Question

The maximum emission wavelength at temperature $2000K$ is $4\mu m$. The maximum wavelength corresponding to temperature $2400K$ will be

Answer 1

Step 1: Given data

Temperature${\mathrm{T}}_1=2000K$,

wavelength$=4\mu m=4\times {10}^{-6}m$,

Second temperature ${\mathrm{T}}_2=2400K$

Step 2: Formula used

Wein's Displacement Law $\lambda T=b$(constant)

$\lambda =$Wavelength

$T=$Temperature

Step 3: Find the wavelength at a temperature $2400K$

From the Wein's Displacement Law:

$$\begin{gathered} {\lambda }_2{T}_2={\lambda }_1{T}_1 \\ \Rightarrow {\lambda }_2=\frac{{\lambda }_1{T}_1}{T_2} \\ \Rightarrow {\lambda }_2=\frac{4\times {10}^{-6}\times 2000}{2400} \\ \Rightarrow {\lambda }_2=3.33\times {10}^{-6}m \end{gathered}$$

Hence, the maximum wavelength corresponding to temperature $2400K$ is $3.33\times {10}^{-6}m$.