Q: A black body at 200 K is found to emit maximum energy at a wavelength of 14 μm. When its temperature is raised to 1000 K, the wavelength at which maximum energy is emitted is

(a) 14 μm

(b) 70 μm

(c) 2.8 μm

(d) 28 μm

**Click to See Answer : **

Ans: (c)

Sol: $\displaystyle \lambda \propto \frac{1}{T} $

$\displaystyle \frac{\lambda_1}{\lambda_2} = \frac{T_2}{T_1}$

$\displaystyle \lambda_2 = \frac{T_1}{T_2}\times \lambda_1 $

$\displaystyle \lambda_2 = \frac{200}{1000}\times 14 $

$\displaystyle \lambda_2 = 2.8 \mu m $