The work function for caesium atom is 1.9 eV. Calculate (a) The threshold wavelength and (b) The threshold frequency of the radiation. If the caesium element is irradiated with a wavelength 500 nm, calculate the kinetic energy and the velocity of the ejected photoelectron.
The work function for caesium atom is 1.9 eV. Calculate (a) The threshold wavelength and (b) The threshold frequency of the radiation. If the caesium element is irradiated with a wavelength 500 nm, calculate the kinetic energy and the velocity of the ejected photoelectron.
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1 Answer
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W0 = 1.9 eV = 1.9 x 1.602 x 10-19 J
Threshold frequency, v0 = W0 / h = (1.9 x 1.602 x 10-19 J) / (6.626 x 10-34Js)
= 0.459 x 1015 s-1 = 4.59 x 1014 s-1
Threshold wavelength? 0 = c / v0 = (3 x 108 ms-1) / (4.59 x 1014 s-1)
= 0.6536 x 10-6 m = 653.6 nm? 654 nm
Kinetic energy, E = E0 + ½ mv2
(1/2 mv2) = E – E0 = hc [ (1/? ) – (1/? 0)]
= (6.626 x 10-34Js) x (3 x 108 ms-1) / (10-9) x [ (1/500) – (1/654)]
= 6.626 x 3 x 154 x 10-34+8+9) / (500 x 654)
= 9.36 x 10-20 J
Velocity, v = [ (2 x 9.36 x 10-20) / m]1/2
= [ (2 x 9.36 x 10-20) kg m2 s-2 / 9.1 x 10-31 kg]1/2
= (2.057 x 1011 m2s-2)1/2= (20.57 x 1010 m2s-2)1/2
= 4.5356 x 105 ms-1
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