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 Wiens displacement law. |
| Wiens 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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