A) \[4800\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[9600\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[2400\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[19200\overset{\text{o}}{\mathop{\text{A}}}\,\]
Correct Answer: B
Solution :
Wein's displacement law states that there is an inverse relationship between the wavelength \[({{\lambda }_{m}})\] of the peak of the emission of a black body and its temperature (T). \[\therefore \] \[{{\lambda }_{m}}=\frac{b}{T}\] (b = constant) \[\therefore \] \[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{{{T}_{2}}}{{{T}_{1}}}\] \[\Rightarrow \] \[{{\lambda }_{2}}=\frac{{{\lambda }_{1}}{{T}_{1}}}{{{T}_{2}}}\] Given, \[{{\lambda }_{1}}=4800\overset{\text{o}}{\mathop{\text{A}}}\,,\,\,\,\,{{T}_{1}}=6000K,\] \[{{T}_{2}}=3000K,\] \[\therefore \] \[{{\lambda }_{2}}=\frac{4800\times 6000}{3000}=9600\overset{\text{o}}{\mathop{\text{A}}}\,\]
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