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, $T=1227+273=1500K$
$T=1227+1000+273=2500K$
${\lambda }_m=5000\mathring{A}$
Hence, ${\lambda }_m=\frac{1500}{2500}\times 5000=3000\mathring{A}$