First slide

Radiation

Question

The power radiated by a black body is P and it radiates maximum energy at wavelength, $λ_{0}$ . If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4} λ_{0}$ the power radiated by it becomes nP. The value of n is

Moderate

A

$\frac{3}{4}$
B

$\frac{4}{3}$
C

$\frac{256}{81}$
D

$\frac{81}{256}$

Solution

$From Wien's law, λ_{\max} T = constant$
$So, λ_{\max_{1}} T_{1} = λ_{\max_{2}} T_{2}$
$\Rightarrow λ_{0} T = \frac{3 λ_{0}}{4} T^{'} \Rightarrow T^{'} = \frac{4}{3}$
According to Stefan-Boltzmann law, energy emitted unit time by a black body is $A e σ T^{4}, i.e.,$ power radiated.
$∴ P \propto T^{4}$
$So, \frac{P_{2}}{P_{1}} = {(\frac{T^{'}}{T})}^{4} \Rightarrow n = {(\frac{4}{3})}^{4} = \frac{256}{81}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App