A heated body maintained at $T\,K$ emits thermal radiation of total energy $E$ with a maximum intensity at frequency $v$ . The emissivity of the material is $0.5$ . If the temperature of the body be increased and maintained at temperature $3T\,K$ , then
$(i)$ The maximum intensity of the emitted radiation will occur at frequency $v /3$
$(ii)$ The maximum intensity of the emitted radiation will occur at frequency $3v $
$(iii)$ The total energy of emitted radiation will become $81\,E$
$(iv)$ The total energy of emitted radiation will become $27\,E$
Medium
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The frequency at which maximum intensity of emission occurs is proportional to $T$ , while the rate of the emitted radiation is proportional to $T^4$
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