Question

A black body emits maximum radiation of wavelength ${\lambda }_1=2000A$ at a certain temperature $T_1$ On increasing the temperature the total energy of radiation emitted is increased $16$ times at temperature $T_2$ If ${\lambda }_2$ is the wavelength corresponding to which maximum radiation emitted at temperature $T_2$ Calculate the value of $\left(\frac{{\lambda }_1}{{\lambda }_2}\right)$

• A. $2:1$
• B. $1:2$
• C. $3:4$
• D. $4:3$

Answer 1

The correct option is A $2:1$

The rate of radiation, emitted by per unit area of a body at temperature $T$ , is given by Stefan-Boltzmann's law as,

$E\propto T^4$ ,

hence , $E_1/E_2=(T_1/T_2{)}^4$ ,

given , $E_2=16E_1$ ,

therefore ,

$E_1/16E_1=(T_1/T_2{)}^4$ ,

or $T_2/T_1=2$ ,

now by Wein's law ,

${\lambda }_m\propto 1/T$ ,

hence ${\lambda }_{m1}/{\lambda }_{m2}=T_2/T_1$ ,

therefore , ${\lambda }_{m1}/{\lambda }_{m2}=T_2/T_1=2$ ,