Question

Frequency for maximum energy radiation

of ideal black body at temperature T is υm. If

Wein’s constant is b and velocity

of heat radiation in vacuum is c then –

(A) υm = b/T (B) υm = b/

cT (C) υm = cT/b (D)

υm = bT/c ​

Answer 1

Answer : The correct option is (c) "$\nu_m=\dfrac{c\ T}{b}$"

Explanation :

According to Wein's law, the temperature peak curve of a black body at any wavelength is inversely proportional to the temperature.

Mathematically,

$\lambda_{max}\propto\dfrac{1}{T}$

$\lambda_{max}=\dfrac{b}{T}$.............(1)

Where,

$\lambda_{max}$ is the maximum wavelength.

b is the Wein's constant.

T is the temperature.

The frequency for the maximum energy radiation is $\nu_m$

$\because\ c =\nu\ \lambda$

or

$\lambda=\dfrac{c}{\nu}$

c is the speed of light.

So, equation (1) becomes :

$\dfrac{c}{\nu_m}=\dfrac{b}{T}$

$\nu_m=\dfrac{c\ T}{b}$

So, the correct option is (C).

Answer 2

All objects with a temperature above absolute zero (0 K, -273.15 oC) emit energy in the form of electromagnetic radiation. A blackbody is a theoretical or model body which absorbs all radiation falling on it, reflecting or transmitting none.