Question

The energy of a photon is $3 \times {10^{ - 12}}ergs$. What is its wavelength in nm? $\left[ {h = 6.62 \times {{10}^{ - 27}}erg,c = 3 \times {{10}^{10}}cm/s} \right]$
A. 0.066
B. 1324
C. 5.62
D. 6.62

Answer 1

Hint: We know that erg is the dimension of in the centimeter - gram - second or ‘CGS’ system of units. Now, to find the solution of the given question, write down all the given physical quantities and then apply the formula of the energy of photon, i.e. $E = \dfrac{{hc}}{\lambda }$. Each quantum of light has energy ‘hv’, where h is Planck’s constant and ‘v’ is the frequency of the light. Additionally, the physical quantities such as the wavelength and frequency are inversely proportional to each other.
Formula Used: $E = \dfrac{{hc}}{\lambda }$

Complete answer:
It is given that,
The Energy of the photon, E = $3 \times {10^{ - 12}}erg$
Planck’s constant h = $6.62 \times {10^{ - 27}}erg$
The Speed of light c = $3 \times {10^{10}}cm/s$
We have to find the wavelength ‘$\lambda $’.
The quantum of electromagnetic radiation is understood as a photon. In other words, the phrase quantum means to the smallest elementary unit of quantity and one amount of electromagnetic energy is known as a photon. A photon is characterized either by wavelength ‘$\lambda $’ or the same energy ‘E’. The energy of a photon is known to be inversely proportional to the wavelength of a photon.
Now, we know that the energy of the photon is given mathematically given as,
E = $\dfrac{{hc}}{\lambda }$
Wavelength ‘$\lambda $’ is given as,
$\lambda = \dfrac{{hc}}{E}$
$\eqalign{
  & \Rightarrow \lambda = \dfrac{{6.62 \times {{10}^{ - 27}} \times 3 \times {{10}^{10}}}}{{3 \times {{10}^{ - 12}}}} \cr
  & \Rightarrow \lambda = 6.63 \times {10^{ - 5}} \cr
  & \Rightarrow \lambda = 0.066 \times {10^{ - 9}}m \cr
  & \therefore \lambda = 0.066nm \cr} $
Thus, its wavelength in nm is 0.066.

Hence, option (A) is the correct answer for the given question.

Note:
Photons are electrically neutral particles and are hence not deflected by electric and magnetic fields. The rest mass of a photon is zero, which means that photos do not exist in rest state at all. Additionally, all photons of a specific frequency and wavelength will have an equivalent energy and momentum independent of the intensity of radiation.