Dual Nature of Radiation and Matter

When a light beam enters into water from air, then which of the following does not change?

• Velocity

• Frequency

• Wavelength

• Amplitude

Speed of light in vacuum is

• $\frac{1}{\sqrt{{\mathrm{\mu }}_0{\mathrm{\epsilon }}_0}}$

• $\sqrt{\frac{{\mathrm{\mu }}_0}{{\mathrm{\epsilon }}_0}}$

• $\sqrt{{\mathrm{\mu }}_0{\mathrm{\epsilon }}_0}$

• $\sqrt{\frac{{\mathrm{\epsilon }}_0}{{\mathrm{\mu }}_0}}$

Light of wavelength 488 nm is produced by organ laser, which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectron is 0.38 V. Find the work function of the material from which the emitter is made.

• 1.25 eV

• 2.17 eV

• 4.07 eV

• 3.57 eV

The graph given below showing the variation of stopping potential with the frequency of incident radiation for two different photosensitive materials having work functions W₁ and W₂ ( W₁ < W₂ ).

The slope of graph showing the variation of stopping potential with the frequency of incident radiation gives the value of

• h/e where, h is Planck's constant and e electronic charge

• h i.e, Planck's constant

• e i.e, electronic charge

• None of the above

The photoelectric threshold wavelength of silver is 3520 x 10^-10 m. The velocity of the electron ejected from a silver surface by ultraviolet light ofwavelength 2536 x 10^-10 m is (Given, h = 4.14 × 10^-15 eV , c = 3 × 10⁸ m/s)

• 0.3 × 10⁶ m/s

• 0.6 ×10⁵ m/s

• 0.6 × 10⁶ m/s

• 61 × 10³ m/s

Light of wavelength λ , strikes a photoelectric surface and electrons are ejected with an energy E. If E is to be increased to exactly twice its original value, the wavelength changes to λ', where

• $\mathrm{\lambda }\text{'} \mathrm{is} \mathrm{less} \mathrm{than} \frac{\mathrm{\lambda }}{2}$

• $\mathrm{\lambda }\text{'} \mathrm{is} \mathrm{greater} \mathrm{than} \frac{\mathrm{\lambda }}{2}$

• $\mathrm{\lambda }\text{'} \mathrm{is} \mathrm{greater} \mathrm{than} \frac{\mathrm{\lambda }}{2} \mathrm{but} \mathrm{less} \mathrm{than} \mathrm{\lambda }$

• $\mathrm{\lambda }\text{'} \mathrm{is} \mathrm{exactly} \mathrm{equal} \mathrm{to} \frac{\mathrm{\lambda }}{2}$

When a certain metal surface is illuminated with light of frequency v, the stopping potential for photoelectric current is V₀. When the same surface is illuminated by light of frequency $\frac{\mathrm{v}}{2}$,the stopping potential is $\frac{{\mathrm{V}}_0}{4}$. The threshold frequency for photoelectric, emission is

• $\frac{\mathrm{v}}{6}$

• $\frac{\mathrm{v}}{3}$

• $\frac{2\mathrm{v}}{3}$

• $\frac{4\mathrm{v}}{3}$

For photoelectric emission from certain metal the cut-off frequency is v. If radiation of frequency 2v impinges on the metal plate, the maximumpossible velocity of the emitted electron will be (m is the electron mass)

• $\sqrt{\frac{\mathrm{hv}}{\left(2\mathrm{m}\right)}}$

• $\sqrt{\frac{\mathrm{hv}}{\mathrm{m}}}$

• $\sqrt{\frac{2\mathrm{hv}}{\mathrm{m}}}$

• $2\sqrt{\frac{\mathrm{hv}}{\mathrm{m}}}$

The wavelength λ_e of an electron and λ_p of a photon of same energy E are related by

• λ_p ∝ λ_e²

• λ_p ∝ λ_e

• ${\mathrm{\lambda }}_{\mathrm{p}} \propto \sqrt{{\mathrm{\lambda }}_{\mathrm{e}}}$

• ${\mathrm{\lambda }}_{\mathrm{p}} \propto \frac{1}{\sqrt{{\mathrm{\lambda }}_{\mathrm{e}}}}$

Find the correct statement(s) about photoelectric effect.

• There is no significant time delay between the absorption of a suitable radiation and the emission of electrons.

• Einstein analysis gives a threshold frequency above which no electron can be emitted

• The maximum kinetic energy of the emitted photoelectrons is proportional to the frequency of incident radiation.

• The maximum kinetic energy of electrons does not depend on the intensity of radiation.