As per the Wien's displacement law, the spectral distribution of the energy emitted at a given temperature has

The correct option is 4

Concept:

Wien's displacement law is a principle in physics that states that the wavelength at which the intensity of radiation from a black body (an idealized physical body that absorbs all incident electromagnetic radiation) is at a maximum, and is inversely proportional to the temperature of the body.

In terms of the spectral distribution of black body radiation, this means that there is a particular wavelength at which the emitted radiation reaches a peak, i.e., a definite maximum. As the temperature of the black body increases, this peak emission shifts towards shorter wavelengths.

So option 4) is correct. As temperature increases, the maximum shifts to shorter wavelengths, which is a direct consequence of the Wien's displacement law. This law is crucial for measurements of an object's temperature based on the spectrum of its thermal emissions, such as in the case of stars in astrophysics.