Thermal Properties of Matter - Result Question 37
38. A black body has maximum wavelength $\lambda_m$ at temperature $2000 K$. Its corresponding wavelength at temperature $3000 K$ will be[2001]
(a) $\frac{3}{2} \lambda_m$
(b) $\frac{2}{3} \lambda_m$
(c) $\frac{4}{9} \lambda_m$
(d) $\frac{9}{4} \lambda_m$
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Answer:
Correct Answer: 38. (b)
Solution:
- (b) According to Wein’s displacement law, $\lambda_m T=2.88 \times 10^{-3}$
When $T=2000 K$,
$\lambda_m(2000)=2.88 \times 10^{-3}$
When $T=3000 K$,
$\lambda_m^{\prime}(3000)=2.88 \times 10^{-3}$
Dividing (1) by (2),
$ \frac{2}{3} \frac{\lambda_m}{\lambda_m^{\prime}}=1 \Rightarrow \frac{\lambda_m}{\lambda_m^{\prime}}=\frac{3}{2} \Rightarrow \lambda_m^{\prime}=\frac{2}{3} \lambda_m $
