Question

According to Wien's displacement law, how is the surface temperature of a star related to its maximum intensity wavelength?

• A. $\lambda_{\text{max}} \propto T$
• B. $\lambda_{\text{max}} \propto \frac{1}{T}$
• C. $\lambda_{\text{max}} \propto T^2$
• D. $\lambda_{\text{max}} \propto \frac{1}{T^2}$

Hint:

Remember: Hotter object → shorter wavelength ($\lambda_{\text{max}} \downarrow$).

Answer 1

The Correct Option is B

Concept: Wien's displacement law relates the temperature of a black body to the wavelength at which it emits maximum radiation.
Step 1: Wien's law formula.
\[ \lambda_{\text{max}} T = b \] where $b$ is Wien's constant.
Step 2: Rewriting the relation.
\[ \lambda_{\text{max}} = \frac{b}{T} \]
Step 3: Understanding the relationship.
As temperature increases, the peak wavelength decreases.
Step 4: Evaluating the options.

• $\lambda_{\text{max}} \propto T$ $\rightarrow$ Incorrect
• $\lambda_{\text{max}} \propto \frac{1}{T}$ $\rightarrow$ Correct
• $\lambda_{\text{max}} \propto T^2$ $\rightarrow$ Incorrect
• $\lambda_{\text{max}} \propto \frac{1}{T^2}$ $\rightarrow$ Incorrect

Step 5: Conclusion.
Thus, $\lambda_{\text{max}}$ is inversely proportional to temperature.