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Thermal Properties of Matter — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsThermal Properties of Matter3 Marks
Question
A black body at 2000K emits maximum energy at a wavelength of $1.56\mu\text{m}.$ At what temperature will it emit maximum energy at a wavelength of $1.8\mu\text{m}\ ?$
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Answer

Here, $\lambda_{\text{m}1}=1.56\mu\text{m},\text{T}=2000\text{K}$ $\lambda_{\text{m}2}=1.8\mu\text{m}, \text{T}_2=\ ?$ According to Wien's displacement law, $\lambda_\text{m}=\frac{\text{b}}{\text{T}}$ $\therefore\frac{\lambda_{\text{m}1}}{\lambda_{\text{m}1}}=\frac{\text{T}_2}{\text{T}_1}$ $\Rightarrow\frac{1.56}{1.8}=\frac{\text{T}_2}{2000}\Rightarrow\text{T}_2=\frac{1.56\times2000}{1.8}$ $\therefore\text{T}_2=1733.3\text{K}$

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