Question

A black body at $ 1227^{\circ} C $ emits radiations with maximum intensity at a wavelength of $ 5000\,\mathring{A} $ . If the temperature of the body is increased by $ 1000^{\circ} C $ , the maximum intensity will be observed at

• A. $ 4000\,\mathring{A}$
• B. $ 5000\,\mathring{A}$
• C. $ 6000\,\mathring{A} $
• D. $ 3000\,\mathring{A} $

Answer 1

Answer: (D)

According to Wiens law $\lambda_{m} T=$ constant (say $b$)
where $\lambda_{m}$ is wavelength corresponding to maximum intensity of radiation and $T$ is temperature of the body in Kelvin.
$\therefore \frac{\lambda_{m}}{\lambda_{m}}=\frac{T}{T}$
Given, $T=1227+273=1500\, K$
$ T=1227+1000+273=2500\,K $
$ {{\lambda }_{m}}=5000\,\mathring{A} $
Hence, $ \lambda_{m}=\frac{1500}{2500}\times 5000=3000\,\mathring{A}$