Question

A heated body emits radiation which has maximum intensity at frequency $v_m$. If the temperature of the body is doubled

• A. the maximum intensity radiation will be at frequency $2v_m$
• B. the maximum intensity radiation will be at frequency $\frac{1}{2}{v}_m$
• C. the total emitted energy will increase by a factor of $16$
• D. the total emitted energy will increase by a factor of $2$

Answer 1

Answer: (A), (C)

the maximum intensity radiation will be at frequency $2v_m$
the total emitted energy will increase by a factor of $16$

Wien's displacement law states maximum intensity wavength ${\lambda }_m\propto \frac{1}{T}$
Also for any photon,$\lambda \propto \frac{1}{\nu }$
Hence, frequency ${\nu }_m\propto T$
Doubling of temperature leads to doubling of frequency from ${\nu }_m$ to $2{\nu }_m$
From Stefan's law, power is directly proportional to $T^4$
Hence $T\to 2T\Rightarrow E\to (\frac{2T}{T}{)}^{4}E=16E$