Problem 7: A metal whose work function is 3.0 eV is illuminated by light of wavelength 3 × 10-7 m. Calculate (1) The threshold frequency (b) The maximum energy of photoelectron (c) The stopping potential.

Solution

Work function, ϕ of a metal is defined as the minimum energy required by an electron to escape from the metal surface. Mathematically, ϕ = f0h, where ‘h’ is the Plank’s constant and its value is 6.63 × 10-34 J s, f0 is the threshold frequency at which the electron just ejects from the metal.

Given: Work function, ϕ = 3.0 eV = 3.0 × 1.6 × 10-19 J
(∵ 1 eV = 1.6 × 10-19 J)
Wavelength of the incident light, λ = 3 × 10-7 m
Plank constant, h = 6.63 × 10-34J s

(b) Max K.E of the emitted electron
(c) V0

(a) Apply the formula given in the above theory,

(b)K.E of the emitted electron is the difference of the energy of the incident photon and the work function of the metal. The energy of the photon is hf, where f is its frequency. Therefore,

Now

Therefore

Put in equation (Z),

(c)Stopping potential is given by,

where e is charge on the electron.