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Cambridge Physics for the IB Diploma Mark scheme for Support Worksheet – Topic 6, Worksheet 3 1 a b 2 a b 3 a b 4 5 The energy carried by a wave is distributed along wavefronts; if we consider a very low intensity beam of light incident on the metal the energy is being delivered to the metal at a very low rate and so the time required for the electron to accumulate the energy needed to escape would be very large. [2] According to the photon theory of light, the energy of light is carried by individual photons; and the entire energy carried by the photon is transferred to the electron at once when the photon is absorbed. [2] (Whereas the energy carried by mechanical waves depends on both frequency and amplitude) the energy carried by electromagnetic waves depends only on the amplitude and not the frequency; hence the energy of the emitted electron cannot have any dependence on frequency. [2] According to the photon theory the energy of a photon is given by hf ; hence the energy of the emitted electron is hf and so depends on the light frequency. [2] The intensity has no effect on the energy of the electrons; increased intensity implies more photons not more energetic photons. [2] More electrons would be ejected; increased intensity implies more photons and hence greater probability for more electrons to be ejected from the metal. [2] The work function is the minimum energy required to eject an electron from a metal surface. EK hf 1.00 10 hc 19 [1] 6.63 10 34 3 108 2.2 1.6 10 19 4.2 10 7 J 1 2 2.00 10 19 mv 1.00 10 19 J v 4.7 10 5 m s 1 31 2 9.1 10 6 a b 7 a b [3] Stopping voltage is that voltage between the anode and the cathode in a photoelectric effect experiment for which the photocurrent becomes zero. From eVS hf VS [1] hf h the slope is , i.e. Planck’s constant divided e e e by the elementary charge. [1] Particles show wavelike behaviour; with a wavelength that equals Plank’s constant divided by the particle’s momentum. [2] See Physics for the IB Diploma, pages 394–395. [3] Copyright Cambridge University Press 2012. All rights reserved. Page 1 of 2 Cambridge Physics for the IB Diploma 8 9 10 p2 150 1.6 10 19 p 6.6110 24 Ns; and so 2m h 6.63 10 34 1.0 10 10 m 24 p 6.61 10 2L with n 1,2,3 n a The allowed wavelengths are b E a The product of the uncertainties in momentum and position is never less than Planck’s constant divided by 4π . b p2 h2 ; and so E 2m 2m 2 h2 h 2 n2 2 2L 2m( )2 8mL n Since x : 1010 m (this is an order of magnitude calculation so you may 1 choose x : 10 10 m if you wish); 2 h 6.63 1034 p 5.3 1025 1024 Ns 10 4πx 4π 10 Copyright Cambridge University Press 2012. All rights reserved. [2] [1] [2] [1] [2] Page 2 of 2