Monochromatic radiation of wavelength 640.2 nm (1nm = 10⁻⁹ m) from a neon lamp irradiates photosensitive material made of caesium on tungsten. The stopping voltage is measured to be 0.54 V. The source is replaced by an iron source and its 427.2 nm line irradiates the same photo-cell. Predict the new stopping voltage.

Wavelength of the monochromatic radiation,

λ = 640.2 nm = 640.2 x 10⁻⁹ m

Stopping potential of the neon lamp, Vo = 0.54 V

Charge on an electron, e = 1.6 x 10⁻¹⁹ C

Planck’s constant, h = 6.6 x 10^-34 Js

Let φ_O be the work function and v be the frequency of emitted light.

We have the photo-energy relation from the photoelectric effect as: eV₀ = hv — φ_O,

φ_O = hc/λ  – eV₀

₌ ( 6.6 x 10^-34) x ( 3 x 10⁸ ) /( 640.2 x 10⁻⁹) – (1.6 x 10⁻¹⁹) x 0.54

= 3.093 x 10⁻¹⁹ -0.864 x 10⁻¹⁹ = 2.229 x10⁻¹⁹ J

=   (2.229 x10⁻¹⁹) /(1.6 x 10⁻¹⁹) = 1.39 eV

Wavelength of the radiation emitted from an iron source,

λ’ = 427.2 nm = 427.2 x 10^-9 m

Let V₀ be the new stopping potential. Hence, photo-energy is given as:

eV0′ = hc/λ’- φ_O

=(6.6 x 10^-34) x (3 x 10⁸ ) /(427.2 x 10^-9) – (2.229 x10⁻¹⁹)n

= 4.63 x 10⁻¹⁹ – 2.229 x10⁻¹⁹

=2.401 x 10⁻¹⁹J

= (2.401 x 10⁻¹⁹)/(1.6 x x10⁻¹⁹) = 1.5eV

Hence, the new stopping potential is 1.50 eV.