Question

The intensity of radiation emitted by the sun has its maximum value at a wavelength of $510 \, nm$ and that emitted by the north star has the maximum value at wavelength of $350 \, nm$ . If these stars behave like black bodies, then the ratio of surface temperatures of the sun and north star is

• A. 1.46
• B. 0.69
• C. 1.21
• D. 0.83

Answer 1

Answer: (B)

From Wien's displacement law
$\lambda _{m}T$ =constant
$\Rightarrow \, \, \lambda _{m 1}T_{1}=\lambda _{m 2}T_{2}$
Or $\frac{T_{1}}{T_{2}}=\frac{\lambda _{m 2}}{\lambda _{m 1}}$ ...(i)
Here, $\lambda _{m 1}=510 \, nm, \, \lambda _{m 2}=350 \, nm$
So, on putting these values in Eq. (i)
$\frac{T_{1}}{T_{2}}=\frac{350}{510} \, \Rightarrow \, \frac{T_{1}}{T_{2}}=\frac{35}{51}=0.69$