Question

Energy of a photon having wave number $1{\text{cm}}^{-1}$ is.

• A. $6.62\times {10}^{-32}\text{J}$
• B. $1.99\times {10}^{-23}\text{J}$
• C. $6.62\times {10}^{-34}\text{J}$
• D. $1.99\times {10}^{-36}\text{J}$

Answer 1

The correct option is B

$1.99\times {10}^{-23}\text{J}$

Step 1: Given data

Wave number, $=1{\text{cm}}^{-1}$

Hence, wavelength

$$\begin{gathered} \lambda =\frac{1}{wavenumber}=\frac{1}{1{\text{cm}}^{-1}} \\ =.01\text{m} \end{gathered}$$

To Find

The energy of a photon.

Step 2: Calculate the energy of the photon

$$\begin{gathered} E=\frac{hc}{\lambda } \\ h=Planck\text{'}s\mathrm{co}nstant=6.62\times {10}^{-34}Js,c=speedoflight=3\times {10}^{8}m/s \end{gathered}$$

Substituting the values

$$\begin{gathered} E=\frac{\left(6.62\times {10}^{-34}\text{Js}\right)\times \left(3\times {10}^8{\displaystyle \frac{\text{m}}{\text{s}}}\right)}{.01\text{m}} \\ =1.99\times {10}^{-23}\text{J} \end{gathered}$$

Hence, the Energy of photons is $1.99\times {10}^{-23}\text{J}$.