Question

If the absolute temperature of a black body is doubled, the frequency corresponding to maximum emissive power becomes:

• A. halved
• B. doubled
• C. four times
• D. unchanged

Hint:

Remember: Temperature up $\rightarrow$ Wavelength down $\rightarrow$ Frequency up.

Answer 1

The Correct Option is B

Step 1: Concept
According to Wien's Displacement Law, the wavelength ($\lambda_{m}$) corresponding to maximum emissive power is inversely proportional to the absolute temperature ($T$), i.e., $\lambda_{m} \propto 1/T$.

Step 2: Meaning
Since the speed of light $c = \nu \lambda$, the frequency $\nu_{m}$ corresponding to maximum emissive power is directly proportional to temperature: $\nu_{m} = c/\lambda_{m} \propto T$.

Step 3: Analysis
If the absolute temperature $T$ is doubled ($T' = 2T$), then the new frequency $\nu'_{m}$ will be $\nu'_{m} \propto 2T$. This means the frequency also doubles.

Step 4: Conclusion
Therefore, doubling the temperature results in doubling the frequency of maximum emission. Final Answer: (B)