Question

Star $S_1$ emits maximum radiation of wavelength $420\text{nm}$ and the star $S_2$ emits maximum radiation of wavelength $560\text{nm}$, what is the ratio of the temperature of $S_1$ and $S_2$ :

• A. $\frac{4}{3}$
• B. ${\left(\frac{4}{3}\right)}^{1/4}$
• C. $\frac{3}{4}$
• D. ${\left(\frac{3}{4}\right)}^{1/2}$

Answer 1

The correct option is A $\frac{4}{3}$

By Wein's Displacement law,
${\lambda }_{max}T=b$ (constant)
${\lambda }_1{T}_{S_1}={\lambda }_2{T}_{S_2}$
$\frac{T_{S_1}}{T_{S_2}}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{560}{420}$
$\frac{T_{S_1}}{T_{S_2}}=\frac{4}{3}$