Embibe Experts Solutions for Chapter: Dual Nature of Matter and Radiation, Exercise 4: Exercise - 4

Find the velocity of photoelectrons liberated by electromagnetic radiation of wavelength $\mathrm{\lambda } = 18.0 \mathrm{nm}$ from stationary ${\mathrm{He}}^{+}$ ions in the ground state. ($h=4.14\times {10}^{-15} \mathrm{eV} \mathrm{s} \text{\&} \mathrm{c}=3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$)

(I) Find the maximum wavelength of light which can ionize a $\mathrm{H}$-atom in the ground state.
(II) Light of wavelength $\mathrm{\lambda }$ is incident on a $\mathrm{H}$-atom which is in its first excited state. Find the kinetic energy of the electron coming out.

In a photo electric effect set - up, a point source of light of power $3.2 \times {10}^{-3} \mathrm{W}$ emits mono energetic photons of energy $5.0 \mathrm{eV}$. The source is located at a distance of $0.8 \mathrm{m}$ from the centre of a stationary metallic sphere of work function $3.0 \mathrm{eV}$ & of radius $8.0 \mathrm{x} {10}^{-3} \mathrm{m}$. The efficiency of photo electrons emission is one for every ${10}^6$ incident photons. Assume that the sphere is isolated and initially neutral, and that photo electrons are instantly swept away after emission.
(a) Calculate the number of photo electrons emitted per second.
(b) Find the ratio of the wavelength of incident light to the De - Broglie wave length of the fastest photo electrons emitted.
(c) It is observed that the photo electron emission stops at a certain time $\mathrm{t}$ after the light source is switched on. Why?
(d) Evaluate the time $\mathrm{t}$.