The work function for caesium atom is 1.9 eV. Calculate (a) the threshold wavelength and (b) the threshold frequency of the radiation.



Q.51:- 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 500nm, calculate the kinetic energy and the velocity of the ejected photoelectron.

 

 

Answer:-



(a) Work function (W0) = hν0
∴ ν= W0/h = 1.9×1.602×10-19 J/6.626×10-34 Js = 4.59×1014 s-1            (1eV = 1.602×10-19 J)
(b) λ0 = c/ν= 3.0×10ms-1/4.59×1014 s-1 = 6.54×10-7 m = 654×10-9 m = 654 nm
(c) K.E. of ejected electron = h(ν  ν0) = hc (1/λ – 1/λ)
= (6.626×10-34 Js×3.0×10ms-1)×(1/500×10-9 m – 1/654×10-9 m)
= (6.626×3.0×10-26/10-9)×(154/500×654) J = 9.36×10-20 J
K.E. = 1/2 mv= 9.36×10-20 J
∴ 1/2×(9.11×10-31 kg) v= 9.36×10-20 kgm2s-2
⇒ v= 2.055×1011 m2s-2 = 20.55×1010 m2s-2

⇒ v = 4.53×10ms-1