A) 2
B) 2.5
C) 4.00
D) 4.5
Correct Answer: C
Solution :
If\[{{T}_{A}}\]and\[{{\lambda }_{A}}\]are the temperature and wavelength of body A respectively and \[{{T}_{B}}\]and \[{{\lambda }_{B}}\] be the temperature and wavelength of body B respectively Here: \[{{T}_{A}}=4{{T}_{B}}\]and \[{{\lambda }_{B}}-{{\lambda }_{A}}=3\mu \,m\] So, \[{{\lambda }_{B}}-{{\lambda }_{A}}=3\] ?(i) According to Weins displacement law \[{{\lambda }_{A}}{{T}_{A}}={{\lambda }_{B}}{{T}_{B}}\] \[\frac{{{\lambda }_{B}}}{{{\lambda }_{A}}}=\frac{{{T}_{A}}}{{{T}_{B}}}=\frac{4{{T}_{B}}}{{{T}_{B}}}=4\] ?(ii) From Eqs. (i) and (ii) \[4{{\lambda }_{A}}-{{\lambda }_{A}}=3\] \[3{{\gamma }_{A}}=3\Rightarrow {{\gamma }_{A}}=1\] Now, putting value of \[{{\lambda }_{A}}=1\]in Eq.(i) \[{{\lambda }_{B}}-1=3\] \[{{\lambda }_{B}}=3+1=4\mu m\]
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