A) \[\frac{2}{3}\lambda \]
B) \[\frac{16}{81}\lambda \]
C) \[\frac{81}{16}\lambda \]
D) \[\frac{4}{3}\lambda \]
Correct Answer: A
Solution :
Key Idea: The relation between the wavelength corresponding to maximum intensity of radiation at any temperature is given by Wien?s displacement law. Wien?s displacement law is given by \[{{\lambda }_{m}}T=\text{cosntant}\] \[or{{\lambda }_{1}}{{T}_{1}}={{\lambda }_{2}}{{T}_{2}}\] \[or{{\lambda }_{2}}={{\lambda }_{1}}\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)\] Here, \[{{T}_{1}}=2000\,K,\,{{T}_{2}}=3000\,K,\,{{\lambda }_{1}}=\lambda \] \[\therefore {{\lambda }_{2}}=\lambda \times \frac{2000}{3000}=\frac{2}{3}\,\lambda \]
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