MODERN PHYSICS DUAL NATURE OF MATTER AND RADIATION

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1 PMP 1 MODERN PHYSICS Syllabus : ELECTROMAGNETIC WAVES Electromagnetic waves and their characteristics. Transverse nature of electromagnetic waves. Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays). Applications of e.m. waves. DUAL NATURE OF MATTER AND RADIATION Dual nature of radiation. Photoelectric effect, Hertz and Lanard s observations; Einstein s photoelectric equation; particle nature of light. Matter waves-wave nature of particles, de Broglie relation. Davisson-Germer experiment. ATOMS AND NUCLEI Alpha particles scattering experiment; Rutherford s model of atom; Bohr model, energy levels, hydrogen spectrum Composition and size of nucleus, atomic masses, isotopes, isobars. Radioactivity-alpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number, nuclear fission and fusion ELECTRONIC DEVICES Semiconductors; semiconductor diode; I-V characteristics in forward and reverse bias; diode as a rectifier; I-V characteristics of LED, photodiode, socal cell and Zener diode; Zener diods as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor; transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch. COMMUNICATION SYSTEMS Propagation of electromagnetic waves in the atmosphere; Sky and space wave propagation, Need for modulation, Amplitude and Frequency Modulation, Bandwidth of signals, Bandwidth of Transmission medium, Basic Elements of a Communication System (Block Diagram only). Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

2 PMP C O N C E P T S C1A Electromagnetic waves : Properties of electromagnetic waves : 1. These are transverse waves such that the electric field, the magnetic fields and direction of propogation of the wave are mutually perpendicular to each other In vacuum the speed of an e.m. wave is given by c 310 m / s. µ 1 3. The direction of propagation is along the vector S (E B). S is called the Poynting vector. Its S.I. µ unit is W/m. 4. The electric and magnetic fields are related as E = cb. Classification of Electromagnetic Waves Name Approximate wavelength range Energy Gamma Rays m m MeV X-Rays 10 1 m 10 9 m kev U.V. Rays 10 9 m 10 7 m 4eV to 100 ev Visible Light m m ev to 3eV Infrared m 10 3 m mili ev Microwaves 10 3 m 0.3 m very less energy Radiowaves 0.3 m 10 4 m very-very small energy Practice Problems : 1. If E and B be the electric and magnetic field of electromagnetic waves, then the direction of propagation of e.m. wave is along the direction of E B E B None of these. The electromagnetic radiations are in descending order of wavelength in the following sequence infra-red waves, radio waves, X-rays, visible light rays Radio-waves, infra-red waves, visible light, X-rays Radio waves, visible light, infra-red waves, X-rays X-rays, visible light, infra-red wave, radiowaves 3. Consider an electric charge oscillating with a frequency of 10 MHz. The radiation emitted will have a wavelength equal to 0 m 30 m 40 m 10 m [Answers : (1) c () b (3) b] C1B Photons : An electromagnetic wave (light) is quantized, and its quanta are called photons. Important point for Photons : 1. It is energy carrying particle where energy, E = h E hc, where is the wavelength of photon and c is the velocity of photons ( m/s). The above relation is converted in 1400 wavelength (Å) of a photon of energy E (ev), is given by Å. E(eV) Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

3 PMP 3 E h. Momentum of photon : p. c 3. If a packet will contain n photons of frequency then its energy equals to nh. 4. Number of photons emitted by a source of power P per unit time is given by P. h 5. The rest mass of the photon is zero whereas relativistic mass equals to carried by the photons. E, where E is the energy c 6. Photons are chargeless and spinless particle and they are not affected in the presence of electric or magnetic field. Practice Problems : 1. The momentum of a photon of an electromagnetic radiation is kg m/s. The frequency of the associated waves is (h = Js, c = m/s) Hz Hz Hz Hz. Which one of the following statements about photons is incorrect? Rest mass of a photon is zero Momentum of a photon of frequency v is hv/c Energy of a photon of frequency v is hv Photons exert no pressure 3. An X-ray has a wavelength of Å. Its momentum in kg m/s and energy in joule is given by respectively , J , J , J , J 4. Radio waves received by a radio telescope from distant starts may have a wavelength of about 0.0 m. If the speed of the wave is km/s, then frequency of the wave will be Hz Hz Hz Hz 5. A radio transmitter operates at a frequency of 880 khz and power of 10 kw. The number of photons per second emitted are [Answers : (1) d () d (3) d (4) d (5) a] C Photoelectric Effect : The emission of electrons from a metallic surface when irradiated by electromagnetic radiation is called the phenomenon of photoelectric effect. The emitted electrons are called as photoelectrons. The governing relation is h = K max +, in which h is the photon energy, K max is the kinetic energy of the most energetic emitted electrons, and is the work function of the target material that is, the minimum energy an electron must have if it is to emerge from the surface of the target. If h is less than, the photoelectric effect does not occur. Effect of Potential Difference When the frequency and intensity of radiation are kept constant and the positive potential of collector plate is gradually increased, then the photoelectric current i increases with the potential difference V. At some value of the potential difference, when all the emitted photoelectrons are collected then the photoelectric will have the maximum value known as saturation current. On further increasing the potential difference, their is no effect on the current. If the collector plate will make negative and its potential will increase then photoelectric current will decrease. At a certain negative potential the photoelectric current will become zero, this potential is known as stopping potential and the relation between k max and stopping potential V s is Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

4 PMP 4 given by k max = ½mv = ev The variation of photoelectric current with the potential as shown in the max s. graph : Effect of frequency For a given intensity of radiation, if frequency of radiation will increase then maximum kinetic energy of ejected photo electrons will increase and hence the stopping potential will increase. Effect of intensity If the frequency remains constant and intensity will increase then photoelectric current at the saturation stage will increase. Effect of work function Work function depends on the metallic surface. On changing the metallic surface, for the same frequency of incident radiation, k max will change. Practice Problems : 1. The work function of a metal is 4 ev. Which of the following wavelength is not capable to eject the photoelectron or does not give any photoelectric current? 1700 Å 700 Å 3100 Å 5900 Å. The work function of a metallic surface is 5.00 ev. Photoelectrons are emitted when light of wavelength 000 Å falls on it. Choose the correct statement from the following The maximum kinetic energy of the emitted photoelectron is 1. ev The stopping potential is 1. V The kinetic energy of the emitted photoelectron is from 0 to 1. ev All the above statements are correct 3. The photoelectric threshold wavelength for a metal surface is 6600 Å. The work function for the metal is 1.87 V 1.87 ev 18.7 ev 0.18 ev 4. The threshold wavelength for photoelectric emission from a material is 500 Å. Photoelectrons will be emitted when this material is illuminated with monochromatic radiation from a 50 watt infrared lamp 1 watt ultraviolet lamp 50 watt ultraviolet lamp both and are correct 5. If Planck s constant is denoted by h, the electronic charge by e and work function of metallic surface is then, experiments on photoelectric effect allow the determination of only h only h/e both h and h/e h, h/e and 6. In photoelectric emission the number of electrons ejected per second is proportional to the intensity of light wavelength of light frequency of light work function of the material 7. The maximum kinetic energy (E k ) of photoelectrons varies with the frequency (v) of the incident radiation as Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

5 8. In photoelectric effect, the photoelectric current PMP 5 does not depend on the photon frequency, but only on the intensity of the incident beam depends both on the intensity and the frequency of the incident beam increases when the frequency of the incident photon increases decreases when the frequency of the incident photon increases. 9. Stopping potential or maximum kinetic energy of photoelectrons does not depend on the frequency of the incident light does not depend on the nature of cathode material depends on both the frequency of the incident light and the nature of the cathode material depends on the intensity of the incident light 10. Photons of energy 5 ev, incident on a metalsurface, liberate electrons which are stopped by a negative potential of 3.5 V. The work function of the metal is 5 ev 1.5 ev 7 ev 17.4 ev 11. In a photo-emissive cell, with exciting wavelengths, the fastest electron has speed v. If the exciting wavelength is changed to 3/4, the speed of the fastest emitted electron will be v (3/4) 1/ v (4/3) 1/ less than v (4/3) 1/ greater than v (4/3) 1/ [Answers : (1) d () d (3) b (4) d (5) d (6) a (7) d (8) a (9) c (10) b (11) d] C3 de-broglie Waves The wavelength of the wave associated with a moving particle is equal to Planck s quantum constant divided by the momentum of the particle and given by mass m. Practice Problems : h mv, where v is the speed of the particle of 1. Photons of energy 5 ev, incident on a metal surface of work function 4 ev. The minimum de-broglie wavelength of the ejected photoelectron is 1.7 Å 1.7 Å 0.17 Å none. The kinetic energy of electrons is 10 0 J and the photons also have the same energy. The wavelengths associated with these particles are e and ph respectively. These wavelengths are related in the following way ph = e ph < e e / ph = c (velocity of light) ph > e 3. An electron of mass m, when accelerated through a potential V, has de-broglie wavelength. The de-broglie wavelength associated with a proton of mass M accelerated through the same potential difference will be M m m M M m m M [Answers : (1) a () d (3) b] C4 Atomic Model In 1911 Ernest Rutherford proposed that the positive charge of the atom is densely concentrated at the center of the atom, forming its nucleus, and that, furthermore, the nucleus is responsible for most of the mass of the atom. Rutherford proposal was based on the results of -particle scattering experiment. In 1913, Bohr proposed a model of the hydrogen atom (one electron system) based on a clever combination of classical and early quantum concepts. His basic assumption - that atoms exist in discrete quantum states of well-defined energy for which the magnitude of angular momentum of the electron in such orbits is Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

6 PMP 6 h quantised given by L mvr n = n where v is the speed of the electron in the orbit, r is the radius of the orbit, n is the principle quantum number. The energies of atom are quantized; that is, the atom have only certain specific values of energy associated with different quantum series. Atom can make transitions between different quantum states by emitting or absorbing a photon; the frequency f associated with that light is given by h = E high E low, where E high is the higher energy and E low is the lower energy of the pair of quantum states involved in the transition. Atoms also have quantized angular momenta and magnetic dipole moments. Important Points for Bohr Atom 1. Radius of nth orbit : r 0 n Ze h m = n 0.53 Z Å. Velocity of the electron in the nth orbit : Ze Z c v = nh n Total Energy of the Electron in the nth orbit : E n 0 4 Z e m 8 n h Kinetic energy of the electron in the nth orbit : K n = E n = E n Potential energy of the electron in the nth orbit : U n = E n 4. Wavelength of photon emitted for a transition from n to n 1 1 R 1 n1 1 n Z where R = m 1 (for a stationary nucleus) is known as Rydberg Constant R If nucleus is not considered to be stationary then R, where m is the mass of electron (revolving m 1 M particle) and M is the mass of nucleus. Practice Problems : 1. The wavelength of the energy emitted when electron come from fourth orbit to second orbit in hydrogen is 0,397 cm 1. The wavelength of the energy for the same transition in He + is 5,099 cm 1 0,497 cm 1 40,994 cm 1 81,988 cm 1. When the electron jumps from a level n = 4 to n = 1, momentum of the recoiled hydrogen atom will be kg m/s kg m/s kg m/s zero 3. If the series limit wavelength of Lyman series for the hydrogen atom is 91 Å, then the series limit wavelength for the Balmer series of hydrogen atom is 91 Å 91 Å 91 4 Å (91/) Å 4. When a hydrogen atom is raised from the ground state an excited state, then both K.E. and P.E. decrease P.E. increases and K.E. decreases P.E. decreases and K.E. increases both kinetic energy (K.E.) and potential energy (P.E.) increase 5. Which of the following statements are true regarding Bohr s model of hydrogen atom? I. Orbiting speed of electron decreases as it shifts to discrete orbits away from the nucleus Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

7 PMP 7 II. Radii of allowed orbits of electron are proportional to the principal quantum number III. Frequency with which electron orbits around the nucleus in discrete orbits is inversely proportional to the principal quantum number IV. Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbits Select the correct answer using the codes given below : Codes I and III II and IV I, II and III II, III and IV 6. If the potential energy of the electron in the first allowed orbit in hydrogen atom is E, its ionisation potentials is E/ kinetic energy is E/ total energy is E/ all of the above statements are true 7. In hydrogen atom H -line arise due to transition of electron from 3 rd orbit to nd orbit. In the spectrum of singly ionised helium there is a line having almost the same wavelength as that of H line, this is due to transition of electron between the orbits 3 to 1 to 5 to 3 6 to 4 8. The ratio of the frequencies of the long wavelength limits of the Lyman and Balmer series of hydrogen is 7 : 5 5 : 7 4 : 1 1 : 4 9. E n and J n denote the total energy magnitude and the angular momentum of an electron in the nth allowed orbit of a Bohr atom. Then E n J n E n 1/J n E n J n E n 1/J n 10. Consider an electron in the nth orbit of a hydrogen atom in the Bohr model. The circumference of the orbit can be expressed in terms of de-broglie wavelength of that electron as (0.59) n n (13.6) n 11. In Bohr model of hydrogen atom, choose the incorrect statement from the following : the radius of nth orbit is proportional to n the total energy of electron in nth orbit is proportional to n the angular momentum of the electron in an orbit is an integral multiple of h/ the magnitude of the potential energy of an electron in any orbit is greater than its kinetic energy [Answers : (1) a () a (3) c (4) b (5) a (6) d (7) d (8) b (9) d (10) d (11) b] C5 X-rays : X-rays are electromagnetic waves having energy in KeV. When a solid target, such as solid copper or tungsten, is bombarded with electrons whose kinetic energies are in the kiloelectron-volt range, electromagnetic radiation called X rays is emitted. Figure shows the wavelength spectrum of the x rays produced when a beam of 35 KeV electrons falls on a molybdenum target, We see a broad, continuous spectrum of radiation on which are superimposed two peaks of sharply defined wavelengths. A continuous spectrum x-rays is emitted when high-energy electrons lose some of their energy in a collision Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

8 PMP 8 with atomic nuclei. The cutoff wavelength min is the wavelength emitted when such electrons lose all their initial energy in a single such encounter and is electrons that strike the target. min hc K 0, in which K 0 is the initial kinetic energy of the The characteristic x-ray spectrum arises when high-energy electrons eject electrons from deep within the atom; when a resulting hole is filled by an electron from farther out in the atom, a photon of the characteristic x-ray spectrum is generated. In 1913 British physicist H.G.J. Moseley measured the frequencies of the characteristic x rays from a number of elements. He noted that when the square root of the frequency is plotted against the position of the element in the periodic table, a straight line results, as in the Moseley plot of figure. This allowed Moseley to conclude that the property that determines the position of an element in the periodic table is not its atomic mass but its atomic number Z - that is, the number of protons in its nucleus. He found that relation between f and Z, given by f = a (Z b), where a and b are constant. Practice Problems : 1. An X-ray tube is operating at 40 kv, which of the following wavelength will be absent in the X-ray spectrum? 0. Å 0.4 Å 0.6 Å 100 Å [Answers : (1) a] C6 Radioactivity Most known nuclides are radioactive; they spontaneously decay at a rate R (= dn/dt) that isproportional to the number N of radioactive atoms present, the proportionally constant being the disintegration constant. This leads to the law of exponential decay : N = N 0 e t, R = N = R 0 e t The half-life T ½ = (ln )/ of a radioactive nuclide is the time required for the decay rate R (or the number N) in a sample to drop to half its initial value. Units of Activity 1 becauerel (Bq) = 1 disintegration per second (dps) 1 curie = dps 1 rutherford = 10 6 dps Mean life of a radioactive sample is defined as the average of the lives of all nucleus. T av 0 N Practice Problems : t 0e N 0 dt 1 T The decay constant of a radioactive sample is. The half life and mean life of the sample are respectively given by 1/ and (ln)/ (ln)/ and 1/ (ln) and 1/ /(ln) and 1/ Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

9 PMP 9. Plutonium decays with a half life of 4000 years. If plutonium is stored for 7000 years, the fraction of it has remains is 1/ 1/3 1/4 1/8 3. The half life of Bi 10 is 5 days. If we start with 50,000 atoms of this isotope, the number of atoms left over after 10 days is 5,000 5,000 1,500 0, A radioactive isotope X with a half-life of years decays to Y which is stable. A sample of rocks from the moon was found to contain both the elements X and Y which were in the ratio 1 : 7. The age of the rocks is years years years years 5. The radioactivity of a sample is R 1 at a time T 1 and R at a time T. If the half-life of the specimen is T, the number of atoms that have disintegrated in the time (T T 1 ) is proportional to (R 1 T 1 R T ) (R 1 R ) (R 1 R )/T (R 1 R )T 6. The decay constant for the radioactive isotope 57 Co is s 1. The number of disintegrations taking place in a milligram of pure 57 Co per second is The half life of radium is 160 years and its atomic weight is 6 kg per kilomol. The number of atoms that will decay from its 1 g sample per second will be A freshly prepared radioactive source of half life hr. emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is 6 hr 1 hr 4 hr 18 hr 9. Which of the following statement is true? I. All radioactive elements decay exponentially with time. II. Half life time of a radioactive element is the time required for one half of the radioactive atoms to disintegrate. III. IV. Age of the earth can be determined by radioactive dating Half-life time of a radioactive element is fifty per cent its average life period Select the correct answer using the codes given below : I and II I, III and IV I, II and III II and III 10. What percentage of original radio active atoms is left after five half lives 0% 10% 5 % 3.15% 11. The count-rate of Geiger Muller counter for the radiation of the -radioactive material of half-life of 30 minutes decrease to 5 second 1 after hours. The initial count rate was 0 second 1 5 second 1 80 second 1 65 second 1 [Answers : (1) b () d (3) c (4) c (5) d (6) b (7) a (8) b (9) c (10) d (11) c] C7 C8 Mass-Energy Equivalence An object of mass m and the energy equivalent E of that mass are related by E = mc. The energy equivalent of one amu is MeV. About the Nucleus 1. Nuclei have a mean radius r given by r = r 0 A 1/3 where r 0 = 1. fm and A is the mass number.. The density of the nucleus is of the order of kg/m Nuclei in the nucleus are held together by an attractive force (known as nuclear force) acting among the mucleous. It is thought to be a secondary effect of the strong force acting between the quarks that make up the nucleons. Nuclear force is the strongest force in nature. Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

10 PMP The mass M of a nucleus is less than the total mass m of its individual protons and neutrons. That means that the mass energy Mc of a nucleus is less than the total mass energy (mc ) its individual protons and neutrons. The difference between these two energies is called the binding energy of the neucleus E be = ( mc ) Mc. Binding energy per neucleon E ben, which is the ratio of the binding energy E be of a nucleus to the number A of nucleons in that nucleus : Ebe Eben. A 5. The average binding energy per nucleon is about 8.8 MeV/nucleon. 6. The variation of average binding energy per nucleon with mass number A is as shown in figure of The nucleons in a nucleus on the right side of the plot would be more tightly bound if that nucleus were to split into two nuclei that lie near the top of the plot. Such a process, called fission, occurs naturally with large (high mass number A) nuclei such as uranium, which can undergo fission spontaneously (that is, without an external cause of source of energy). The process can also occur in nuclear weapons in which many uranium or plutonium nuclei are made to fission all at once, to create an explosion. The nucleons in any pair of nuclei on the left side of the plot would be more tightly bound if the pair were to combine to form a single nucleus that lies near the top of the plot. Such a process, called fusion, occurs naturally in stars. Were this not true, the Sun would not shine and thus life could not exist on Earth. 7. Decay Process Alpha decay Beta decay ( ) Beta decay ( + ) Electron capture A Z A Z A Z A Z X X X X e A 4 Z A Z1 A Z1 Y 4 Y e Y e A Z1 He Y + x-ray Gamma decay A Z * A Z X X 8. Nuclear reactions can occur when a target nucleus X is bombarded by a particle a, resulting in a nucleus Y and an outgoing particle b : a + X Y + b or X(a, b)y The rest energy transformed to kinetic energy in such a reaction, called the reaction energy Q, is Q = (M a + M X M Y M b )c A reaction for which Q is positive is called exothermic. A reaction for which Q is negative is called endothermic. The minimum kinetic energy of the incoming particle necessary for such a reaction to occur is called the threshold energy. Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

11 Practice Problems : PMP The volume of a nucleus directly proportional to A x where A is mass number of the nucleus. The value of x is Which of the following is incorrect for nuclear force? short range force charge independent force strongly attractive force all are incorrect 3. In positive beta decay, which of the following particles will be emmited? positron and neutrino electron and antineutrino positron and antineutrino electron and neutrino 4. During a negative beta decay an atomic electron is ejected an electron which is already present within the nucleus is ejected a neutron in the nucleus decays emitting an electron a part of the binding energy of the nucleus is converted into an electron 5. The radioactive nuclide 8 88 Ra decays by the emission of three -particles and one particle. The nuclide X finally formed is X 86 X 83 X 88 X A A4 A4 A4 6. In the transformation sequence represented by X Y Y K the decays are in the order,,,,,,,, 7. A nucleus ruptures into two nuclear parts which have their velocity ratio equal to : 1. What will be the ratio of their nuclear size (nuclear radius)? 1/3 : 1 1 : 1/3 3 1/ : 1 1 : 3 1/ 8. In a -decay Z Z Z Z1 the parent and the daughter nuclei have the same number of protons the daughter nucleus has one proton less than the parent nucleus the daughter nucleus has one proton more than the parent nucleus the daughter nucleus has one neutron more than the parent nucleus 9. If the binding energy of deutron is.3 MeV, its mass defect in atomic mass unit is Which of the following is a fusion reaction? H H He n N C H n 9 U 93 Np He H If the total binding energies of H, 4 He, 56 Fe and 35 U nuclei are., 8.3, 49 and 1786 MeV respectively, identify the most stable nucleus out of the following 56 6 Fe H 9 U He When 9 U undergoes fission, 0.1% of its original mass is changed into energy. How much energy is released if 1 kg of 35 9 U undergoes fission? J J J J Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

12 13. Choose the correct statement for nuclear fission : In this process the neutrons split the uranium nuclei into two fragments of about the same size (barium & krypton) and several neutrons. The energy released per fission of 35 U is 00 MeV Nuclear reactor is based on controlled nuclear fission All are correct 14. Choose the correct statement for the nuclear fusion : This process takes place at very high temperature The link of this process are protons The source of energy at sun is nuclear fusion All are correct 15. Choose the correct statement : The binding energy per nucleon is maximum for Fe The average binding energy per nucleon is of the order of 7.5 MeV Both & are correct None of these 16. In nuclear reactions we have conservation of mass only momentum only energy only mass, energy and momentum 17. The ratio of the radii of the nuclei 13 Al 7 and 5 Te 15 is approximately 6 : : 5 40 : : 73 PMP 1 [Answers : (1) a () d (3) a (4) c (5) c (6) d (7) b (8) c (9) c (10) a (11) a (1) d (13) d (14) d (15) c (16) b (17) a] C9 Semiconductor and Electronic Devides : On the basis of energy band in solids, the solid are divided into insulator, semi-conductor and conductor. The band gap or energy gap between the conduction band and valence band or forbidden band for insulator, semi-conductor and conductor are more than 3eV, approx. 0. to 3eV and negligible energy gap respectively. Intrinsic semiconductor or pure semi-conductor or elemental semiconductor : 1. Si and Ge are pure semiconductor.. The band gap for Si is 1.1 ev and for Ge is 0.67 ev 3. The conductivity of the semiconductor is due to holes and electrones 4. For pure semiconductor, number of electrones per unit volume (n i ) and number of holes per unit volume (p i ) are equal i.e., n i = p i. 5. The conductivity of the semiconductor increases with the increment of temperature. Extrinsic semiconductor or impure semi-conductor : The conductivity of pure semi-conductor can be increased by adding some impurity known as dopent and this process is known as doping. On this basis there are two types of extrinsic semiconductors : n type semiconductor : 1. n-type semiconducting Si or Ge is obtained by doping with pentavalent atoms (donors) like As,Sb, P, etc.. electrons are the majority carrier i.e. n >> p. p type semiconductor : 1. p-type semiconducting Si or Ge is obtained by doping with trivalent atoms (acceptors) like B, Al, In etc.. holes are the majority carrier i.e. p >> n. Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

13 PMP 13 Remember that n i p i = n i = p i = np where n and p are number of electrons per unit volume and number of holes per unit volume respectively. Conductivity of a semiconductor : For all types of semiconductors, the conductivity is given by e(nµ pµ ) where e is the electronic charge, µ e is the electron mobility that µ p is the hole mobility. e Practice Problems : p 1. A piece of copper and another of germanium are cooled from room temperature to 80 K. The resistance of each of them increases each of them decreases copper increases and germanium decreases copper decreases and germanium increases. Majority carriers in a semiconductor are holes in n-type and electrons in p-type holes in both n-type and p-type electrons in n-type and holes in p-type electrons in both n-type and p-type. 3. Read the following statements carefully : Y : Z : The resistivity of a semiconductor decreases with increase of temperature In a conducting solid, the rate of collisions between free electrons and ions increases with increase of temperature. State the correct statement(s) from the following : Y is true but Z is false Y is false but Z is true both Y and Z are true Y is true and Z is the correct reason for Y [Answers : (1) d () c (3) c] C10 p-n junction or diode : When p-n is made, a depletion layer is formed consisting of immobile ion-cores devoid of their electrons or holes. This is responsible for a junction potential battier. The thickness of the order of 10 5 m. Symbol of p-n junction or diode is given by p-n junction diode under forward bias : When the diode is connected as shown in figure then it said to be in forward bias in which diffusion current will dominate as compare to drift current and the current will flow from p to n. The width of the depletion layer will decrease and also the barrier potential will decrease. The order of current is in ma. p-n junction diode under reverse bias : When the diode is connected as shown in figure Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

14 PMP 14 then it said to be in reverse bias in which drift current will dominate as compare to diffusion current and the current will flow from n to p. The width of the depletion layer will increase and also the barrier potential will increase. The order of current is in µa. V-I characteristics of a silicon diode : Important Points : (1) The characteristics is not a linear curve and hence ohms law is not obeyed in case of semiconductor () The resistance is not constant hence we define the dynamic resistance = dv/di. Application of diode as rectifier : Rectifier is use to convert the A.C. into D.C. There are two types of rectifier which are shown in the figure The frequency of output in half wave rectifier is f and in full wave rectifier is f where f is the frequency of input. Special purpose diodes : 1. Zener diode : It works in reverse bias and it maintains a constant voltage across an output (voltage regulation).. Photo diode : It works in reverse bias and it is used to calculate the intensity of light. 3. Light emitting diode and diode laser : It generates light energy. 4. Solar cell : It works in reverse bias and it converts photon energy into electricity Practice Problems : 1. In half wave rectifier, the RMS value of A.C. component of the wave is equal to D.C. value more than D.C. value less than D.C. value zero. The reverse biasing in a junction diode decreases the potential barrier increases the potential barrier increases the number of minority charge carriers increases the number of majority charge carriers. Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

15 PMP A full-wave rectifier circuit along with the output is shown in the figure below. The contribution(s) from the diode 1 is (are) C A, C B, D A, B, C, D 4. The depletion layer in the pn junction region is caused by drift of holes diffusion of carriers migration of impurity ions drift of electrons 5. In the given diagram, the input is across the terminals A and C and the output is across B and D. Then the output is : zero same as the input full-wave rectified half-wave rectified 6. In a pn junction diode the current in the reverse biased condition is generally very small the current in the reverse biased condition is small but the forward biased current is independent of the bias voltage. the reverse biased current is strongly dependent on the applied bias voltage the forward biased current is very small in comparison to reverse biased current [Answers : (1) b () b (3) c (4) b (5) c (6) a] C11 Transistor : Transistor is an n-p-n or p-n-p junction device. The central block (thin and lightly doped) is called Base while the other electrodes are Emitter and Collectors. The emitter-base junction is forward biased while collector-base junction is reverse biased which is shown in figure : Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

16 PMP 16 Here I E is the emmeter current, I C is the collector current and I B is the base current. The relation between them is given by I E = I C + I B. I Transistor parameter : I C B I and I C E. is known as D.C. current gain. The relation between and is given by. Here < 1 and >> 1. 1 Practice Problems : 1. Two P-N junctions can be connected in series by three methods as shown in the figure. If the potential difference in the junctions is the same, then the correct connections will be in circuits (1) and () in circuits () and (3) in circuits (1) and (3) only in circuit (1). In an NPN transistor, the emitter current is slightly more than collector current slightly less than the collector current equal to the collector current equal to the base current 3. In a transistor let the emitter current is I E, base current is I B and collector currents is I C. Choose the incorrect statement. I E > I C I E = I C + I B I C I B I C < I B 4. In an npn transistor circuit, the collector current in 10 ma. If 90% of the electrons emitted reach the collector. the emitter current will be 9 ma the emitter current will be 11 ma the base current will be 1 ma both and are correct [Answers : (1) b () a (3) d (4) d] C1 Transistor as an amplifier (common emitter configuration) : When the transistor is operated in the active region then it will be used as amplifier in which output voltage is amplified as compare to input voltage. The circuit is shown in figure : Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

17 PMP 17 Important Points : 1. Current gain =. Voltage gain = A ac V I I V V 0 i C B ac R R 3. Power gain = current gain voltage gain = 4. Transconductance (g m ) = Here R i is the input resistance of the transistor. R ac i L i R ac L R i 5. The phase difference between the input and output voltage is in case of CE amplifier. Practice Problems : 1. To use a transistor as an amplifier biased the emitter base junction is forward biased and the collector base junction is reverse no bias voltage is required both junctions are forward biased both junctions are reverse biased. In the circuit shown here the transistor used has a current gain = 100. What should be the bias resistor R B so that V CE = 5 V? (neglect V BE ) [Answers : (1) a () b] C13 Transistor as oscillator : The L-C oscillations are damped due to the power loss in the resistance of the circuit to maintain undamped oscillation in the circuit, it is essential to supply energy at the same rate at which losses occur. This can be done by using a transistor which provides a feedback mechanism. Practice Problems : 1. An oscillator is nothing but an amplifier with positive feedback large gain no feedback negative feedback [Answers : (1) a] Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

18 PMP 18 C14 Transistor as switch : When the transistor used in the cut-off or saturation state it acts as a switch. C15 Logic Gates : A logic gate is a digital circuit which follows certain logical relationship between the input and output voltages. There are three basic logic gates : 1. OR gate. AND gate 3. NOT gate The OR Gate It has two or more inputs and one output. Its logic symbol, truth table and Boolen expression are given below : Logic Symbols : Truth Table : A B Y Boolen Expression : A + B = Y (Read as A or B) This gate is realised using the diodes. The AND Gate : It has two or more inputs and one output. Its logic symbol, truth table and Boolen expression are given below : Logic Symbol : Truth Table : A B Y Boolen Expression : A. B = Y (read as A and B) This gate is realised using the diodes. The NOT Gate : It has one input and one output. Its logic symbol, truth table and Boolen expression are given below : Logic Symbol : Truth Table : A Y Boolean Expression : A Y This gate is realised using the transistor. Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

19 Combination of Gates : PMP The NAND gate : If the output of an AND gate is connected to the input of a NOT gate, the circuit is called NAND gate. The logic symbol, truth table and Boolean expression for the NAND gate are given below : Logic Symbol : Truth Table : A B Y Boolean Expression : A.B Y Using the NAND gate we can formed the all other types of gate, that s why this gate is known as basic builiding block gate.. The NOR gate : If the output of an OR gate is connected to the input of a NOT gate, the circuit is called a NOR gate. The logic symbol, truth table and Boolean expression of the NOR gate are given below : Logic Symbol : Truth Table : A B Y Boolean Expression : A B Y Using the NOR gate we can formed the all other types of gate, that s why this gate is known as basic builiding block gate. Practice Problems : 1. Boolean algebra is essentially based on truth logic symbol numbers. How many NAND gates are used to form AND gate? Truth table shown below is for XOR AND XNOR OR 4. The following configuration of gate is equivalent to Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

20 PMP 0 NAND XOR OR None of these 5. The combinations of the NAND gates shown here in figure are equivalent to an OR gate and an AND gate respectively. an AND gate and a NOT gate respectively. an AND gate an an OR gate respectively. an OR gate and a NOT gate respectively. [Answers : (1) b () b (3) c (4) b (5) a] C16 Important Points for communication : 1. Electronic communication refers to the transfer of information or message (available in the form of electrical voltage and current) from one point to another point.. Transmitter, transmission channel and receiver are three basic units of a communication system. 3. Low frequencies cannot be transmitted to long distances. Therefore, they are superimposed on a high frequency carrier signal by a process known as modulation. 4. In modulation, some characteristic of the carrier signal like amplitude, frequency or phase varies in accordance with the modulating or message signal. Correspondingly, they are called Amplitude Modulated (AM). Frequency Modulated (FM) or Phase Modulated (PM) waves. 5. Pulse modulation could be classified as : Pulse Amplitude Modulation (PAM), Pulse Duration Modulation (PDM) or Pulse Width Modulation (PWM) and Pulse Position Modulation (PPM). 6. For transmission over long distances, signals are radiated into space using devices called antennas. The radiated signals propagate as electromagnetic waves and the mode of propagation is influenced by the presence of the earth and its atmosphere. Near the surface of the earth, electromagnetic waves propagate as surface waves. Surface wave propagation is useful up to a few MHz frequencies. 7. Long distance-communication between two points on the earth is achieved through reflection of electromagnetic waves by ionosphere. Such waves are called sky waves. Sky wave propagation takes place up to frequency of about 30 MHz. Above this frequency, electromagnetic waves essentially propagate as space waves. Space waves are used for line-of-sight communication and satellite communication. 8. If an antenna rediates electromagnetic waves from a height h T, then the range d T is given by RhT where R is the radius of the earth. 9. Amplitude modulated waves can be produced by application of the message signal and the carrier wave to a non-linear device, followed by a band pass filter. 10. AM detection, which is the process of recovering the modulating signal from an AM waveform, is carried out using a rectifier and an envelope detector. Practice Problems : 1. A TV transmitting antenna is 81m tall. The service area can it cover if the receiving antenna is at the ground level (radius of the earth is 6400 km) 358 km 3355 km 455 km 583 km [Answers : (1) a] Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

21 PMP 1 1. A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed m away, the electrons emitted by the photocathode carry one quarter of their previous energy carry one quarter of their previous momenta are half as numerous are one-quarter as numerous.. In Rutherford scattering experiment, the correct angle of scattering of alpha particles for impact parameter equal to zero is Choose the correct statement from the following. In stable nuclei, the number of nuetrons (N) is related to the number of protons (Z) as N Z The nuclei 6 C 13 and 7 N 14 can be described as isotones The mass density of a nucleus varies with the mass number A as A 0 All the above are correct 4. Out of the following, the one which can pass through 0 cm thickness of steel is -rays -rays -rays ultra-violet rays 5. Which of the following statement is correct for -rays? -rays are not deflected by the presence of electric field or magnetic field. the velocity of -rays is c the energy of -rays is of the order of MeV All are correct 6. In the statements given below, the only one correct statements is -radioactivity is the process in which an electron is emitted from an unstable atom whose atomic number remains unchanged -radioactivity is the process in which the daughter nucleus has atomic number 1 unit more than that of the parent nucleus INITIAL STEP EXERCISE -radioactivity is the process in which an unstable atom emits the nucleus of a helium atom -radioactivity is the process in which a heavy atom emits electromagnetic radiations of very high frequency. 7. Choose the correct statement for the neutrons from the following : The energy of a neutron is in thermal equilibrium at room temperature is 0.5 ev Thermal neutrons can cause fission in 35 U Fast neutrons can easily be slowed down by heavy water (known as moderator) in a nuclear reactor All are correct 8. An element A decays to an element C by a two step process 4 A B + He B C + e.then A and C are isotopes A and C are isobars A and B are isotope A and B are isobars 9. Choose the correct statement for the nuclear reactor : The control rods (cadmium or boron) is used to absorb the excess neutrons. Coolant (water or CO ) are used to absorb heat produced in the reactor. Moderator (heavy water or graphite) is used to control the chain reaction. All are correct 10. When two deuterium nuclei fuse together to form a tritium nucleus, we get a neutron deutron -particle proton 11. Consider the following statement : I. Free proton cannot decay II. III. A bounded proton decays into a neutron, positron & neutrino A free neutron or bounded neutron decays into a proton, an electron and anti-neutrino Which of the above statments are correct? Only (I) (II) & (III) (I) and (III) All are correct Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

22 PMP 1. Ozone layer blocks the radiations of wavelength less than m equal to m more than m all of these 13. The most penetrating radiation out of the following is X-rays Beta-rays Alpha particles Gamma rays 14. The phenomenon of pair production is the production of an electron and a positron from -rays ejection of an electron from a metal surface when exposed to ultra-violet light ejection of an electron from a nucleus ionization of a neutral atom 15. In a cloud chamber, and particles are sent. The nature of tracks produced by these particles respectively will be thin and long, thick and short, thin and very long thick and short, thin and long, fuzzy thick and long, thin and short, fuzzy thick and short, thin and long 16. At any instant, the ratio of the amount of radioactive substances is : 1. If their half lives be respectively 1 and 16 hours, then after two days, what will be the ratio of the substances? 1 : 1 : 1 1 : 1 : A radioactive sample with a half life of 1 month has a label : Activity = micro Curies on What would be its acitivity two months earlier? 1.0 micro Curie 0.5 micro Curie 4 micro Curie 8 micro Curie 18. If the nuclear force between two protons, two neutrons and between proton and neutron is denoted by F pp, F nn and F pm respectively, then F pp F nn F pm F pp Fnn but F pp = F pn F pp = F nn = F pn F pp F nn F pn 19. If element with principal quantum number n > 4 were not allowed in nature, the number of possible elements would be FINAL STEP EXERCISE 1. In an atom, two electrons move round the nucleus in circular orbits of radii R and 4R. The ratio of the time taken by them to complete one revolution is 1 : 4 4 : 1 1 : 8 8 : 1. When a metallic surface is illuminated by a monochromatic light of wavelength, the stopping potential for photoelectric current is 3V 0. When the same surface is illuminated by light of wavelength, the stopping potential is V 0. The threshold wavelength for this surface for photoelectric effect is 6 4/ The masses of neutron and proton are amu and amu respectively. If two neutrons and two protons combine to form a helium nucleus of mass amu, the binding energy of the helium nucleus will be 8.4 MeV 0.8 MeV 7.3 MeV 14. MeV 4. The minimum light intensity that can be perceived by the eye is about W/m. The number of photons of wavelength m that must enter the pupil, of area 10 6 m per sec for vision is approximately (use h = joule-sec) 3 10 photons photons photons photons 5. Consider a radioactive material of half life 1.0 minute. If one of the nuclei decays now, the next one will decay after 1.0 minute 1/log e minutes 1/N minutes when N is the number of nuclei present at that moment any time 6. If 10% of a radioactive material decays in 5 days, Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

23 PMP 3 then the amount of original material left after 0 days is approximately 60% 65% 70% 75% 7. If the binding energy per nucleon in 7 Li and 4 He nuclei are 5.60 MeV and 7.06 MeV, then energy of the reaction 7 Li + 1 H 4 He is 19.6 MeV.4 MeV 8.4 MeV 17.3 MeV 8. Carbon-14 decays with a half-life of about 5,800 years. In a sample of bone, the ratio of carbon-14 to carbon-1 is found to be 1/4 of what it is in free air. This bone may belong to a period about x centuries ago, where x is / In the -decay process occurring in different types of nuclei at rest the kinetic energy of the daughter nucleus is always greater than the kinetic energy of the -particle. the kinetic energy of the daughter nucleus is always less than the kinetic energy of the -particle. the magnitudes of the linear momenta of the -particle and the daughter nucleus are always equal both and are correct MeV of energy is obtained in the fission of one nucleus of 35 U.A reactor is generating 1000 kw of power. The rate of nuclear fission in the reactor is the probability of decay of an atom in unit time. decreases as the age of atoms increases increases as the age of atoms increases is perpendicular of the age of the atom behaviour of with time depends on the material 13. The intensity of gamma radiation from a given source is I 0. On passing through 37.5 mm of lead it is reduced to I 0 /8. The thickness of lead which will reduce it to I 0 / is (37.4) 1/3 mm (37.5) 1/4 mm (37.5/3) mm (37.5/4) mm 14. The half life of radium is 160 years and its atomic weight is 6. The number of atoms that will decay from its 1 gm sample per second will be In hydrogen atom, the electron is making rev./sec. around the nucleus in an orbit of radius 0.58 Å. The magnetic moment (A m ) will be In a hypothetical Bohr hydrogen, the mass of the electron is doubled. The energy E 0 and radius r 0 of the first orbit will be (a 0 is the Bohr radius) E 0 = 7. ev ; r 0 = a 0 E 0 = 13.6 ev ; r 0 = a 0 / E 0 = 7. ev ; r 0 = a 0 / E 0 = 13.6 ev ; r 0 = a N atoms of a radioactive element emit n alphaparticles per second. The half-life of the element in seconds is n/n N/n N/n n/n 1. The decay constant of a radioactive material is Einstein Classes, Unit No. 10, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,