Question

When the temperature of a black body increase by $0.1\%$, the wavelength corresponding to maximum emission changes by 0.13 $\mu$m. The initial wavelength corresponding to maximum emission is

• A. $0.26\mu m$
• B. $0.13\mu m$
• C. $0.13mm$
• D. $0.26mm$

Answer 1

The correct option is C $0.13mm$

Using Wein’s displacement law,
${\lambda }_{m}T=b...\left(1\right)$
$\Rightarrow ({\lambda }_m-0.13\mu m)(\frac{0.1}{100}T+T)=b$
$\Rightarrow {\lambda }_m.\frac{1001}{1000}T-0.16\times {10}^{-6}\times \frac{1001}{1000}T=b...\left(2\right)$
From (1) and (2)
${\lambda }_{m}T={\lambda }_{m}T.\frac{1001}{1000}-0.13\times {10}^{-6}\times \frac{1001}{1000}T$
$\Rightarrow \frac{{\lambda }_{m}T}{1000}=\frac{0.13\times {10}^{-6}\times 1001}{1000}T$
$\therefore {\lambda }_m=130.13\mu m=0.13mm$.