Question

If a photon has velocity c and frequency \[\nu \] , then which of the following represents its wavelength.
A. \[\dfrac{{hc}}{E} \\ \]
B. \[\dfrac{{h\nu }}{c} \\ \]
C. \[\dfrac{{h\nu }}{{{c^2}}} \\ \]
D. \[h\nu \]

Answer 1

Hint: The total amount of energy carried by a single photon is termed as the energy of the photon. This amount is directly proportional to the electromagnetic frequency and inversely proportional to the wavelength, i.e., the higher the frequency, the higher the energy and inversely lower its wavelength.

Formula Used:
The formula to find the energy of a photon is,
\[E = h\nu \]
Where, h is Planck’s constant and \[\nu \] is frequency of photon.

Complete step by step solution:
Whenever an electron or an atom jumps from the higher energy state to the lower energy state, a packet of light is emitted known as a photon and it has energy associated with it.
The energy of a photon is,
\[E = h\nu \]………… (1)

The frequency of photon can be written as,
\[\nu = \dfrac{c}{\lambda }\]
here, c is speed of light and \[\lambda \] is wavelength of the photon
substituting the value of frequency in the equation (1) we get,
\[E = \dfrac{{hc}}{\lambda }\]
If we rearrange the equation for wavelength we get,
\[\lambda = \dfrac{{hc}}{E}\]
Therefore, the equation for wavelength is \[\dfrac{{hc}}{E}\].

Hence, Option A is the correct answer.

Note:Photon is the smallest packet (quanta) of energy and 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, and refraction, etc. The energy contained in the photon is quantized, that is it cannot be divided, it is only available in discrete packets of energy.