Question

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

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

Answer 1

Answer: (B)

$0.69$

According to Wein's displacement law, ${\lambda }_{m}T=constant$ where ${\lambda }_m$ is the wavelength for which intensity of radiation emitted is maximum
$({\lambda }_m{)}_s{T}_s=({\lambda }_m{)}_{NS}\times T_{NS}$
$S=sun$
$NS=northstar$
$\Rightarrow \frac{T_S}{T_{NS}}=\frac{({\lambda }_m{)}_{NS}}{({\lambda }_m{)}_S}=\frac{350}{510}=0.69$.