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

Q-  2.51: 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 500 nm, calculate the kinetic energy and the velocity of the ejected photoelectron.
Answer
It is given that the work function (W₀) for caesium atom is 1.9 eV.
(a) From the expression,
, we get:
Where,
λ₀ = threshold wavelength
h = Planck’s constant
c = velocity of radiation
Substituting the values in the given expression of (λ₀):

6.53 × 10^-7 m
Hence, the threshold wavelength is 653 nm.
(b) From the expression, , we get:

Where,
ν₀ = threshold frequency
h = Planck’s constant
Substituting the values in the given expression of ν_0: 
 



(1 eV = 1.602 × 10^-19 J)
ν₀ = 4.593 × 10¹⁴ s^-1
Hence, the threshold frequency of radiation (ν₀) is 4.593 × 10¹⁴ s^-1.
(c) According to the question:
Wavelength used in irradiation (λ) = 500 nm Kinetic energy = h (ν - ν₀)