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Thermal Properties Of Matter

Question

A black body has a wavelength of ) λ at temperature 2000 K. Its corresponding wavelength at temperature 3000 K will be

$\frac{2 λ}{3}$

$\frac{3 λ}{2}$

$\frac{4 λ}{9}$

$\frac{9 λ}{4}$

Solution

$\frac{2 λ}{3}$

According to Wien's displacement law wavelength λ_mfor which energy is the maximum decrease with increasing temperature.

This relation between λ_mand T is given by

λ_m T = constant

⇒ $\frac{λ_{2}}{λ_{1}} = \frac{T_{1}}{T_{2}}$

⇒ $\frac{λ_{2}}{λ} = \frac{2000}{3000}$

⇒ $\frac{λ_{2}}{λ} = \frac{2}{3}$

⇒ λ₂ = $\frac{2}{3}$ λ