RI 19 Quantum Physics tutorial solution

RAFFLES INSTITUTION YEAR 5-6 PHYSICS DEPARTMENT 1 Tutorial 19 Quantum Physics Suggested Solutions D1 (a) Since p I λ= = × dN hcPA dt , the rate of incident photons 69 p 15 1 34 8 (210)(12 10 )(254 10 ) 3.22 10 s(6.63 10 )(3.00 10 ) IAλ −− − − ××= = = ××× dN dt hc (b) Since e 0i = ×dN edt , the rate of emission of photoelectrons 10 91e0 19 4.8 10 3.00 10 s1.60 10 i − − − ×= = = ×× dN dt e (c) (i) Quantum yield 9 7e 15 p 3.00 10 9.3 103.22 10 −×= = = ×× dN dtQ dN dt (ii) Any two of the following: • P hotons are mostly reflected off the metal surface and so are not involved in photoemission. • Besides energy, a photon imparts momentum to the electron. These electrons are generally “back-scattered” (away from surface). To escape from the metal, these electrons must acquire sufficient energy by colliding with other electrons. This process has a very low probability. • After acquiring energy from a photon, an electron near the surface of the metal will lose energy through multiple collisions with other electrons or ions as it migrates towards the surface of the metal. (d) The wavelength of 313 nm is greater than the threshold wavelength. Hence, photons of such radiation have insufficient energy to overcome the work function of the metal. D2 (a) Energy of photon 34 8 19 7 (6.63 10 )(3.00 10 ) 7.8 10 J2.55 10λ − − − ××= = = ×× hcE (b) (i) The photoelectric current depends on the rate of emission of photoelectrons, which in turn depends on the intensity of the incident radiation. Increasing V accelerates the electrons but does not affect the rate of emission of photoelectrons. Hence, current reaches a maximum value no matter how large V is made. (ii) Electrons are emitted with a range of kinetic energy (up to K.E.max). Some energetic electrons still have sufficient K.E. to overcome the retarding p.d. to reach the gauze.

RAFFLES INSTITUTION YEAR 5-6 PHYSICS DEPARTMENT 2 (c) (i) The rate of incidence photon increases with increasing intensity of light. Increasing rate of incident photon increases the rate of emission of photoelectrons (assuming constant quantum yield) and hence maximum photoelectric current increases. (ii) The stopping potential sV is the minimum value of the potential difference between the gauze (collector) and plate (emitter) needed to prevent the most energetic photoelectrons from reaching the gauze. s maxK.E.eV = K.E. of most energetic photoelectrons is dependent only on the frequency of the light and the work function of the surface but is independent of the intensity of light. So the stopping potential remains unchanged. (d) Since nickel has a greater work function, K.E. of most energetic photoelectrons is lower. Hence a lower stopping potential is needed to prevent the most energetic photoelectrons from reaching the gauze. Since the intensity and frequency of the light did not change, the saturated photocurrent remains con