Question

The intensity of radiation emitted by to stars $A$ and $B$ are in the ratio of $16:1$. The wavelength corresponding to their peak emission of radiation will be the ratio of :

• A. $2:1$
• B. $4:1$
• C. $1:2$
• D. $16:1$

Answer 1

The correct option is C $1:2$

$\because$ Intensity of radiation $E\propto \frac{1}{{\lambda }_4}$
$\therefore \frac{E_{{\lambda }_1}}{E_{{\lambda }_2}}={\left(\frac{{\lambda }_2}{{\lambda }_1}\right)}^4$
$\frac{{\lambda }_2}{{\lambda }_1}=\sqrt[4]{4\frac{E_{{\lambda }_1}}{E_{{\lambda }_2}}}$
$\frac{{\lambda }_2}{{\lambda }_1}=\sqrt[4]{4\frac{16}{1}}$
$=\frac{2}{1}$
or $\frac{{\lambda }_1}{{\lambda }_2}=\frac{1}{2}$
${\lambda }_1:{\lambda }_2=1:2$.