ATOMIC WORLD P.1. ejected photoelectrons. current amplifier. photomultiplier tube (PMT)

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1 ATOMIC WORLD P. HKAL PAPER I 0 8 The metal Caesium has a work function of.08 ev. Given: Planck constant h = J s, charge of an electron e = C (a) (i) Calculate the longest wavelength of visible light that can cause emission of photoelectrons from Caesium. ( marks) (ii) Light of wavelength m is incident on Caesium. Find the maximum kinetic energy (in ev) of photoelectrons emitted from it. ( marks) (b) Figure 8. shows a schematic diagram of a photomultiplier tube (PMT) which consists of a Caesium photocathode, a current amplifier and a collector anode. When dim light enters the tube, photoelectrons are emitted from the photocathode. These electrons are multiplied in number by a million fold through the current amplifier. They are finally collected by a collector anode and give rise to a measurable electrical signal. photocathode dim light ejected photoelectrons electrons collector anode Figure 8. current amplifier photomultiplier tube (PMT) Given that the number of photoelectrons emitted per second by the photocathode is when dim light is incident on it. The corresponding output current of the PMT is 0.0 ma. Find the gain of the PMT (i.e. the number of folds of increase of electrons). ( marks) (c) Figure 8. shows a night vision device (NVD) which enables a person to see in a very dark environment. Figure 8. A night vision device mounted on a soldier s helmet. The simplified diagram of a NVD in Figure 8.3 shows how it works. Very dim light enters the PMT inside the NVD through its objective. The resulting amplified electrical signal is then focused on a phosphor-coated screen to produce an image of sufficient intensity for viewing. dim light phosphor-coated screen screen Figure 8.3 photomultiplier tube tube (PMT) objective amplified amplified electrical signal electrical signal eyepiece (i) Suggest a reason why a NVD can operate with dim light. ( mark) (ii) Explain why a circuit has to be installed in the PMT to limit the maximum current. ( mark) (iii) The electrons incident on the phosphor-coated screen excite its atoms from the ground state of energy level 7.0 ev to their first excited state of energy level 4.89 ev. Estimate the

2 ATOMIC WORLD P. wavelength of the photons emitted when the excited atoms return to their ground state. Hence, state the colour of images produced by the NVD s screen. (3 marks) (a) Explain the physical meaning of the terms h and in Einstein s photoelectric equation KE max = h -. ( marks) (b) Light of wavelength 450 nm is incident on a metal surface. The power of the light reaching the metal surface is 5.0 mw. (Given: Planck constant h = J s; charge of an electron e = C) (i) Find the number of photons arriving the metal surface per second. (3 marks) (ii) If on average only one photoelectron is emitted for every two thousand photons absorbed by the metal surface, calculate the resulting photoelectric current. ( marks) (c) Light of different wavelengths is allowed to illuminate the metal surface. The corresponding maximum kinetic energy KE max of the photoelectrons emitted is tabulated below. KE max / ev / nm (i) Choose a suitable physical quantity to complete the table so as to plot a straight line graph. Use the graph to find the stopping potential which can reduce the current found in (b)(ii) to zero. Show your working. (6 marks) (ii) Suppose the experiment is repeated with another piece of metal of larger work function. Use a dotted line to sketch the expected result on the graph in (c)(i). ( marks) The set-up shown in Figure 6. is used to study photoelectric effect. Light of a certain frequency is directed towards the photo-sensitive electrode B of a photocell. The potential difference across the electrodes A and B can be varied by adjusting the variable supply. Given: Planck constant h = J s Charge of electron e = C Figure 6. electrometer A light phtocell B (a) Variable supply When the voltage V B of the electrode B is zero, the electrometer still detects a current. Explain this phenomenon and state the direction of the current in the photocell. ( marks)

3 ATOMIC WORLD P.3 (b) The work function of electrode B is.3 ev. The graph in Figure 6. shows the variation of the current I with the voltage V B when the variable supply is adjusted. I / 0-0 A Figure 6. (c) V B /V (i) Explain why the current drops when V B is increased. ( marks) (ii) What is the maximum kinetic energy, in ev, of the photoelectrons produced? Hence, find the wavelength of the light waves used and name this kind of light waves. (4 marks) (i) In Figure 6., sketch the current-voltage variation when the experiment is repeated with the light intensity doubled. ( marks) (ii) Referring to the graphs in Figure 6., elaborate one observation of the photoelectric effect that cannot be explained by the wave theory. ( marks) In a photoelectric experiment, a thin plate of dimension ( (8.0 0 ) (8.0 0 ) m is illuminated with a parallel beam of ultraviolet light of wavelength 30 nm. The work function of the metal is. ev. 34 Given: Planck constant = Js 9 Charge of an electron =.60 0 C (a) What is meant by the work function of a metal? ( mark) (b) Explain why photoelectrons are emitted with different speeds though the energy of each incident photon is fixed. ( mark) (c) (i) Calculate the maximum kinetic energy of the photoelectrons emitted. ( marks) (ii) Find the stopping potential. ( mark) (d) The intensity of the ultraviolet light is 3 Wm - and it falls normally on one side of the metal plate. Find, in the absence of the stopping potential, the number of photoelectrons emitted per second. Assume that every incident photon can successfully release a photoelectron. (3 marks) (e) State the change in (i) the stopping potential and (ii) the number of photoelectrons emitted per second, if another source of ultraviolet light with the same intensity, but having a shorter wavelength, is used. Explain briefly. (4 marks) 99 Figure. V (a) (b) In an experiment with an illuminated photocell using caesium as the cathode, a small current is detected by the microammeter even when the anode is made slightly negative with respect to the cathode, using the circuit of Figure.. Briefly account for this. ( marks) The current falls to zero only when the.5 reverse p.d. across the reaches a value V s, which varies with the frequency f of the radiation used to illuminated the.0 cathode. Figure. shows the relationship between V s and f. V s /V 0.5 Figure f/0 4 Hz

4 ATOMIC WORLD P.4 (i) What is the relationship between V s and f as predicted by Einstein s photoelectric theory? ( marks) (ii) What is the value of the threshold frequency for caesium? ( mark) (iii) If the electronic charge is.6 x 0-9 C, estimate a value for the Planck constant. ( marks) (iv) Calculate the work function for caesium in electron-volts. (3 marks) (v) Sketch on Figure. the corresponding variation between V s and f for a photocell whose cathode has a larger work function than caesium. ( marks) Figure 4 represents the energy levels of a hypothetical hydrogen-like atom: zero energy level Diagram not to scale 4 3 Energy (a) Mark on Figure 4 the ground state of the atom. (b) Briefly explain what is meant by the ground state of the atom. (c) What is the significance of the zero energy level? (d) During the transition from level 3 to level of the atom, photons of wavelength 600 nm are emitted. Calculate the ionisation potential for the atom. (e) Determine the energy (in ev) corresponding to the levels, and 3. (Electron charge =.6 x 0-9 C Planck constant = 6.6 x 0-34 Js) HKAL PAPER II Figure An -particle ( He ) of initial kinetic energy 7.7 MeV approaches a gold nucleus ( 79 Au ) from far away. The -particle is deflected as shown. Estimate the kinetic energy of the -particle at point P where it is m from the gold nucleus which is assumed to be stationary throughout. Given: charge of an electron = C permittivity of free space = F m A. 3.5 MeV B. 4. MeV C. 7.3 MeV D.. MeV The diagram shows the electron transitions within an excited atom. Light of wavelength, and 3 are emitted, where > > 3. Deduce the relationship between, and 3. A. 3 3 B. Energy levels 3 C. D particle P gold nucleus 4

5 ATOMIC WORLD P Since the beginning of the 0th century, -particles had been used as energetic projectiles to bombard various substances to trigger reactions. Many great discoveries came from this kind of experiments. Which of the following discoveries is NOT a nuclear reaction? A. In the discovery of protons, -particles were used to bombard nitrogen gas. B. In the discovery of neutrons, -particles were used to bombard beryllium. C. In the discovery of artificial radioactivity, -particles were used to transmute aluminium into phosphorus. D. In the discovery of large angle deflection, -particles were used to bombard gold foil The figure, drawn to scale, represents the energy levels for an electron in a certain atom. The transition from E 3 to E gives a green line (in the spectrum). Which of the following transitions may give a red line? A. E 4 to E B. E 4 to E C. E 3 to E D. E to E The work function W of five metals are tabulated below. Energy E 4 E 3 E E Metal Caesium Barium Calcium Magnesium Berylium W / 0-9 J If monochromatic light of wavelength 400 nm is incident on each of the metals, how many of them would exhibit photoelectric effect? (Give: Planck constant = J s) A. B. C. 3 D In a photoelectric emission experiment using light of a certain wavelength, the potential difference V required to stop any electrons from reaching the anode is measured for different light intensity I. Which of the following graphs shows how V depends on I? A. V B. V C. V D. V 0 I 0 I 0 I 0 I The figure above shows the possible energy levels of a mercury atom. A free electron with kinetic energy 8.4 ev collides with a mercury atom, which is in its ground state. The change in kinetic energy of the mercury atom in the collision may be neglected. Which is/are the possible value(s) for the kinetic energy of the electron after collision? () 0.7 ev ().9 ev (3) 3.5 ev A. () only B. () only C. () and (3) only D. () and (3) only n = 4 n = 3 n = n =.6 ev.7 ev 5.5 ev 0.4 ev 5

6 ATOMIC WORLD P Which of the following phenomena supports the fact that a nucleus is made up of other fundamental constituents? A. emission of electrons when a metal illuminated by light B. the emission of line spectrum by atoms C. the scattering of -particle from a gold foil D. the decay of radioactive substances The ionization energy for a hydrogen atom in ground state is 3.6 ev. If the atom is in the first excited state, the energy for ionizing it should be A. 3.4 ev B. 4.5 ev C. 6.8 ev D. 0. ev 003 The wavelength of infra-red radiation ranges from about mm to m. What is the approximate energy of a photon of red light? (Given: Planck constant = J s) A. 0-9 J B. 0-3 J C. 0-5 J D J The second line in the Lyman series (corresponding to the K-shell) of the hydrogen spectrum has a wavelength of 0 nm. What is the wavelength of the first line in the series? A nm B. nm C. 36 nm D. 53 nm In an experiment on the photoelectric effect, a student measured the potential V s required to prevent photoemission when a metal was illuminated with radiations of varying wavelength. His observations led him to plot the graph as shown, but he omitted the axes labels. The correct labels for the axes are x y y A. V s B. V s C. V s x 0 D. V s A beam of red light falls on one electrode of a photocell and electrons are emitted. The red beam is then replaced by a blue one that has the same intensity. Which of the following physical quantities would decrease as a result of this change? A. The maximum kinetic energy of the photoelectrons emitted B. The energy of each photon striking the electrode C. The number of photons striking the electrode per second D. The magnitude of the potential difference across the photocell required to reduce the photo-electric current to zero 6

7 ATOMIC WORLD P In which of the following calculations is it necessary to use the Planck constant? () Finding the momentum of an electron from its kinetic energy () Finding the energy of a photon emitted as a result of the transition of an electron between two energy levels in an atom (3) Finding the maximum kinetic energy of photoelectrons from the wavelength of incident radiation A. () only B. (3) only C. () and () only D. () and (3) only A hydrogen atom describes a photon of wavelength such that the electron in the ground state (energy level corresponding to n = ) is brought to an excited state (energy level corresponding to n = 3). What is the maximum wavelength of a photon that can cause ionization of a hydrogen atom in the ground state? 8 A. 9 9 B. 8 3 C. D A certain photocell emits electrons when illuminated with yellow light. PROBABLY NOT emit electrons when illuminated with A. blue light. B. green light. C. red light. D. ultra-violet light. E. X-rays. This photocell will Which of the following electron transitions between energy levels in an atom will emit electromagnetic radiation of the highest frequency? A. n= to n= B. n=3 to n= C. n=4 to n=3 D. n=4 to n= E. n=5 to n= The energy levels of a certain are as shown. Which of the following may undergo an inelastic collision with the atom? () an electron with kinetic energy 3E () a photon with energy E (3) a photon with energy 3E A. () only B. (3) only C. () and () only D. () and (3) only E. (), () and (3) Energy 0-4E -6E 7

8 ATOMIC WORLD P In a series of photoelectric emission experiments on a certain metal surface, relationships between the following physical quantities were investigated. y f = frequency of incident light I = intensity of incident light i = photoelectric current K = maximum kinetic energy of photoelectrons 0 x Two of these quantities, when plotted on a graph of y against x, would give a straight line through the origin. Which of the following correctly identifies x and y? (Assume the frequencies used are greater than the threshold frequency.) x y A. K i B. f K C. f i D. I K E. I i The above graph shows the variation in maximum kinetic energy K of photoelectrons with the frequency f of the incident radiation on a metallic surface. If radiation of twice the intensity is used, which of the following graphs (dotted line) shows the variation of K with f? A. K D. K 0 f 0 f B. K E. K C. 0 f K 0 f 0 f The diagram shows some energy levels (drawn to scale) of a certain atom. Transition X results in the emission of a photon of wavelength 600 nm. Which transition (P to T) would result in the emission of a photon of wavelength 300 nm? A. P B. Q C. R D. S E. T Energy X R Q P T S 8

9 ATOMIC WORLD P The transition of electrons between three energy levels in a particular atom gives rise to three spectral lines. The shortest and longest wavelengths of those spectral lines are and respectively. The wavelength of the other spectral line is A. B. C. D. E A d.c. source is applied to a photocell as shown. Monochromatic radiation is incident on cathode C so that photoelectrons are emitted from the cathode surface. The maximum kinetic energy of the photoelectrons reaching anode A can be increased by using Incident () a d.c. source of higher voltage. monochromatic () monochromatic radiation of longer wavelength. radiation (3) the same monochromatic radiation but of higher intensity. A. () only B. (3) only C. () and () only D. () and (3) only E. (), () and (3) A C + d.c. source A metal surface is illuminated with monochromatic light so that it emits photoelectrons. maximum kinetic energy of the emitted photoelectrons depends on () the distance of the metal surface from the light source. () The work function of the metal surface. (3) The wavelength of the incident monochromatic light. A. () only B. (3) only C. () and () only D. () and (3) only E. (), () and (3) The When an electron in an atom undergoes a transition from a higher energy level to a lower one, the time taken is about 0-9 s. Which of the following statements about the transition is/are correct? () Electromagnetic radiation is emitted during the transition. () The length of the wave train from such a transition is about 0.3 m. (3) The energy of the photon emitted depends on the energy difference between the two levels. A. () only B. (3) only C. () and () only D. () and (3) only E. (), () and (3) When light of frequency f is shone on to a metal surface, the maximum energy of the electrons emitted is E. If the same surface is illuminated with light of frequency f, the maximum energy of the electrons emitted is E. The Planck constant is given by fe fe A. f f 9

10 ATOMIC WORLD P.0 B. C. D. E. fe fe f f E E f f E E f f E E f f When a radioactive atom emits rays, which of the following statements about the atom is/are correct? () Its mass number remains unchanged. () The energy of the atomic nucleus decreases. (3) An electron falls from a higher energy level to a lower one. A. () only B. (3) only C. () and () only D. () and (3) only E. (), () and (3) The ionisation potential of a hydrogen atom is 3.6 V. What is the minimum excitation potential of a ground state hydrogen atom? A..9 V B. 3.4 V C. 6.8 V D. 0. V E..8 V The work function of a metal is the least energy required to A. release one mole of electrons from the surface of the metal. B. bring one mole of electrons from the interior of the metal to the surface. C. release one electron from the surface of the metal. D. bring one electron from the interior of the metal to the surface. E. bring one electron from the interior of the metal to the surface and release it Which of the following conclusion could NOT be deduced from Rutherford s scattering experiment? () Alpha particles are helium nuclei. () There are discrete energy levels in an atom. (3) The positive charge in an atom is confined to a very small region. A. (), () and (3) B. () and () only C. () and (3) only D. () only A beam of monochromatic light falls on a surface. If the frequency of the light is doubled but the intensity remains unchanged, which of the following statements is/are correct? () The photon energy is doubled. () The momentum of a photon is doubled. (3) The number of photons falling on the surface per second is halved. A. (), () and (3) B. () and () only C. () and (3) only D. () only 0

11 ATOMIC WORLD P In an experiment on the photoelectric effect, a beam of monochromatic light is directed onto a metal plate to liberate electrons. Which of the following statements is true? A. The velocity of the fastest electrons is directly proportional to the frequency of the incident light. B. The velocity of the fastest electrons is directly proportional to the intensity of the incident light. C. The kinetic energy of the fastest electrons is directly proportional to the frequency of the incident light. D. The velocity of the fastest electrons is independent of the intensity of the incident light. E. The velocity of the fastest electrons is independent of the type of metal Electron transitions occur in an atom resulting in the emission of the following light wavelength: from level C to level A : 600 nm from level B to level A : 500 nm Which of the following statements is/are correct? () Level A has a lower energy than both levels B and C. () Level C has a higher energy than level B. (3) The wavelength of light emitted for the transition between C and B is 00 nm. A. (), () and (3) B. () and () only C. () and (3) only D. () only The diagram shows the energy levels of a certain atom. When an electron changes energy from 4 E to E, a photon of wavelength is emitted. Which of the following wavelengths of photons could be produced by other transitions between the energy levels shown? A. / 3 and / 3 4 E B. / 3 and 3 3 E C. / 3 and 3 / D. / 3 and 3 E. 3 / and 3 E The photoelectric effect occurs when monochromatic light falls upon a metal surface in a photocell. What happens when the light intensity increases? A. More electrons are emitted with unchanged speed. B. More electrons are emitted with increased speed. C. The same number of electrons is emitted with increased speed. D. More photons are emitted from the surface. E. Photons of greater energy are emitted from the surface A gold-leaf electroscope is positively charged. Which of the following objects, when placed near the cap, will cause the leaf of the electroscope to fall? () a lighted match () a strong -source (3) an earthed metal plate A. (), () and (3) B. () and () only C. () and (3) only D. () only

12 ATOMIC WORLD P An atom emits light of wavelength nm and 03 nm when one of its electrons returns to its ground state from its first and second excited states, respectively. The wavelength of light emitted when the electron passes from the second excited state to the first excited state is A. 9 nm B. nm C. 3 nm D. 5 nm E. 66 nm When light of wavelength m is incident on the surface of a metal, the kinetic energy of the 9 electrons emitted has a maximum value of J. What is the longest wavelength of light which would cause electrons to be emitted from the metal? (Planck constant Js, speed of light in air ms - ) A m B m C m D m E m The diagram shows the first five energy level of an atom. Which of the spectra below best corresponds to the transitions indicated? E low frequency high 5 E 4 A. E 3 B. E C. D. E Light falls on the photo-sensitive metal surface of a photocell. A battery and a sensitive meter are connected to the photocell as shown. Which of the following statements is correct? A. The number of electrons emitted from the metal surface per second is proportional to the potential difference between the metal surface and the anode. B. No current is observed in the meter until after a considerable time, when the metal surface has heated up. C. The maximum energy of the electrons emitted is proportional to the intensity of light. D. The maximum kinetic energy of the electrons emitted is independent of the particular metal used. E. No current is observed in the meter unless the frequency of light is above a minimum value.

13 ATOMIC WORLD P current I II III IV + p.d. The above figure shows the currents observed in a photocell circuit as a function of the p.d. between the plates of the photocell when light beams I, II, III and IV were each directed in turn at the cathode. Which of the beams has the highest frequency? A. I B. II C. III D. IV E. They all have the same frequency In an experiment on particle scattering, particles are directed onto a gold foil, and detectors are placed at positions P, Q and R as shown. What is the distribution of particles as recorded at P, Q and R respectively? P Q R A. all none none B. none none all C. most some none D. most some few E. few some most P gold foil R In the diagram above, E and E represent (to scale) the energy levels of a hydrogen atom in its ground state and the ionised state, respectively. Which of the drawn lines represents the energy level of the atom in its first excited state? A. I B. II C. III D. IV E. V E V IV III II I When a beam of light of intensity I and frequency f is shone on the surface of a metal connected to earth, 00 electrons are ejected from the surface per second. If a light beam of intensity I and frequency f is used, the number of electrons ejected from the metal per second will be A. 50. B. 00. C. 00. D E E 3

14 ATOMIC WORLD P In an alpha-particle scattering experiment, alpha particles having the same kinetic energy collide headon with 47 Ag and 3Al nuclei respectively. The ratio of the distance of closest approach for 47 Ag to that for 3 Al is A. 0.5 B. 0.8 C..00 D. 3.6 E Which of the following best represents the order of magnitude of the radius of a nucleus? A. 0 - m B. 0-6 m C. 0-0 m D. 0-4 m E. 0-8 m In a gold-foil experiment, an -particle and a proton, having the same kinetic energy, collide head-on with gold-nuclei. The ratio of the distance of closest approach of the -particle to that of the proton is A. : 4 B. : C. : D. : E. 4 : A dish containing a strong -source is placed inside a gold leaf electroscope containing dry air. If the gold-leaf is originally positively charges, what will happen to it after a few minutes? A. It will increase in divergence. B. It will increase in divergence and then decrease. C. It will collapse. + + D. It will collapse and then rediverge. E. There will be no change in divergence C X battery red light A microammter Red light shines on the photoelectric cell C as shown. If the reading of the microammeter is zero, this may be explained by the fact that () the e.m.f. of the battery is too small. () the intensity of the light is too low. (3) electrode X is made of a material with too great a work function. A. (), () and (3) B. () and () only C. () and (3) only D. () only 4

15 ATOMIC WORLD P Which of the following phenomena can provide direct evidence for the existence of discrete electron energy levels in atom? () electron diffraction () photo-electric emission (3) the spectrum of light from a sodium lamp A. (), () and (3) B. () and () only C. () and (3) only D. () only For the photoelectric effect, which of the following is the correct relationship between the energy E of a photon, the work function w of the surface which it strikes, and the maximum kinetic energy K of the emitted photoelectron? A. E = w + K B. E = w K C. E = K w D. K = (w + E) E. W = ½ (K + E) The ionisation energy of an atom in its ground state is A. the energy required to separate all the electrons from the remainder of the atom. B. the maximum energy required to separate one electron from the remainder of the atom. C. the minimum energy required to separate one electron from the remainder of the atom. D. the minimum energy required to add one electron to the atom. E. the minimum energy required for an electron to change its state while at the same time remaining attached to the nucleus The allowed energy levels for an atom are E n = - W/n where W is a constant and n is any positive integer. The frequency of a photon corresponding to the energy transition from n = m + to n = m () is directly proportional to W () decreases as m increases (3) increases as the temperature increases A. (), () and (3) B. () and () only C. () and (3) only D. () only The figure shows a photoelectric cell. E is the emitter and C is the collector. The stopping potential for photoelectrons depends on () the nature of E E () the distance between E and C (3) the surface area of E A. (), () and (3) C B. () and () only C. () and (3) only D. () only 5

16 ATOMIC WORLD P When alpha particles are fired in a beam at a thin sheet of gold, they are scattered through a wide range of angles, from zero to 80 0 from the incident beam. This experiment shows that the gold atom has () electrons in different orbits. () A volume consisting mainly of empty space. (3) A small, dense, charged nucleus. A. (), () and (3) B. () and () only C. () and (3) only D. () only 98 3 Which of the following graphs best represents the variation of the maximum velocity v of photoelectrons emitted from a target with the frequency f of the incident light? A. B. C. D. E. v v v v v f f f f f In the Rutherford experiment on alpha particle scattering, an alpha particle strikes a thin metal foil X and is deflected through an angle. Which of the following statements is/are true? () cannot be greater than 90 o () The closer the alpha particle approaches to a nucleus, the greater is the value of. (3) For the same approach path, is larger for slower alpha particles than for faster ones. A. (), () and (3) B. () and () only C. () and (3) only D. () only 98 9 For the photoelectric effect, which of the following is the correct relationship between the energy E of a photon, the work function w of the surface which it strikes, and the maximum kinetic energy K of the emitted photoelectrons? A. E = w + K B. E = w K C. E = K w D. K = (w + E) E. W = ½ (K + E) X 6

17 ATOMIC WORLD P In an experiment with a photocell, readings were taken of the stopping potential V s for a series of frequencies v of the incident light, and the results plotted as a graph of V s against v are shown in the diagram below: Incident light V s V _ + 0 v variable d.c. If the emitting electrode source is now changed to one of a different metal, which also gives photoelectrons, the new graph () cuts the V s axis at the same point () cuts the v axis at the same point (3) has the same slope A. (), () and (3) B. () and () only C. () and (3) only D. () only 7