Discussion
If a black body at a temperature T radiates the maximum energy at a wavelength \(\lambda_{m}\) then to radiate the maximum energy at the wavelength \(\frac{\lambda_{m}}{3}\),its temperature should be
Answer: A
The temperature should be increased to 3T.
By Wien's displacement law, \(\lambda_{m}T\) is constant, so the peak wavelength is inversely proportional to the temperature:
\[ T' = T\cdot\frac{\lambda_{m}}{\lambda_{m}/3} = 3T \]
A shorter peak wavelength means a hotter body, so 'decreased' is wrong. 9T and \(\sqrt{3}\)T apply power laws that Wien's law does not contain.
For example, a star with peak emission at 1500 nm would need to be three times hotter for its peak to shift to 500 nm.
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