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Question: Minimum acceleration potential to be applied on an electron so that kinetic energy of electron equal...

Minimum acceleration potential to be applied on an electron so that kinetic energy of electron equals energy of a quantum of wavelength 310 nm would be:

& \text{A}\text{. }1.2V \\\ & \text{B}\text{. }4V \\\ & \text{C}\text{. 6}\text{.4 x }{{10}^{-19}}V \\\ & \text{D}\text{. 2 x 1}{{\text{0}}^{-15}}V \\\ \end{aligned}$$
Explanation

Solution

Before solving this problem try to remember the relation between the energy and wavelength. Using the energy relation of a quantum of wavelength we can easily find out the Kinetic Energy of the electron.

Formula used:
E=hceλE=\dfrac{hc}{e\lambda }
where, hh = Planck’s constant=6.63 x 10−346.63\text{ x }{{10}^{-34}},
cc = speed of light and λ\lambda = photon wavelength and
e=1.6 x 10−19e=1.6\text{ x }{{10}^{-19}}

Complete step by step answer:
Using the formula for the energy of a quantum of wavelength, which is given by,
E=hcλE=\dfrac{hc}{\lambda }
From the above formula, we can establish a relation between the energy and the wavelength. The energy increases with a decrease in wavelength.
Now, putting the corresponding values in the formula we get,
E=6.63 x 10−34x 3 x 1081.6 x 10−19x 310 x 10−9=4VE=\dfrac{6.63\text{ x }{{10}^{-34}}\text{x 3 x 1}{{\text{0}}^{8}}}{1.6\text{ x }{{10}^{-19}}\text{x 310 x }{{10}^{-9}}}=4\text{V}

So, the correct answer is “Option B”.

Additional Information:
When a photon from electromagnetic radiation such as visible light strikes a metal surface, it can eject electrons from the metal surface depending on the energy of the photon that strikes the metal surface. This phenomenon is called the photoelectric effect and it was given by Albert Einstein. Electrons emitted in this manner are called photoelectrons. The photoelectric effect is used in the production of electricity in solar cells. The photons from the sun strike the metal surface of the solar cell. This ejects the electron from the metal surface. Which is used in the production of electricity. That can be further used for domestic or industrial purposes. The accelerating potential imparts additional speed and energy to the electrons

Note:
Electrons only occupy certain discrete energy levels. When an atom goes in an excited state, one or more electrons are pushed into a higher energy level which requires energy. When an electron drops into a lower energy level it releases a photon which corresponds to the difference between the two energy levels.