Question

For an enclosure maintained at $1000\, K$, the maximum radiation occurs at wavelength $\lambda_{m}$. If the temperature is raised to $2000\, K$, the peak will shift to

• A. $\frac{5}{2}\lambda_{m}$
• B. $\frac{1}{2}\lambda_{m}$
• C. $\frac{7}{2}\lambda_{m}$
• D. $\frac{3}{2}\lambda_{m}$

Answer 1

Answer: (B)

$\frac{1}{2}\lambda_{m}$

Answer 2

We know from Wien?? displacement law, $\lambda_{m} T =$ constant $\therefore \lambda_{m}T_{1} = \lambda'_{m}T_{2}$ $\Rightarrow \lambda'_{m} = \frac{\lambda_{m}T_{1}}{T_{2}}$ $= \frac{\lambda_{m}\times1000}{2000} = \frac{\lambda_{m}}{2}$