For a certain metal the threshold wavelength is

PHYSICS · Multi-part · CBSE · Physics · Dual Nature of Radiation and Matter · Dual Nature of Radiation and Matter

Problem

\lambda_0 = 540\,\text{nm}

. Let

\lambda

(

<\lambda_0

) be the wavelength of normally incident radiation. Use

h = 6.63\times10^{-34}\,\text{J\,s}

c = 3.0\times10^{8}\,\text{m\,s}^{-1}

and

e = 1.6\times10^{-19}\,\text{C}

. (i) Derive an expression for the maximum kinetic energy

K_{\text{max}}

of the photo-electrons in terms of

\lambda

and

\lambda_0

. (ii) Using the expression obtained in (i), find the value of

\lambda

(in nanometre) for which

K_{\text{max}}

equals one-half of the incident photon energy. (iii) Calculate

K_{\text{max}}

in electron-volt when

\lambda = 350\,\text{nm}

and also find the energy liberated per mole of such electrons.