Question

The photoelectric there should for a certain metal surface is $330{A^\circ }$. What is the maximum kinetic energy of photoelectric released, if any, by a radiation of wavelength $1100{A^\circ }$?
(A) $1eV$
(B) $2eV$
(C) $7.5eV$
(D) No electron is emitted.

Answer 1

Hint:Photoelectric effect is the phenomenon in which electrically charged particles are released from or within a material when it absorbs electromagnetic radiation. The effect is often defined as the ejection of electrons from a metal plate when light falls on it.

Complete step by step answer:
We have been given that the wavelength of incident radiation is $\lambda = 1100{A^0}$
$\lambda = 1100 \times {10^{ - 10}}{\text{m}}$
$\therefore $We can derive the frequency of the incident radiation, which is,
$\vartheta = \dfrac{c}{\lambda } = \dfrac{{3 \times {{10}^8}}}{{1100 \times {{10}^{ - 10}}}}$
$ \simeq \;0.3 \times {10^{16}}{H_z}$
The threshold wavelength is,
${\lambda _0} = 330{{\text{A}}^0}$
$ = 330 \times {10^{ - 10}}{\text{m}}$
$\therefore $ Threshold frequency is,
${\vartheta _0} = \dfrac{c}{{{\lambda _0}}} = \dfrac{{3 \times {{10}^8}}}{{330 \times {{10}^{ - 10}}}}$
$ \simeq {10^{16}}{H_z}$
Since $\vartheta < {\vartheta _{0,}}$ no photoelectron is emitted
The answer is (D) No electron is emitted.

Note:The photoelectric threshold is equal to the minimum photon energy needed to raise an electron in the solid to the vacuum level, where escape into the vacuum is energetically possible. If the energy is less than the photoelectric threshold, then no electron will be emitted which is the case of this problem.