atomic number = 1) (i) L n = angular momentum in the n th orbit = n h. (ii) r n = radius of n th circular orbit = (0.59 Aº) n ; (1Aº = m) ; r n n. (iii) E n Energy of the electron in the n th orbit = ev i.e. E n n 1 n. Note : Total energy of the electron in an atom is negative, indicating that it is bound. Binding Energy (BE) n = - E n = ev n. (iv) E n - E n1 = Energy emitted when an electron jumps from n th orbit to n th 1 orbit (n > n 1 ). 1 1 E = (13.6 ev). n n 1 E = h ; = frequency of spectral line emitted. 1 1 = wave no. [ no. of waves in unit length (1m)] = R n Where R = Rydberg's constant, for hydrogen = m -1. (v) For hydrogen like atom/species of atomic number Z : 1 n Bohr radius r nz = n = (0.59 Aº) n ; E Z nz = ( 13.6) Z Z n ev R z = RZ Rydberg's constant for element of atomic no. Z. Note : If motion of the nucleus is also considered, then m is replaced by. 1.

4 Where = reduced mass of electron - nucleus system = mm/(m+m). In this case E n = ( 13.6 ev) n Z. 7. SPECTRAL SERIES : (i) Lyman Series : (Landing orbit n = 1). 1 1 Ultraviolet region R ; n > 1 1 n (ii) Balmer Series : (Landing orbit n = ) 1 1 Visible region R ; n > n (iii) Paschan Series : (Landing orbit n = 3) 1 1 In the near infrared region R ; n > 3 3 n (iv) Bracket Series : (Landing orbit n = 4) 1 1 In the mid infrared region R ; n 4 > 4 n (v) Pfund Series : (Landing orbit n = 5) m e 1 1 In far infrared region R ; n > 5 5 n In all these series n = n is the line = n 1 + is the line = n is the line... etc. where n 1 = Landing orbit 8. EXCITATION POTENTIAL OF ATOM : Excitation potential for quantum jump from n 1 n = En En1. electron charge 9. IONIZATION ENERGY : The energy required to remove an electron from an atom. The energy required to ionize hydrogen atom is = 0 ( 13.6) = 13.6 ev. 10. IONIZATION POTENTIAL : E n Potential difference through which a free electron is moved to gain ionization energy = electronic charge 11. X - RAYS : (i) Short wavelength (0.1 Aº to 1 Aº) electromagnetic radiation. (ii) Are produced when a metal anode is bombarded by very high energy electrons. (iii) Are not affected by electric and magnetic field. (iv) They cause photoelectric emission. Characteristics equation ev = h m e = electron charge ; V = accelerating potential m = maximum frequency of X - radiation I k k -Characteristic Spectrum Continous Spectrum m k k volt

5 (v) Intensity of X - rays depends on number of electrons hitting the target. (vi) Cut off wavelength or minimum wavelength, where V (in volts) is the p.d. applied to the tube 1400 min V (vii) Continuous spectrum due to retardation of electrons. (viii) Characteristic Spectrum due to transition of electron from higher to lower v = a (z - b) [ MOSELEY'S LAW ] b = 1 for k transition Note : (i) Binding energy = - [ Total Mechanical Energy ] (ii) Velocity of electron in n th orbit for hydrogen atom n1 n Series limit means minimum wave length of that series. (iii) For x - rays R z b (iv) c 137 n ; c = speed of light.

6 EXERCISE # I Q.1 When a monochromatic point source of light is at a distance of 0. m from a photoelectric cell, the cut off voltage and the saturation current are respectively 0.6 volt and 18.0 ma. If the same source is placed 0.6 m away from the photoelectric cell, then find (a) the stopping potential (b) the saturation current Q. 663 mw of light from a 540 nm source is incident on the surface of a metal. If only 1 of each incident photons is absorbed and causes an electron to be ejected from the surface, the total photocurrent in the circuit is. Q.3 Light of wavelength 330 nm falling on a piece of metal ejects electrons with sufficient energy which requires voltage V 0 to prevent a electron from reading collector. In the same setup, light of wavelength 0 nm, ejects electrons which require twice the voltage V 0 to stop them in reaching a collector. Find the numerical value of voltage V 0.(Take plank's constant, h = Js and 1 ev = J) Q.4 The surface of cesium is illuminated with monochromatic light of various wavelengths and the stopping potentials for the wavelengths are measured. The results of this experiment is plotted as shown in the figure. Estimate the value of work function of the cesium and Planck s constant. Q.5 When photons of energy 4.5eV strike the surface of a metal A, the ejected photoelectrons have maximum kinetic energy T a ev and de Broglie wavelength a. The maximum kinetic energy of photoelectrons liberated from another metal B by photons of energy 4.7eV is T b = (T a 1.5) ev. If the De Broglie wavelength of these photoelectrons is b = a, then find (a) The work function of a (b) The work function of b is (c) T a and T b Q.6 An electron of mass "m" and charge "e" initially at rest gets accelerated by a constant electric field E. The rate of change of DeBroglie wavelength of this electron at time t is... Q.7 A hydrogen atom in a state having a binding energy 0.85eV makes a transition to a state of excitation energy 10.eV. The wave length of emitted photon is...nm. Q.8 A hydrogen atom is in 5 th excited state. When the electron jumps to ground state the velocity of recoiling hydrogen atom is... m/s and the energy of the photon is...ev. Q.9 The ratio of series limit wavlength of Balmer series to wavelength of first line of paschen series is... Q.10 An electron joins a helium nucleus to form a He+ ion in ground state. The wavelength of the photon emitted in this process if the electron is assumed to have had no kinetic energy when it combines with nucleus is...nm. Q.11 Three energy levels of an atom are shown in the figure. The wavelength corresponding to three possible transition are 1, and 3. The value of 3 in terms of 1 and is given by. Q.1 A hydrogen like atom has its single electron orbiting around its stationary nucleus. The energy to excite the electron from the second Bohr orbit to the third Bohr orbit is 47. ev. The atomic number of this nucleus is. Q.13 A single electron orbits a stationary nucleus of charge Ze where Z is a constant and e is the electronic charge. It requires 47.eV to excite the electron from the nd Bohr orbit to 3rd Bohr orbit. Find (i) the value of Z, (ii) energy required to excite the electron from the third to the fourth orbit (iii) the wavelength of radiation required to remove the electron from the first orbit to infinity (iv) the kinetic energy, potential energy and angular momentum in the first Bohr orbit (v) the radius of the first Bohr orbit.

7 Q.14 A hydrogen like atom (atomic number Z) is in higher excited state of quantum number n. This excited atom can make a transition to the first excited state by successively emitting two photons of energy.95ev and 5.15eV respectively. Alternatively, the atom from the same excited state can make transition to the second excited state by successively emitting two photons of energies.4ev and 8.7eV respectively. Find the values of n and Z. Q.15 Which level of the doubly ionized lithium has the same energy as the ground state energy of the hydrogen atom. Find the ratio of the two radii of corresponding orbits. Q.16 A 0 KeV energy electron is brought to rest in an X-ray tube, by undergoing two successive bremsstrahling events, thus emitting two photons. The wavelength of the second photon is m greater than the wavelength of the first emitted photon. Calculate the wavelengths of the two photons. Q.17 Figure shows K & K X-rays along with continuous X-ray. Find the energy of L X-ray. (Use hc = 140 evå). EXERCISE # II Q.1 A small plate of a metal (work function = 1.17 ev) is placed at a distance of m from a monochromatic light source of wave length m and power 1.0 watt. The light falls normally on the plate. Find the number of photons striking the metal plate per square meter per sec. If a constant uniform magnetic field of strength 10 4 tesla is applied parallel to the metal surface. Find the radius of the largest circular path followed by the emitted photoelectrons. Q. Electrons in hydrogen like atoms (Z = 3) make transitions from the fifth to the fourth orbit & from the fourth to the third orbit. The resulting radiations are incident normally on a metal plate & eject photo electrons. The stopping potential for the photoelectrons ejected by the shorter wavelength is 3.95 volts. Calculate the work function of the metal, & the stopping potential for the photoelectrons ejected by the longer wavelength. (Rydberg constant = m 1 ) Q.3 A beam of light has three wavelengths 4144Å, 497Å & 616 Å with a total intensity of W.m equally distributed amongst the three wavelengths. The beam falls normally on an area 1.0 cm of a clean metallic surface of work function.3 ev. Assume that there is no loss of light by reflection and that each energetically capable photon ejects one electron. Calculate the number of photoelectrons liberated in two seconds. Q.4 In a photo electric effect set-up, a point source of light of power W emits mono energetic photons of energy 5.0 ev. The source is located at a distance of 0.8 m from the centre of a stationary metallic sphere of work function 3.0 ev & of radius m. The efficiency of photo electrons emission is one for every 10 6 incident photons. Assume that the sphere is isolated and initially neutral, and that photo electrons are instantly swept away after emission. (a) Calculate the number of photo electrons emitted per second. (b) Find the ratio of the wavelength of incident light to the De - Broglie wave length of the fastest photo electrons emitted. (c) It is observed that the photo electron emission stops at a certain time t after the light source is switched on. Why? (d) Evaluate the time t. Q.5 A neutron with kinetic energy 5 ev strikes a stationary deuteron. Find the de Broglie wavelengths of both particles in the frame of their centre of mass.

8 Q.6 Assume that the de-broglie wave associated with an electron can form a standing wave between the atoms arranged in a one dimensional array with nodes at each of the atomic sites. It is found that one such standing wave is formed if the distance 'd' between the atoms of the array is Å. A similar standing wave is again formed if 'd' is increased to.5 Å but not for any intermediate value of d. Find the energy of the electrons in electron volts and the least value of d for which the standing wave of the type described above can form. Q.7 A stationary He + ion emitted a photon corresponding to the first line its Lyman series. That photon liberated a photoelectron from a stationary hydrogen atom in the ground state. Find the velocity of the photoelectron. Q.8 A hydrogen atom in ground state absorbs a photon of ultraviolet radiation of wavelength 50 nm. Assuming that the entire photon energy is taken up by the electron, with what kinetic energy will the electron be ejected? Q.9 A monochromatic light source of frequency illuminates a metallic surface and ejects photoelectrons. The photoelectrons having maximum energy are just able to ionize the hydrogen atoms in ground state. When the whole experiment is repeated with an incident radiation of frequency (5/6), the photoelectrons so emitted are able to excite the hydrogen atom beam which then emits a radiation of wavelength of 115 Å. Find the work function of the metal and the frequency. Q.10 An energy of 68.0 ev is required to excite a hydrogen like atom from its second Bohr orbit to the third. The nuclear charge Ze. Find the value of Z, the kinetic energy of the electron in the first Bohr orbit and the wavelength of the electro magnetic radiation required to eject the electron from the first Bohr orbit to infinity. Q.11 Simplified picture of electron energy levels in a certain atom is shown in the figure. The atom is bombarded with high energy electrons. The impact of one of these electron has caused the complete removal of K-level is filled by an electron from the L-level with a certain amount of energy being released during the transition. This energy may appear as X-ray or may all be used to eject an M-level electron from the atom. Find : (i) the minimum potential difference through which electron may be accelerated from rest to cause the ejectrion of K-level electron from the atom. (ii) energy released when L-level electron moves to fill the vacancy in the K-level. (iii) wavelength of the X-ray emitted. (iv) K.E. of the electron emitted from the M-level. Q.1 A neutron of kinetic energy 65 ev collides inelastically with a singly ionized helium atom at rest. It is scattered at an angle of 90º with respect of its original direction. (i) Find the allowed values of the energy of the neutron & that of the atom after collision. (ii) If the atom gets de-excited subsequently by emitting radiation, find the frequencies of the emitted radiation. (Given : Mass of he atom = 4 (mass of neutron), ionization energy of H atom =13.6 ev) EXERCISE # III Q.1 A particle of mass M at rest decays into two particles of masses m 1 and m, having non-zero velocities. The ratio of the de-broglie wavelengths of the particles, 1 /, is (A) m 1 /m (B) m /m 1 (C) 1.0 (D) m / m 1 [JEE 99] Q. Photoelectrons are emitted when 400 nm radiation is incident on a surface of work function 1.9eV. These photoelectrons pass through a region containing -particles. A maximum energy electron combines with an -particle to form a He + ion, emitting a single photon in this process. He + ions thus formed are in their fourth excited state. Find the energies in ev of the photons, lying in the to 4eV range, that are likely to be emitted during and after the combination. [Take, h = ev s ] [JEE 99]

9 Q.3(a) Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength (given in terms of the Rydberg constant R for the hydrogen atom) equal to (A) 9/(5R) (B) 36/(5R) (C) 18/(5R) (D) 4/R [JEE 000 (Scr)] (b) The electron in a hydrogen atom makes a transition from an excited state to the ground state. Which of the following statements is true? (A) Its kinetic energy increases and its potential and total energies decrease. (B) Its kinetic energy decreases, potential energy increases and its total energy remains the same. (C) Its kinetic and total energies decrease and its potential energy increases. (D) Its kinetic, potential and total energies decrease. [JEE 000 (Scr)] Q.4(a) A hydrogen - like atom of atomic number Z is in an excited state of quantum number n. It can emit a maximum energy photon of 04 ev. If it makes a transition to quantum state n, a photon of energy 40.8 ev is emitted. Find n, Z and the ground state energy (in ev) for this atom. Also, calculate the minimum energy (in ev) that can be emitted by this atom during de-excitation. Ground state energy of hydrogen atom is 13.6 ev. [JEE' 000] (b) When a beam of 10.6 ev photon of intensity W/m falls on a platinum surface of area m and work function 5.6 ev, 0.53% of the incident photons eject photoelectrons. Find the number of photoelectrons emitted per sec and their minimum and maximum energies in ev. [JEE' 000] Q.5 The potential difference applied to an X - ray tube is 5 kv and the current through it is 3. ma. Then the number of electrons striking the target per second is [JEE' 00 (Scr.)] (A) (B) (C) (D) Q.6 A Hydrogen atom and Li ++ ion are both in the second excited state. If l H and l Li are their respective electronic angular momenta, and E H and E Li their respective energies, then (A) l H > l Li and E H > E Li (B) l H = l Li and E H < E Li (C) l H = l Li and E H > E Li (D) l H < l Li and E H < E Li [JEE 00 (Scr)] Q.7 A hydrogen like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transition between a group of levels. These levels have energies between 0.85 ev and ev (including both these values) (a) Find the atomic number of the atom. (b) Calculate the smallest wavelength emitted in these transitions. [JEE' 00] Q.8 Two metallic plates A and B each of area m, are placed at a separation of 1 cm. Plate B carries a positive charge of C. A monochromatic beam of light, with photons of energy 5 ev each, starts falling on plate A at t = 0 so that photons fall on it per square meter per second. Assume that one photoelectron is emitted for every 10 6 incident photons. Also assume that all the emitted photoelectrons are collected by plate B and the work function of plate A remains constant at the value ev. Determine (a) the number of photoelectrons emitted up to t = 10 sec. (b) the magnitude of the electric field between the plates A and B at t = 10 s and (c) the kinetic energy of the most energetic photoelectron emitted at t = 10 s when it reaches plate B. (Neglect the time taken by photoelectron to reach plate B) [JEE' 00] Q.9 The attractive potential for an atom is given by v = v 0 ln r / r 0, v 0 and r 0 are constant and r is the radius of the orbit. The radius r of the n th Bohr's orbit depends upon principal quantum number n as : (A) r n (B) r 1/n (C) r n (D) r 1/n [JEE' 003 (Scr)]

10 Q.10 Frequency of a photon emitted due to transition of electron of a certain elemrnt from L to K shell is found to be Hz. Using Moseley's law, find the atomic number of the element, given that the Rydberg's constant R = m 1. [JEE' 003] Q.11 In a photoelctric experiment set up, photons of energy 5 ev falls on the cathode having work function 3 ev. (a) If the saturation current is i A = 4 A for intensity 10 5 W/m, then plot a graph between anode potential and current. (b) Also draw a graph for intensity of incident radiation of 10 5 W/m? [JEE' 003] Q.1 In a photoelectric experiment anode potential is plotted against plate current [JEE-004 (Scr.)] (A) A and B will have different intensities while B and C will have different frequencies. (B) B and C will have different intensities while A and C will have different frequencies. (C) A and B will have different intensities while A and C will have equal frequencies. (D) A and B will have equal intensities while B and C will have different frequencies. Q.13 A proton has kinetic energy E = 100 kev which is equal to that of a photon. The wavelength of photon is and that of proton is 1. The ratio of / 1 is proportional to [JEE-004 (Scr.)] (A) E (B) E 1/ (C) E 1 (D) E 1/ Q.14 In a photoelectric setup, the radiations from the Balmer series of hydrogen atom are incident on a metal surface of work function ev. The wavelength of incident radiations lies between 450 nm to 700 nm. Find the maximum kinetic energy of photoelectron emitted. (Given hc/e = 14 ev-nm). [JEE-004] Q.15 The wavelength of K X-ray of an element having atomic number z = 11 is. The wavelength of K X-ray of another element of atomic number z' is 4 Then z' is (A) 11 (B) 44 (C) 6 (D) 4 [JEE' 005 (Scr)] Q.16 A photon of 10. ev energy collides with a hydrogen atom in ground state inelastically. After few microseconds one more photon of energy 15 ev collides with the same hydrogen atom.then what can be detected by a suitable detector. (A) one photon of 10. ev and an electron of energy 1.4 ev (B) photons of energy 10. ev (C) photons of energy 3.4 ev (D) 1 photon of 3.4 ev and one electron of 1.4 ev [JEE' 005 (Scr)] Q.17 In Young s double slit experiment an electron beam is used to form a fringe pattern instead of light. If speed of the electrons is increased then the fringe width will : [JEE' 005 (Scr)] (A) increase (B) decrease (C) remains same (D) no fringe pattern will be formed Q.18 The graph between 1/ and stopping potential (V) of three metals having work functions 1, and 3 in an experiment of photoelectric effect is plotted as shown in the figure. Which of the following statement(s) is/are correct? [Here is the wavelength of the incident ray]. (A) Ratio of work functions 1 : : 3 = 1 : : 4 (B) Ratio of work functions 1 : : 3 = 4 : : 1 (C) tan is directly proportional to hc/e, where h is Planck s constant and c is the speed of light (D) The violet colour light can eject photoelectrons from metals and 3. [JEE 006]

11 Q.19 In hydrogen-like atom (z = 11), n th line of Lyman series has wavelength equal to the de-broglie s wavelength of electron in the level from which it originated. What is the value of n? [Take: Bohr radius (r 0 ) = 0.53 Å and Rydberg constant (R) = m 1 ] [JEE 006] Q.0 The largest wavelength in the ultraviolet region of the hydrogen spectrum is 1 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is [JEE 007] (A) 80 nm (B) 83 nm (C) 188 nm (D) 1648 nm Q.1 STATEMENT-1 [JEE 007] If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change. because STATEMENT- When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy (A) Statement-1 is True, Statement- is True; Statement- is a correct explanation for Statement-1 (B) Statement-1 is True, Statement- is True; Statement- is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement- is False (D) Statement-1 is False, Statement- is True Q. Electrons with de-broglie wavelength fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is [JEE 007] (A) 0 = mc h h (B) 0 = mc m c (C) 0 = h 3 (D) 0 = Q.3 Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube? [JEE 008] (A) Wavelength of characteristic X-rays decreases when the atomic number of the target increases (B) Cut-off wavelength of the continuous X-rays depends on the atomic number of the target (C) Intensity of the characteristic X-rays depends on the electrical power given to the X-rays tube (D) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube Paragraph for Question Nos. 4 to 6 In a mixture of H He + gas (He + is singly ionized He atom), H atoms and He + ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He + ions (by collisions). Assume that the Bohr model of atom is exactly valid. Q.4 The quantum number n of the state finally populated in He + ions is [JEE 008] (A) (B) 3 (C) 4 (D) 5 Q.5 The wavelength of light emitted in the visible region by He + ions after collisions with H atoms is [JEE 008] (A) m (B) m (C) m (D) m Q.6 The ratio of the kinetic energy of the n = electron for the H atom to that of He + ion is [JEE 008] (A) 4 1 (B) 1 (C) 1 (D)

12 Paragraph for Question Nos. 7 to 9 When a particle is restricted to move along x-axis between x = 0 and x = a, where a is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x = 0 and x = a. The wavelength of this standing wave is related to the linear momentum p of the particle according to the de Broglie relation. The energy of the particle of mass m is related to its linear momentum as p E. Thus, the energy of the particle can be denoted by a quantum number n taking values 1,,3, m... (n = l, called the ground state) corresponding to the number of loops in the standing wave. Use the model described above to answer the following three questions for a particle moving in the line x = 0 to x = a. Take h = Js and e = 1.6 x C. Q.7 The allowed energy for the particle for a particular value of n is proportional to [JEE-009] (A) a (B) a 3/ (C) a 1 (D) a Q.8 If the mass of the particle is m = kg and a = 6.6 nm, the energy of the particle in its ground state is closest to : [JEE-009] (A) 0.8 mev (B) 8 mev (C) 80 mev (D) 800 mev Q.9 The speed of the particle, that can take discrete values, is proportional to [JEE-009] (A) n 3/ (B) n 1 (C) n 1/ (D) n Q.30 Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions p =.0 ev, q =.5 ev and r = 3.0 ev, respectively. A light beam containing wavelengths of 550 nm, 450 nm and 350 nm with equal intensities illuminates each of the plates. The correct I-V graph for the experiment is : [Take hc = 140 ev nm] [JEE-009] (A) I p q r V (B) p q r I V (C) I r q p V (D) r q p I V

13 OBJECTIVE QUESTION BANK ONLY ONE OPTION IS CORRECT. Take approx. minutes for answering each question. Q.1 Let n r and n b be respectively the number of photons emitted by a red bulb and a blue bulb of equal power in a given time. (A) n r = n b (B) n r < n b (C) n r > n b (D) data insufficient Q W of 5000 Å light is directed on a photoelectric cell. If the current in the cell is 0.16 A, the percentage of incident photons which produce photoelectrons, is (A) 0.4% (B).04% (C) 0% (D) 10% Q.3 In a photo-emissive cell, with exciting wavelength, the maximum kinetic energy of electron is K. If the 3 exciting wavelength is changed to the kinetic energy of the fastest emitted electron will be: 4 (A) 3K/4 (B) 4K/3 (C) less than 4K/3 (D) greater than 4K/3 Q.4 If the frequency of light in a photoelectric experiment is doubled, the stopping potential will (A) be doubled (B) halved (C) become more than doubled (D) become less than double Q.5 The stopping potential for the photo electrons emitted from a metal surface of work function 1.7 ev is 10.4 V. Identify the energy levels corresponding to the transitions in hydrogen atom which will result in emission of wavelength equal to that of incident radiation for the above photoelectric effect (A) n = 3 to 1 (B) n = 3 to (C) n = to 1 (D) n = 4 to 1 Q.6 When a photon of light collides with a metal surface, number of electrons, (if any) coming out is (A) only one (B) only two (C) infinite (D) depends upon factors Q.7 The frequency and the intensity of a beam of light falling on the surface of photoelectric material are increased by a factor of two. Treating efficiency of photoelectron generation as constant, this will : (A) increase the maximum energy of the photoelectrons, as well as photoelectric current by a factor of two. (B) increase the maximum kinetic energy of the photo electrons and would increase the photoelectric current by a factor of two. (C) increase the maximum kinetic energy of the photoelectrons by a factor of greater than two and will have no effect on the magnitude of photoelectric current produced. (D) not produce any effect on the kinetic energy of the emitted electrons but will increase the photoelectric current by a factor of two. Q.8 A point source of ligth is used in a photoelectric effect. If the source is removed farther from the emitting metal, the stopping potential : (A) will increase (B) will decrease (C) will remain constant (D) will either increase or decrease. Q.9 In a photoelectric experiment, the potential difference V that must be maintained between the illuminated surface and the collector so as just to prevent any electron from reaching the collector is determined for different frequencies f of the incident illumination. The graph obtained is shown. The maximum kinetic energy of the electrons emitted at frequency f 1 is (A) hf 1 (B) V1 (f f ) 1 0 (C) h (f 1 f 0 ) (D) ev 1 (f 1 f 0 )

14 Q.10 Radiation of two photon energies twice and five times the work function of metal are incident sucessively on the metal surface. The ratio of the maximum velocity of photoelectrons emitted is the two cases will be (A) 1 : (B) : 1 (C) 1 : 4 (D) 4 : 1 Q.11 Cut off potentials for a metal in photoelectric effect for light of wavelength 1, and 3 is found to be V 1, V and V 3 volts if V 1, V and V 3 are in Arithmetic Progression and 1, and 3 will be: (A) Arithmetic Progression (B) Geometric Progression (C) Harmonic Progression (D) None Q.1 Photons with energy 5 ev are incident on a cathode C, on a photoelectric cell. The maximum energy of the emitted photoelectrons is ev. When photons of energy 6 ev are incident on C, no photoelectrons will reach the anode A if the stopping potential of A relative to C is (A) 3 V (B) 3V (C) 1V (D) 4 V Q.13 In a photoelectric experiment, the collector plate is at.0v with respect to the emitter plate made of copper = 4.5eV). The emitter is illuminated by a source of monochromatic light of wavelength 00nm. (A) the minimum kinetic energy of the photoelectrons reaching the collector is 0. (B) the maximum kinetic energy of the photoelectrons reaching the collector is 3.7eV. (C) if the polarity of the battery is reversed then answer to part A will be 0. (D) if the polarity of the battery is reversed then answer to part B will be 1.7eV. Q.14 In a photoelectric experiment, electrons are ejected from metals X and Y by light of intensity I and frequency f. The potential difference V required to stop the electrons is measured for various frequencies. If Y has a greater work function than X ; which one of the following graphs best illustrates the expected results? (A) (B) (C) (D) Q.15 An image of the sun is formed by a lens of focal-length of 30 cm on the metal surface of a photo-electric cell and a photo-electric current I is produced. The lens forming the image is then replaced by another of the same diameter but of focal length 15 cm. The photo-electric current in this case is (A) I/ (B) I (C) I (D) 4I Q.16 Monochromatic light with a frequency well above the cutoff frequency is incident on the emitter in a photoelectric effect apparatus. The frequency of the light is then doubled while the intensity is kept constant. How does this affect the photoelectric current? (A) The photoelectric current will increase. (B) The photoelectric current will decrease. (C) The photoelectric current will remain the same. (D) None of these Q.17 If a parallel beam of light having intensity I is incident normally on a perfectly reflecting surface, the force exerted on the surface, equals F (Assume that the cross section of beam remains constant). When the surface is held at an angle, the force is (A) F tan (B) F cos (C) F cos (D) F Q.18 A proton and an electron are accelerated by same potential difference have de-broglie wavelength p and e. (A) e = p (B) e < p (C) e > p (D) none of these. Q.19 An electron with initial kinetic energy of 100 ev is acceleration through a potential difference of 50 V. Now the de-broglie wavelength of electron becomes (A) 1 Å (B) 1. 5 Å (C) 3 Å (D) 1.7 Å

15 Q.0 If h is Planck s constant is SI system, the momentum of a photon of wavelength 0.01 Å is: (A) 10 h (B) h (C) 10 h (D) 10 1 h Q.1 Let K 1 be the maximum kinetic energy of photoelectrons emitted by a light of wavelength 1 and K corresponding to. If 1 =, then : (A) K 1 = K (B) K 1 = K (C) K 1 < K (D) K 1 > K Q. Imagine a Young's double slit interference experiment performed with waves associated with fast moving electrons produced from an electron gun. The distance between successive maxima will decrease maximum if (A) the accelerating voltage in the electron gun is decreased (B) the accelerating voltage is increased and the distance of the screen from the slits is decreased (C) the distance of the screen from the slits is increased. (D) the distance between the slits is decreased. Q.3 In a hypothetical system a particle of mass m and charge 3q is moving around a very heavy particle having charge q. Assuming Bohr s model to be true to this system, the orbital velocity of mass m when it is nearest to heavy particle is (A) 3q h 0 (B) 3q 4 h 0 (C) 3q h 0 (D) 3q 4 h 0 Q.4 de-broglie wavelength of an electron in the nth Bohr orbit is n and the angular momentum is J n, then: (A) J n n (B) n 1 J n (C) n J n (D) none of these Q.5 Light coming from a discharge tube filled with hydrogen falls on the cathode of the photoelectric cell. The work function of the surface of cathode is 4eV. Which one of the following values of the anode voltage (in Volts) with respect to the cathode will likely to make the photo current zero. (A) 4 (B) 6 (C) 8 (D) 10 3 h Q.6 The angular momentum of an electron in the hydrogen atom is. Here h is Planck s constant. The kinetic energy of this electron is: (A) 4.53 ev (B) 1.51 ev (C) 3.4 ev (D) 6.8 ev Q.7 Consider the following electronic energy level diagram of H-atom: Photons associated with shortest and longest wavelengths would be emitted from the atom by the transitions labelled: (A) D and C respectively (B) C and A respectively (C) C and D respectively (D) A and C respectively Q.8 In a hydrogen atom, the binding energy of the electron in the n th state is E n, then the frquency of revolutionof the electron in the nth orbits is: (A) E n /nh (B) E n n/h (C) E n /nh (D) E n n/h Q.9 If the electron in a hydrogen atom were in the energy level with n = 3, how much energy in joule would be required to ionise the atom? (Ionisation energy of H-atom is J): (A) (B) (C) (D)

16 Q.30 In hydrogen and hydrogen like atoms, the ratio of difference of energies E 4n E n and E n E n varies with its atomic number z and n as: (A) z /n (B) z 4 /n 4 (C) z / n (D) z 0 n 0 Q.31 In a hydrogen atom, the electron is in nth excited state. It may come down to second excited state by emitting ten different wavelengths. What is the value of n: (A) 6 (B) 7 (C) 8 (D) 5 Q.3 Difference between nth and (n +1)th Bohr s radius of H atom is equal to it s (n 1)th Bohr s radius. the value of n is: (A) 1 (B) (C) 3 (D) 4 Q.33 An electron in hydrogen atom after absorbing energy photons can jump between energy states n 1 and n (n > n 1 ). Then it may return to ground state after emitting six different wavelengths in emission spectrum. the energy of emitted photons is either equal to, less than or greater than the absorbed photons. Then n 1 and n are: (A) n = 4, n 1 = 3 (B) n = 5, n 1 =3 (C) n = 4, n 1 = (D) n = 4, n 1 = 1 Q.34 The electron in a hydrogen atom makes transition from M shell to L. The ratio of magnitudes of initial to final centripetal acceleration of the electron is (A) 9 : 4 (B) 81 : 16 (C) 4 : 9 (D) 16 : 81 Q.35 The electron in a hydrogen atom makes a transition n 1 n whose n 1 and n are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The frequency of orbital motion of the electron in the initial state is 1/7 of that in the final state. The possible values of n 1 and n are (A) n 1 = 4, n = (B) n 1 = 3, n = 1 (C) n 1 = 8, n = 1 (D) n 1 = 6, n = 3 Q.36 The ionisation potential of hydrogen atom is 13.6 volt. The energy required to remove an electron from the second orbit of hydrogen is: (A) 3.4 ev (B) 6.8 ev (C) 13.6 ev (D) 7. ev Q.37 Electron in a hydrogen atom is replaced by an identically charged particle muon with mass 07 times that of electron. Now the radius of K shell will be (A) Å (B) Å (C) Å (D) Å Q.38 In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing photons of various energies is passed. In absorption spectrum, five dark lines are observed. The number of bright lines in the emission spectrum will be (Assume that all transitions take place) (A) 5 (B) 10 (C) 15 (D) none of these Q.39 When a hydrogen atom, initially at rest emits, a photon resulting in transition n = 5 n = 1, its recoil speed is about (A) 10 4 m/s (B) 10 m/s (C) 4. m/s (D) m/s Q.40 An electron collides with a fixed hydrogen atom in its ground state. Hydrogen atom gets excited and the colliding electron loses all its kinetic energy. Consequently the hydrogen atom may emit a photon corresponding to the largest wavelength of the Balmer series. The min. K.E.of colliding electron will be (A) 10. ev (B) 1.9 ev (C) 1.1 ev (D) 13.6 ev Q.41 Consider the spectral line resulting from the transition n = n = 1 in the atoms and ions given below. The shortest wavelength is produced by : (A) hydrogen atom (B) deuterium atom (C) singly ionized helium (D) doubly ionized lithium

17 Q.4 In an atom, two electrons move around the nucleus in circular orbits of radii R and 4R. The ratio of the time taken by them to complete one revolution is : (neglect electric interaction) (A) 1 : 4 (B) 4 : 1 (C) 1 : 8 (D) 8 : 1 Q.43 The electron in hydrogen atom in a sample is in n th excited state, then the number of different spectrum lines obtained in its emission spectrum will be : (A) (n 1) (B) ( n ) (C) (n + 1) (D) (n 1) Q.44 A neutron collides head on with a stationary hydrogen atom in ground state (A) If kinetic energy of the neutron is less than 13.6eV, collision must be elastic (B) if kinetic energy of the neutron is less than 13.6eV, collision may be inelastic. (C) inelastic collision takes place when initial kinetic energy of neutron is greater than 13.6eV. (D) perfectly inelastic collision cannot take place. Q.45 The electron in a hydrogen atom make a transition from an excited state to the ground state. Which of the following statement is true? (A) Its kinetic energy increases and its potential and total energies decrease (B) Its kinetic energy decreases, potential energy increases and its total energy remains the same. (C) Its kinetic and toal energies decrease and its potential energy increases. (D) its kinetic potential and total energies decreases. Q.46 The magnitude of angular momentum, orbit radius and frequency of revolution of electron in hydrogen atom corresponding to quantum number n are L, r and f respectively. Then according to Bohr's theory of hydrogen atom, (A) fr L is constant for all orbits (B) frl is constant for all orbits (C) f rl is constant for all orbits (D) frl is constant for all orbits Q.47 Radius of the second Bohr obit of singly ionised helium atom is (A) 0.53 Å (B) 1.06 Å (C) 0.65 Å (D) 0.13 Å Q.48 An electron in Bohr s hydrogen atom has an energy of 3.4 ev. The angular momentum of the electron is (A) h / (B) h / (C) nh / ( n is an integer) (D) h / Q.49 In a characteristic X ray spectra of some atom superimposed on continuous X ray spectra: (A) P represents K line (B) Q represents K line (C) Q and P represents K and K lines respectively (D) Relative positions of K and K depend on the particular atom Q.50 Which of the following wavelength falls in a X-ray region? (A) 10,000 Å (B) 1000 Å (C) 1 Å (D) 10 Å Q.51 The penetrating power of X-ray increases with the (A) Increase of its velocity (B) Increase in its intensity (C) Decrease in its velocity (D) Increases in its frequency. Q.5 The wavelength of the K line for an element of atomic number 57 is. What is the wavelength of the K line for the element of atomic number 9? (A) (B) (C) 4 (D) 8

18 Q.53 If the frequencies of K, K and L X-rays for a material K, K, L respectively, then (A) K = K + L (B) L = K + K (C) K = K + L (D) none of these Q.54 In X-ray tube, when the accelerating voltage V is doubled, the difference between the wavelength of K line and the minimum cut off of continuous X-ray spectrum : (A) remains constant (B) becomes more than two times (C) becomes half (D) becomes less than times. Q.55 The K X-rays emission line of tungsten occurs at = 0.01 nm. The energy difference between K and L levels in this atom is about (A) 0.51 MeV (B) 1. MeV (C) 59 kev (D) 13.6 ev ASSERTION AND REASON Q.1 Statement-1 : Figure shows graph of stopping potential and frequency of incident light in photoelectric effect. For values of frequency less than threshold frequency ( 0 ) stopping potential is negative. V S (0,0) 0 Statement- : Lower the value of frequency of incident light (for > 0 ) the lower is the maxima of kinetic energy of emitted photoelectrons. (A) Statement-1 is true, statement- is true and statement- is correct explanation for statement-1. (B) Statement-1 is true, statement- is true and statement- is NOT the correct explanation for statement-1. (C) Statement-1 is true, statement- is false. (D) Statement-1 is false, statement- is true. Q. Statement-1 : In the process of photo electric emission, all the emitted photoelectrons have same KE. Statement- : According to einstein s photo electric equation KE max = h. (A) Statement-1 is True, Statement- is True, Statement- is a correct explanation for statement-1 (B) Statement-1 is True, Statement- is True, Statement- is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement- is False (D) Statement-1 is False, Statement- is True Q.3 Statement-1 : Work function of aluminum is 4. ev. If two photons each of energy.5 ev strikes on a piece of aluminum, the photo electric emission does not occur. Statement- : In photo electric effect a single photon interacts with a single electron and electron is emitted only if energy of each incident photon is greater then the work function. (A) Statement-1 is True, Statement- is True, Statement- is a correct explanation for statement-1 (B) Statement-1 is True, Statement- is True, Statement- is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement- is False (D) Statement-1 is False, Statement- is True

19 Q.4 Statement-1 : An electron and a proton are accelerated through the same potential difference. The de- Broglie wavelength associated with the electron is longer. Statement- : De-Broglie wavelength associated with a moving particle is = p h where, p is the linear momentum and both have same KE. (A) Statement-1 is True, Statement- is True, Statement- is a correct explanation for statement-1 (B) Statement-1 is True, Statement- is True, Statement- is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement- is False (D) Statement-1 is False, Statement- is True Q.5 Statement-1 : Two photons having equal wavelengths have equal linear momenta. Statement- : When light shows its photon character, each photon has a linear momentum p = h. (A) Statement-1 is True, Statement- is True, Statement- is a correct explanation for statement-1 (B) Statement-1 is True, Statement- is True, Statement- is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement- is False (D) Statement-1 is False, Statement- is True Q.6 Statement-1 : If the accelerating potential of a X-Ray tube is increased then the characteristic wavelength decreases. hc Statement- : The cut-off wavelength for a X-ray tube is given by min =, where V is accelerating ev potential. (A) Statement-1 is True, Statement- is True, Statement- is a correct explanation for statement-1 (B) Statement-1 is True, Statement- is True, Statement- is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement- is False (D) Statement-1 is False, Statement- is True ONE OR MORE THAN ONE OPTION MAY BE CORRECT Take approx. 3 minutes for answering each question. Q.1 In photoelectric effect, stopping potential depends on (A) frequency of the incident light (B) intensity of the incident light by varies source distance (C) emitter s properties (D) frequency and intensity of the incident light Q. Two electrons are moving with the same speed v. One electron enters a region of uniform electric field while the other enters a region of uniform magnetic field, then after sometime if the de Broglie wavelengths of the two are 1 and, then: (A) 1 = (B) 1 > (C) 1 < (D) 1 > or 1 < Q.3 An electron in hydrogen atom first jumps from second excited state to first excited state and then, from first excited state to ground state. Let the ratio of wavelength, momentum and energy of photons in the two cases be x, y and z, then select the wrong answer/(s) : (A) z = 1/x (B) x=9/4 (C) y=5/7 (D) z=5/7 Q.4 An electron is in an excited state in hydrogen-like atom. It has a total energy of 3.4 ev. If the kinetic energy of the electron is E and its de-broglie wavelength is, then (A) E = 6.8 ev, = m (B) E = 3.4 ev, = m (C) E = 3.4 ev, = m (D) E = 6.8 ev, = m

20 Q.5 A particular hydrogen like atom has its ground state binding energy 1.4eV. Its is in ground state. Then: (A) Its atomic number is 3 (B) An electron of 90eV can excite it. (C) An electron of kinetic energy nearly 91.8eV can be brought to almost rest by this atom. (D) An electron of kinetic energy.6ev may emerge from the atom when electron of kinetic energy 15eV collides with this atom. Q.6 A beam ofultraviolet light of all wavelengths passes through hydrogen gas at room temperature, in the x-direction. Assume that all photons emitted due to electron transition inside the gas emerge in the y-direction. Let A and B denote the lights emerging from the gas in the x and y directions respectively. (A) Some of the incident wavelengths will be absent in A. (B) Only those wavelengths will be present in B which are absent in A. (C) B will contain some visible light. (D) B will contain some infrared light. Q.7 If radiation of allow wavelengths from ultraviolet to infrared is passed through hydrogen agas at room temperature, absorption lines will be observed in the : (A) Lyman series (B) Balmer series (C) both (A) and (B) (D) neither (A) nor (B) Q.8 In the hydrogen atom, if the reference level of potential energy is assumed to be zero at the ground state level. Choose the incorrect statement. (A) The total energy of the shell increases with increase in the value of n (B) The total energy of the shell decrease with increase in the value of n. (C) The difference in total energy of any two shells remains the same. (D) The total energy at the ground state becomes 13.6 ev. Q.9 Choose the correct statement(s) for hydrogen and deuterium atoms (considering motion of nucleus) (A) The radius of first Bohr orbit of deuterium is less than that of hydrogen (B) The speed of electron in the first Bohr orbit of deuterium is more than that of hydrogen. (C) The wavelength of first Balmer line of deuterium is more than that of hydrogen (D) The angular momentum of electron in the first Bohr orbit of deuterium is more than that of hydrogen. Q.10 A neutron collides head-on with a stationary hydrogen atom in ground state. Which of the following statements are correct (Assume that the hydrogen atom and neutron has same mass) : (A) If kinetic energy of the neutron is less than 0.4 ev collision must be elastic. (B) If kinetic energy of the neutron is less than 0.4 ev collision may be inelastic. (C) Inelastic collision may be take place only when initial kinetic energy of neutron is greater than 0.4 ev. (D) Perfectly inelastic collision can not take place. Q.11 A free hydrogen atom in ground state is at rest. A neutron of kinetic energy K collides with the hydrogen atom. After collision hydrogen atom emits two photons in succession one of which has energy.55 ev. (Assume that the hydrogen atom and neutron has same mass) (A) minimum value of K is 5.5 ev. (B) minimum value of K is 1.75 ev (C) the other photon has energy 10. ev (D) the upper energy level is of excitation energy 1.75 ev. Q.1 X-rays are produced by accelerating electrons across a given potential difference to strike a meta target of high atomic number. If the electrons have same speed when they strike the target, the X ray spectrum will exhibit. (A) a minimum wavelength (B) a continuous spectrum (C) some discrete comparatively prominent wavelength (D) uniform density over the whole spectrum