The power radiated by a black body is \(P\) and it radiates maximum energy at wavelength ${}_{}$\(\lambda_0.\) Temperature of the black body is now changed so that it radiates maximum energy at the wavelength \(\dfrac{3}{4}\lambda_0.\) The power radiated by it now becomes \(nP.\) The value of \(n\) is:

On observing light from three different stars \(P,\) \(Q,\) and \(R,\) it was found that the intensity of the violet colour is maximum in the spectrum of \(P,\) the intensity of the green colour is maximum in the spectrum of \(R\) and the intensity of the red colour is maximum in the spectrum of \(Q.\) If \(T_P,\) \(T_Q,\) and \(T_R\) are the respective absolute temperatures of \(P,\) \(Q,\) and \(R,\) then it can be concluded from the above observations that:
1. \(T_P>T_Q>T_R\)
2. \(T_P>T_R>T_Q\)
3. \(T_P<T_R<T_Q\)
4. \(T_P<T_Q<T_R\)

A black body at \(1227^\circ\text{C}\) emits radiations with maximum intensity at a wavelength of \(5000~\mathring {A}\). If the temperature of the body is increased by \(1000^\circ\text{C},\) the maximum intensity will be observed at:
1. \(4000~\mathring {A}\)
2. \(5000~\mathring {A}\)
3. \(6000~\mathring {A}\)
4. \(3000~\mathring {A}\)

If \(\lambda_m\) denotes the wavelength at which the radioactive emission from a black body at a temperature \(T\) K is maximum, then:
1. \(\lambda_m\) is independent of \(T\)

2. \(\lambda_m \propto T\)

3. \(\lambda_m \propto T^{-1}\)

4. \(\lambda_m \propto T^{-4}\)

Wien's displacement law expresses the relation between:
 

A black body has a wavelength \(\lambda_m\) corresponding to maximum energy at \(2000~\text{K}\). Its wavelength corresponding to maximum energy at \(3000~\text{K}\) will be: