S. L. Arora Solutions for Chapter: Dual Nature of Radiation and Matter, Exercise 1: Problems For Practice

(I) The work function for the surface of aluminium is $4.2 \mathrm{e}\mathrm{V}$. How much potential difference will be required to stop the emission of maximum energy electrons emitted by the light of $2000 \mathrm{\AA }$ wavelength?
(II) What will be the wavelength of that incident light for which stopping potential will be zero?
Given $\mathrm{h}=6.6\times {10}^{-34} \mathrm{J}\mathrm{s}, \mathrm{c}=3\times {10}^8 \mathrm{m}{\mathrm{s}}^{-1}$

The wavelength of a photon is $1.4 \mathrm{\AA }$. It collides with an electron at rest. Its wavelength after the collision is $2.0 \mathrm{\AA }$. Calculate the energy of the scattered electron.

The work function, for a given photosensitive surface equals $2.5 \mathrm{e}\mathrm{V}$. When light of frequency, $\nu$, falls on this surface, the emitted photoelectrons are comp­letley stopped by applying a retarding potential of $4.1 \mathrm{V}$. What is the value of $\nu$?

When light of frequency $2.4\times {10}^{15} \mathrm{H}\mathrm{z}$, falls on a photosensitive surface, the retarding potential needed to completely stop the emitted photo­electrons is found to be $6.8 \mathrm{V}$. What is the work function in $\mathrm{e}\mathrm{V}$ of the given photosensitive surface?

Ultraviolet radiations of wavelength $800 \mathrm{\AA }$ and $700 \mathrm{\AA }$, when allowed to fall on a photosensitive surface are found to liberate electrons with maximum kinetic energies of $2 \mathrm{e}\mathrm{V}$ and $4.1 \mathrm{e}\mathrm{V}$ respectively. Calculate the value of Planck's constant.

Find the frequency of light which ejects electrons from a metal surface, fully stopped by a retarding potential of $3.3 \mathrm{V}$. If photoelectric emission begins in this metal at a frequency of $8\times {10}^{14} \mathrm{H}\mathrm{z}$, calculate the work function $\left(\mathrm{e}\mathrm{V}\right)$ for this metal. Take $h = 6.63\times {10}^{-34} \mathrm{Js}$.

When $\mathrm{U}\mathrm{V}$ light of wavelength $300 \mathrm{n}\mathrm{m}$ is incident on a metal plate, a negative potential of $0.59 \mathrm{V}$ is required to stop the emission of photoelectrons. Calculate the energy of the incident photon and the work function for the metal in $\mathrm{e}\mathrm{V}$.

A metal has a work function of $2.0 \mathrm{e}\mathrm{V}$ and is illuminated by monochromatic light of wavelength $500 \mathrm{n}\mathrm{m}$. Calculate ($h = 6.6\times {10}^{-34} \mathrm{Js}, c = 3\times {10}^8 \mathrm{m}/\mathrm{s}$)

1. The threshold wavelength
2. The maximum energy of photoelectrons
3. The stopping potential