Question

For an object radiating heat at 300 K, the wavelength corresponding to maximum intensity is $\lambda$. If the temperature of body is increased by 300 K, the new wavelength corresponding to maximum intensity will be

• A. $\frac{\lambda}{2}$
• B. ${2\lambda}$
• C. ${\lambda}$
• D. $\frac{5\lambda}{2}$

Answer 1

Answer: (A)

$\frac{\lambda}{2}$

Answer 2

According to the Wein’s displacement law, the wavelength of the maximum intensity (λ) of radiation is directly proportional to absolute temperature (T). i.e
λ ∝ $\frac{1}{T}$ ⇒ λT= constant
⇒ λ1T1 = λ2T2
Given, for T1 = 300 K, λ1 = λ
Now, if the temperature of the body is increased by 300 K, then final temperature of the body will be
T2 = 300 +300 = 600 K
Therefore, the new wavelength corresponding to maximum intensity will be,
λ2 = $\frac{\lambda_1T_1}{T_2}$ = $\frac{\lambda*300}{600}$ = $\frac{\lambda}{2}$
Answer. A