Question

Find the momentum of a dominant wavelength photon released by a black body at temperature of $500\text{K}.$ (in SI units)

• A. $11.43\times {10}^{-29}{\text{kgms}}^{-1}$
• B. $43.2\times {10}^{-31}{\text{kgms}}^{-1}$
• C. $5.26\times {10}^{-28}{\text{kgms}}^{-1}$
• D. $7.34\times {10}^{-31}{\text{kgms}}^{-1}$

Answer 1

The correct option is A $11.43\times {10}^{-29}{\text{kgms}}^{-1}$

According to Wein's displacement law, ${\lambda }_{m}T=b$

$\Rightarrow \lambda =\frac{2.897\times {10}^{-3}}{500}$

Momentum of a photon is given by
$p=\frac{h}{\lambda }$

$\Rightarrow p=\frac{6.626\times {10}^{-34}\times 500}{2.897\times {10}^{-3}}$

$\Rightarrow p=11.43\times {10}^{-29}{\text{kgms}}^{-1}$

Hence, option $\left(a\right)$ is correct.