Question

The maximum energy in the thermal radiation from a hot source occurs at a wavelength of $11 \times 10^{-5} cm$. According to Wien's law, the temperature of the source(on Kelvin scale) will be $n$ times the temperature of another source (on Kelvin scale) for which the wavelength at maximum energy is $5.5 \times 10^{-5} cm$. The value of $n$ is

• A. 2
• B. 4
• C. 1/2
• D. 1

Answer 1

Answer: (C)

According to Wien's law, $\lambda_{m} T=$ constant
$\therefore \left(\lambda_{m}\right)_{1} T_{1}=\left(\lambda_{m}\right)_{2} T_{2}$
or $\left(11 \times 10^{-5}\right) T_{1}=\left(5.5 \times 10^{-5}\right) T_{2}$ or
$T_{1}=\frac{1}{2} T_{2}$
$\therefore n=\frac{1}{2}$