A black body has maximum wavelength ' _ m ' at temperature 2000 K . Its maximum wavelength at 3000 K will be

Step-by-step solution

Wien's displacement law states that _m T = b , where b is the Wien displacement constant, _m is the peak wavelength, and T is the absolute temperature. Consequently, _m 1 T . For temperatures T₁ = 2000 K and T₂ = 3000 K, the corresponding peak wavelengths _ m1 and _ m2 satisfy _ m1 T₁ = _ m2 T₂ . Substituting the given _ m1 = _m yields _m 2000 = _ m2 3000 , from which _ m2 = _m 2000 3000 = 2 3 _m . The maximum wavelength at 3000 K is 2 3 _m , corresponding to option D.