Question 655: Thermodynamics & KTG

Question

A black body emits radiation of maximum intensity at wavelength ' $\lambda$ ' at temperature T K. Its corresponding wavelength at temperature 1.5 T K will be

Accepted Answer

Step 1: Recall WienÃ¢ÂÂs displacement law
$ \lambda_{	ext{max}} T = 	ext{constant} \quad (b) $
So,
$ \lambda_{	ext{max}} \propto \frac{1}{T}. $
Step 2: Compare two states
At temperature $ T $,
$ \lambda = \frac{b}{T}. $
At temperature $ 1.5T $, the new wavelength is
$ \lambda' = \frac{b}{1.5T}. $
Step 3: Relating $\lambda'$ and $\lambda$
$ \lambda' = \frac{b}{1.5T} = \frac{1}{1.5}\cdot \frac{b}{T} = \frac{1}{1.5}\cdot \lambda = \frac{\lambda}{1.5} = \frac{2}{3}\lambda. $
Final Answer:
$ \boxed{	frac{2 \lambda}{3}} $
Correct Option: A

Answer

$\frac{2 \lambda}{3}$

Answer

$\frac{4 \lambda}{3}$

Answer

$\frac{16 \lambda}{81}$

Answer

$\frac{81 \lambda}{16}$

Thermodynamics & KTG

A black body emits radiation of maximum intensity at wavelength ' \lambda ' at temperature T K. Its corresponding wavelength at temperature 1.5 T K will be

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