Question

Solar radiation emitted by sun correspond to that emitted by black body at a temperature of $6000K$. Maximum intensity is emitted at wavelength of $4800\mathring{A}$. If the sun was to cool down from $6000K$ to $3000K$, then the peak intensity of emitted radiation would occur at a wavelength

• A. $4800\mathring{A}$
• B. $9600\mathring{A}$
• C. $2400\mathring{A}$
• D. $19200\mathring{A}$

Answer 1

Answer: (B)

Wein's displacement law states that there is an inverse relationship between the wavelength $({\lambda }_m)$ of the peak of the emission of a black body and its temperature $(T)$.
$\therefore {\lambda }_m=\frac{b}{T}$
($b=$ constant)
$\therefore \frac{{\lambda }_1}{{\lambda }_2}=\frac{T_2}{T_1}$
$\Rightarrow {\lambda }_2=\frac{{\lambda }_1{T}_1}{T_2}$
Given, ${\lambda }_1=4800\mathring{A}$
$T_1=6000K$
$T_2=3000K$
$\therefore {\lambda }_2=\frac{4800\times 6000}{3000}=9600\mathring{A}$