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

Question

Dr. Abubacker · Accepted Answer

(b) From Wien’s displacement law
$\lambda_{m}T$=constant
$\Rightarrow \ \ \ \ \ \lambda_{m1}T_{1} = \lambda_{m2}T_{2}$
Or $\frac{T_{1}}{T_{2}} = \frac{\lambda_{m2}}{\lambda_{m1}}$ …(i)
Here, $\lambda_{m1} = 510\ nm,\ \ \ \ \lambda_{m2} = 350\ nm$
So, on putting these values in Eq. (i)
$\frac{T_{1}}{T_{2}} = \frac{350}{510}\  \Rightarrow \ \frac{T_{1}}{T_{2}} = \frac{35}{51} = 0.69$

Q. 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

Explanation

Reviewed by Dr. Abubacker

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