Question

A metal irradiated with the light of frequency $3.2X{{10}^{16}}Hz$. The ejected photoelectron has kinetic energy $\dfrac{3}{4}$ th of the energy of the absorbed photon. The threshold frequency of the metal would be:
(A) $1.6X{{10}^{15}}Hz$
(B) $8X{{10}^{15}}Hz$
(C) $2.4X{{10}^{25}}Hz$
(D) $2.4X{{10}^{18}}Hz$

Answer 1

Hint: In the photoelectric effect, when light ejects an electron from a metal surface, then electrons are shared between atoms in a metal, the ionization frequency of metal is different and lower than that of an isolated single atom of the metal. This ionization frequency will be the characteristic frequency of metal.

Complete step by step solution:
The photoelectric effect is defined as “the number of emitted electrons based on the and the kinetic energy should be based on the intensity of lightwave”
let us consider, three conditions based on the wave properties of light and dependence of the ejection on frequency and injection of light,
First, no matter how bright then no electrons are ejected, and no matter how intense will be the light.
Second, electrons are always ejected with no matter how low intense the light.
Finally, for a given frequency, the faster the ejected electrons will be moving after leaving the metal when the light would be more intense.
Conservation energy for the photoelectric process,
The absorbed energy of photon = threshold energy + kinetic energy of the photoelectron
Given that, the ejected photoelectron has the kinetic energy $\dfrac{3}{4}th$ of the absorbed photon, if E is absorbed energy, then the kinetic energy of photoelectron = \[\dfrac{3}{4}E\]
So, the equation of photoelectric effect will be,
\[E={{E}_{0}}+\dfrac{3}{4}E\]
\[{{E}_{0}}=\dfrac{1}{4}E\]
\[h{{v}_{0}}=\dfrac{1}{4}hv\]
Given the frequency of light, \[v=3.2X{{10}^{16}}Hz\]
Then the threshold frequency, \[{{v}_{0}}=\dfrac{1}{4}v=\dfrac{1}{4}X3X{{10}^{16}}=8X{{10}^{15}}Hz\]

The correct answer is option B.

Note: In 1905, Albert Einstein explained the photoelectric effect observed that the energy was carried out by light in photon packets as hv and each photon reason for one electron ejection. A photon moving particle and collide with a stationary particle which gained energy from the photon.