Question

Two stars A and B radiate maximum energy at the wavelengths of $360$nm and $480$nm respectively. Then the ratio of the surface temperatures of A and B is.

• A. $3:4$
• B. $81:256$
• C. $4:3$
• D. $256:81$

Answer 1

Answer: (C)

$4:3$

From Wien's displacement law, $T\lambda =$ constant

$⟹$ $T\propto \frac{1}{\lambda }$ .......(1)

Given : ${\lambda }_A=360$ nm ${\lambda }_B=480$ nm

From (1) we get $\frac{T_A}{T_B}=\frac{{\lambda }_B}{{\lambda }_A}$

$\therefore$ $\frac{T_A}{T_B}=\frac{480}{360}=\frac{4}{3}$