A) 1000 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) 2000 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) 5000 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) 4000 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
E) 3000 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
Correct Answer: E
Solution :
According to Wiens displacement law, if maximum energy is emitted at wavelength \[{{\lambda }_{m}}\] at temperature T, then \[{{\lambda }_{m}}\] T = constant or \[{{\lambda }_{m}}\propto \frac{1}{T}\] or \[\frac{{{({{\lambda }_{m}})}_{1}}}{{{({{\lambda }_{m}})}_{2}}}=\frac{{{T}_{2}}}{{{T}_{1}}}\] \[\therefore \] \[\frac{5000}{{{({{\lambda }_{m}})}_{2}}}=\frac{2227+273}{1227+273}\] or \[\frac{5000}{{{({{\lambda }_{m}})}_{2}}}=\frac{2500}{1500}\] \[\therefore \] \[{{({{\lambda }_{m}})}_{2}}=3000\overset{\text{o}}{\mathop{\text{A}}}\,\]
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