Question

Solar radiation emitted by sun correspond to that emitted by black body at a temperature of $6000\, K$. Maximum intensity is emitted at wavelength of $4800 \,\mathring{A}$. If the sun was to cool down from $6000\, K$ to $3000 \,K$, 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, $\lambda_{1}=4800\,\mathring{A}$
$T_{1}=6000 \,K$
$T_{2}=3000 \,K$
$\therefore \lambda_{2}=\frac{4800 \times 6000}{3000}=9600\,\mathring{A}$