First slide

Radiation

Question

The black body spectrum of an object O₁ is such that its radiant intensity (i.e. intensity per unit wavelength interval) is maximum at a wavelength of 200 nm. Another object O₂ has the maximum radiant intensity at 600nm. The ratio of power emitted per unit area by source O₁ to that of source O₂ is

Moderate

A

1 : 81
B

1 : 9
C

9 : 1
D

81 : 1

Solution

From Wien's displacement law,
$λ_{m} T = b \Rightarrow λ_{m} = \frac{b}{T}$ …(i)
From Stefan's law, $E \propto T^{4}$
$\Rightarrow \frac{E_{1}}{E_{2}} = {(\frac{T_{1}}{T_{2}})}^{4} = {(\frac{λ_{m_{2}}}{λ_{m_{1}}})}^{4}$ [By Eq. (i)]
$\Rightarrow \frac{E_{1}}{E_{2}} = {(\frac{600}{200})}^{4} \Rightarrow E_{1} : E_{2} = 81 : 1$

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