JURONG JUNIOR COLLEGE J2 H1 Physics (2011) 1 Light of wavelength 436 nm is used to illuminate the surface of a piece of clean sodium metal in vacuum.

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JURONG JUNIOR COLLEGE J2 H1 Physics (2011) Tutorial: Quantum Physics 1 Light of wavelength 436 nm is used to illuminate the surface of a piece of clean sodium metal in vacuum.

1 JURONG JUNIOR COLLEGE J2 H1 Physics (2011) Tutorial: Quantum Physics 1 Light of wavelength 436 nm is used to illuminate the surface of a piece of clean sodium metal in vacuum. Calculate the energy of a photon of light of this wavelength. [ J] Use your answer to to determine the maximum energy of the photoelectrons if the maximum wavelength of light which can produce photoelectrons from sodium is 603 nm. [ J] 2 Most photocells are not efficient. In a typical photocell, one photoelectron is produced for every 10 4 photons striking the surface. Suppose such a photocell is illuminated with light of wavelength 600 nm from a 4.0 mw laser. What is the photocurrent? [ A] 3 In a photoelectric experiment, light of frequency Hz falls on a metal surface in a vacuum tube. It is found that the maximum kinetic energy of the emitted electrons is 1.2 ev. Find the work function of the metal and outline briefly how the maximum kinetic energy of the electrons could be measured. [2.2 ev ] jj_sph2011 Page 1 of 7

2 4 Light of wavelength 350 nm is incident on a zinc cathode of work function 3.08 ev in a photoelectric cell. Calculate the stopping potential for the photoelectrons liberated. [ 0.47 V ] Would the stopping potential alter in value if the intensity of the incident light is doubled, the cathode is replaced by a different metal, (c) the anode is changed for one of different metal? 5 What is meant by the term threshold frequency as applied to the photoelectric effect? Explain why the maximum possible kinetic energy of a photoelectron is independent of the intensity of the incident light. 6 A monochromatic light source has a power output of 0.50 W and a wavelength of 480 nm. The light is incident on a tungsten surface which has a work function of 4.25 ev. Calculate the rate of emission of photons from the light source. [ s -1 ] Determine whether photoelectrons are emitted. jj_sph2011 Page 2 of 7

3 7 Explain the following terms: ground state, ionisation energy, (c) excitation energy 8 The diagram below represents some energy levels of the mercury atom. 0 Energy in ev In the unexcited state the level above ev are unoccupied. What is the significance of the zero energy level? Why are the energies negative? (c) What is the ionisation energy? [10.4 ev ] (d) What change is taking place if radiation of wavelength 141 nm is emitted? jj_sph2011 Page 3 of 7

4 9 The ionisation energy of the hydrogen atom is 13.6 ev. Calculate the speed of an electron which could just ionise the hydrogen atom, [ ms -1 ] the minimum wavelength which the hydrogen atom can emit. [ m ] 10 Name the phenomena which lead to the belief that light behaves like (i) waves, a stream of particles (photons). The ionisation energy of hydrogen is J. In the process of photoionisation, a photon interacts with the atom causing the ejection of an electron. Use the principle of conservation of energy to find the kinetic energy of the emitted electron if the incident radiation is of wavelength 63 nm. [ J ] 11. Light of photon energy 3.5 ev is incident on a plane photocathode of work function 2.5 V. Parallel and close to the cathode is a plane collecting electrode. The cathode and collector are mounted in a evacuated tube. Find the maximum kinetic energy E max of photoelectrons emitted from the cathode. (Express your answer in ev). [1.0 ev] Find the minimum value of the potential difference which should be applied between collector and cathode in order to prevent electrons of energy E max from reaching the collector for electrons emitted (i) normal to the cathode, at an angle 60 0 to the cathode. [(i) 1.0 V, 0.75 V] jj_sph2011 Page 4 of 7

5 12. Electromagnetic radiation is incident normally on the surface of a metal. Electrons are emitted from the surface and these are attracted to a positively charged electrode as shown below. Name the effect which gives rise to the emissión of the electrons. State a word equation based on the principle of conservation of energy which describes this effect. (c) The current recorded on the microammeter is 2.1 μa. Calculate the number of electrons emitted per second from the surface. [1.31 x s -1 ] (d) The intensity of the incident radiation 8.2 x 10 3 W m -2. The area of the surface is 2.0 cm 2 and the energy of a photon incident on the surface is 8.29 x J. Calculate (i) the power of the radiation incident on the surface, [1.64 W] the number of photons incident per second on the surface. [1.98 x s -1 ] (iii) Hence determine the ratio [6.33 x 10-6 ] number of electrons emitted per second number of photons incident per second (iv) Comment on your answer to (e)(iii) jj_sph2011 Page 5 of 7

6 13. In a photoelecric emission experiment, ultra-violet radiation of wavelength 254 nm and of power per unit area 210 W m -2, was incident on a silver surface in an evacuated tube, so that an area of 12 mm 2 was illuminated. A photocurrent of 4.8 x A was collected at an adjacent electrode. What was the rate of incidence of photons on the silver surface? [3.22 x s -1 ] What was the rate of emission of electrons? [3.0 x 10 9 s -1 ] (c) The photoelectric quantum yield is defined as ratio (i) number of photoelectrons emitted per second number of photons incident per second Find the quantum yield of this silver surface at the wavelength of 254 nm. [9.32 x 10-7 ] Give two reasons why this value might be expected to be much less than one. (d) When the experiment was repeated with ultra violet radiation of wavelength 313 nm, no photoelectrons were emitted. Explain this observation. 14. A parallel beam of violet light of wavelength 4.5 x 10-7 m and intensity 700 W m -2 is incident normally on a surface. The energy of a photon of violet light is 4.42 x J Calculate the number of photons incident per second on 1.0 x 10-4 m 2 of the surface, [1.58 x s -1 ] jj_sph2011 Page 6 of 7

7 (i) State the de Broglie relation for the momentum p of a particle in terms of its associated wavelength λ. Use equation in (i) to calculate the momentum of a photon of the violet light. [1.47 x N s] (c) (i) Use your answers to and to calculate the change in momentum of photons incident on 1.0 x 10-4 m 2 of the surface in one second. Assume that the photons are absorbed by the surface. [-2.33 x N s] Suggest why the quantity you have calculated in (i) is referred as a radiation pressure. 15 The minimum wavelength of an X-ray spectrum is m. Calculate the potential difference between the target and cathode of the X-ray tube. [20.7 kv] jj_sph2011 Page 7 of 7

1 Electrons are emitted from a metal surface when it is illuminated with suitable electromagnetic radiation. ...[1]

1 Electrons are emitted from a metal surface when it is illuminated with suitable electromagnetic radiation. 1 (a) (b) Name the effect described above....[1] The variation with frequency f of the maximum