Question

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

• A. $14\, mm$
• B. $7\,\mu\, m$
• C. $2.8\, \mu\, m$
• D. $28\,mm$

Answer 1

Answer: (C)

$2.8\, \mu\, m$

Answer 2

From Wien's displacement law
$\lambda_{m} T =$ constant
$\lambda_{1} T_{1} =\lambda_{2} T_{2}$
$\Rightarrow \lambda_{2} =\frac{\lambda_{1} T_{1}}{T_{2}}$
Given, $\lambda_{1} =14\, \mu m ,$
$T_{1} =200\, K,\, T_{2}=1000\, K$
$\therefore \lambda_{2} =\frac{14 \times 200}{1000}$
$=2.8\, \mu m$