A) \[\frac{16}{1}\]
B) \[\frac{4}{1}\]
C) \[\frac{1}{4}\]
D) \[\frac{1}{16}\]
Correct Answer: D
Solution :
By wein's displacement law \[{{\lambda }_{1}}{{T}_{1}}={{\lambda }_{2}}{{T}_{2}}\] or \[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{{{T}_{2}}}{{{T}_{1}}}=\frac{0.26}{0.13}=2\] \[\therefore \]\[{{T}_{2}}=2{{T}_{1}}\] By stefan's Law, emissive power \[E=\sigma {{T}^{4}}\] \[\therefore \]\[{{E}_{1}}=\sigma T_{1}^{4},{{E}_{2}}=\sigma T_{2}^{4},\] \[\therefore \]\[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{\sigma T_{1}^{4}}{\sigma {{(2{{T}_{1}})}^{4}}}=\frac{1}{16}\] Hence, the correction option is [d].
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