A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is , at wavelength 500 nm is and that at 1000 nm is . Wien’s constant, . Which of the following is correct? [2016]

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Solution

Q.
A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is $U_{1}$ , at wavelength 500 nm is $U_{2}$ and that at 1000 nm is $U_{3}$ . Wien’s constant, $b = 2.88 \times 10^{6} nm$ $K$ . Which of the following is correct [2016]

1 $U_{1} > U_{2}$

2 $U_{2} > U_{1}$

3 $U_{1} = 0$

4 $U_{3} = 0$

Ans.
(2)

According to Wien's displacement law

$λ_{m} = \frac{b}{T} = \frac{2.88 \times 10^{6} nm K}{5760 K} = 500$ $nm$

Clearly from graph $U_{2} > U_{3}$ and $U_{2} > U_{1}$

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