PHYSICS 2020 CAPA 15 - PHYS2020 Fall 2006 CAPA Set 15 1[1pt...

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PHYS2020, Fall 2006 CAPA Set 15 1. [1pt] Europium has a work function of 2.50 eV . What is the maximum kinetic energy of electrons if the metal is illuminated by light of wavelength 270 nm ? The energy of the photon first goes into liberating the electron from the atom. The remaining energy is given as kinetic energy to the liberated electron. Thus, KE = hf - W where W is the work function. Since c = λf , we can write this as E = hc/λ - W . For the numbers given here, we get KE = hc/λ - W = 4 . 14 × 10 - 15 eV · s · 3 × 10 8 m/s/ 270 × 10 - 9 m - 2 . 50 eV = 4 . 60 eV - 2 . 50 eV = 2 . 1 eV . 2. [1pt] What is their speed? Since the kinetic energy is (2 . 1 eV ) is much less than the rest mass energy (511000 eV ), this is a non-relativistic problem. Therefore KE = 1 / 2 mv 2 and v = radicalBig 2 · KE m . This can be solved by v = radicalBig 2 · 2 . 1 eV 511000 eV/c 2 = 8 . 22 × 10 - 6 c 2 = 0 . 00287 c = 860000 m/s . Or one can convert the kinetic energy to Joules and use the mass of the electron in kilograms: v = radicalbigg 2 · 2 . 1 eV · 1 . 6 × 10 - 19 J/eV 9 . 11 × 10 - 31 kg = radicalBig 7 . 38 × 10 11 m 2 /s 2 = 860000 m/s . 3. [1pt] By what potential difference must a proton ( m 0 = 1 . 67 × 10 - 27 kg ) be accelerated (from rest) to have a wavelength λ = 4 . 46 × 10 - 12 m ? A wavelength of 4 . 46 × 10 - 12 m corresponds to a momentum of p = h λ = 6 . 63 × 10 - 34 Js 4 . 46 × 10 - 12 m = 1 . 487 × 10 - 22 kg · m/s . We need to know if this is relativistic or not. We initially assume it is non-relativistic
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