Question

The frequency of a photon, having an energy 100eV is \[\left( {6.66 \times {{10}^{ - 34}}Js} \right)\]
A. \[2.42 \times {10^{26}}Hz\]
B. \[2.42 \times {10^{16}}Hz\]
C. \[2.42 \times {10^{12}}Hz\]
D. \[2.42 \times {10^9}Hz\]

Answer 1

Hint:Photon is the smallest packet (quanta) of energy. By the particle nature of light, we can say that the light behaves as particles and this is confirmed by the photoelectric effect, but according to the wave nature of light, light behaves as waves and is confirmed by phenomena like reflection, refraction etc. Now using this Planck quantum formula, we can solve this problem.

Formula Used:
To find the energy of the photon we have,
\[E = h\nu \]
Where, h is Planck’s constant and \[\nu \] is frequency of photon.

Complete step by step solution:
The energy of the photon is defined as the energy carried out by a single photon. The amount of energy of this photon is directly proportional to the photon's electromagnetic frequency and is inversely proportional to the wavelength. The higher the photon's frequency, the higher will be its energy.

The energy of the photon is,
\[E = h\nu \]…… (1)
When the energy is given in electron-Volts, we need to first convert it into Joules.
\[E = 100\,eV\]
\[\Rightarrow E = 100 \times 1.6 \times {10^{ - 19}}J\]
\[\Rightarrow E = 160 \times {10^{ - 19}}J\]

In order to find the frequency, they have given the value of energy and Planck’s constant. substitute the values in the above equation, and we get,
\[\nu = \dfrac{E}{h}\]
\[\Rightarrow \nu = \dfrac{{160 \times {{10}^{ - 19}}}}{{6.66 \times {{10}^{ - 34}}}}\]
\[\therefore \nu = 2.42 \times {10^{16}}Hz\]
Therefore, the frequency of the photon is \[2.42 \times {10^{16}}Hz\].

Hence, option B is the correct answer.

Note:Here the energy is given in eV, so we first need to convert it into Joules and then have to use this formula. But suppose if we want to find the wavelength and the frequency both then we could use the formula directly.