First slide

Radiation

Question

A black body at $1227^{0} C$ emits radiation with maximum intensity at a wavelength of 5000 $\overset{0}{A}$ . If the temperatures of the body is increased by $1000^{0} c$ , the maximum intensity will be observed at

Moderate

A

4000 $\overset{0}{A}$
B

5000 $\overset{0}{A}$
C

6000 $\overset{0}{A}$
D

3000 $\overset{0}{A}$

Solution

The product of wavelength corresponding to maximum intensity of radiation and temperature of the body in Kelvin is constant.
According to Wien's law,
$λ_{m} T = constant (say b)$
Where $λ_{m}$ is a wavelength corresponding to maximum intensity of radiation and T is temperature of the body in Kelvin.
$\frac{λ_{m^{'}}}{λ_{m}} = \frac{T}{T^{'}}$
Given, $T = 1227 + 273 = 1500 K,$
$T^{'} = 1227 + 1000 + 273 = 2500 K$
$λ_{m} = 5000$ $\overset{0}{A}$
Hence, $λ_{m^{'}} = \frac{1500}{2500} \times 5000 = 3000$ $\overset{0}{A}$

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