Question 577: Thermodynamics & KTG

Question

A black body has maximum wavelength ' $\lambda_{\mathrm{m}}$ ' at temperature 2000 K . Its maximum wavelength at 3000 K will be

Accepted Answer

We are dealing with
WienÃ¢ÂÂs displacement law
:
$ \lambda_m T = 	ext{constant} $
At temperature $T_1 = 2000\ \mathrm{K}$, the maximum wavelength is $\lambda_m$.
At temperature $T_2 = 3000\ \mathrm{K}$, the maximum wavelength is $\lambda_m'$.
Using WienÃ¢ÂÂs law:
$ \lambda_m T_1 = \lambda_m' T_2 $
$ \lambda_m' = \lambda_m \cdot \frac{T_1}{T_2} $
$ \lambda_m' = \lambda_m \cdot \frac{2000}{3000} $
$ \lambda_m' = \frac{2}{3} \lambda_m $
Ã¢ÂÂ Correct Answer:
Option D: $	frac{2}{3}\lambda_m$.

Answer

$\frac{3}{2} \lambda_{\mathrm{m}}$

Answer

$\frac{16}{81} \lambda_m$

Answer

$\frac{81}{16} \lambda_m$

Answer

$\frac{2}{3} \lambda_m$

Thermodynamics & KTG

A black body has maximum wavelength ' \lambda_{\mathrm{m}} ' at temperature 2000 K . Its maximum wavelength at 3000 K will be

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