Question

If the radiation emitted by a star has a maximum intensity at a wavelength of 446 nm, its surface temperature is approximately:

• A. 650 K
• B. 65 K
• C. 6500 K
• D. 65000 K

Hint:

Wien’s constant is 2.9 × 10^−3 m K. Make sure to convert nm to m before calculation.

Answer 1

The Correct Option is C

Using Wien's displacement law: $\lambda_{\text{max}} T \approx 2.9 \times 10^{-3} \text{ m} \cdot \text{K}$. Given $\lambda_{\text{max}} = 446 \text{ nm} = 446 \times 10^{-9} \text{m}$,
$T = \frac{2.9 \times 10^{-3}}{446 \times 10^{-9}}$

$\approx \frac{2.9 \times 10^{-3}}{4.46 \times 10^{-7}}$

$\approx 6500 \text{ K}.$