Question

A black body at 200 K is found to emit maximum energy at a wavelength of 14 $\mu m$. When its temperature is raised to 1000 K, the wavelength at which maximum energy is emitted is

• A. 14 $\mu m$
• B. 70 $\mu F$
• C. 2.8 $\mu m$
• D. 2.8 mm

Answer 1

Answer: (C)

2.8 $\mu m$

Answer 2

$\lambda_{m}T =$constant ⇒ $\frac{(\lambda_{m})_{2}}{(\lambda_{m})_{1}} = \frac{T_{1}}{T_{2}} = \frac{200}{1000} = \frac{1}{5}$ ⇒

$(\lambda_{m})_{2} = \frac{(\lambda_{m})_{1}}{5} = \frac{14\mu m}{5}$= 2.8 μm.