Question

A heated body emits radiation which has maximum intensity near the frequency $v_o$ . The emissivity of the material is $0.5$. If the absolute temperature of the body is doubled. Then :

• A. the maximum intensity of radiation will be near the frequency $2v_o$
• B. the maximum intensity of radiation will be near the frequency $\frac{v_o}{2}$
• C. the total energy emitted will increase by a factor of $32$
• D. the total energy emitted will increase by a factor of $8$

Answer 1

The correct option is A the maximum intensity of radiation will be near the frequency $2v_o$

By Wien's Displacement Law,

At max intensity we have $\lambda T$ = constant

If ${\lambda }_1$,${\lambda }_2$ are the wavelengths at which maximun intensity occurs for $T_1$,$T_2$ respectively.

Then, ${\lambda }_1{T}_1$ = ${\lambda }_2{T}_2$

So when temperature is doubled wavelength gets halved.

We know that $\nu \propto \frac{1}{\lambda }$

So the frequency gets doubled as wavelength gets halved.

So the maximum intensity will occur at $2{\nu }_0$.

Observe that the frequency is independent of value of emissivity.