Match List-I with List-II, where h , c , k_B , _s , b , and T represent Planck's constant, speed of light, Boltzmann constant, Stefan-Boltzmann constant, Wien's displacement constant, and temperature, respectively. List-I List-II A. h c k_B T I. [ M L ⁻¹ T ⁻²] B. _s T^4 c II. [ L T ⁻¹] C. b k_B h III. [ M ^0 L ^0 T ^0] D. _s b^4 h c^2 IV. [ L ] Choose the correct answer from the options given below:

Step-by-step solution

Let us find the dimensional formula for each expression in List-I. A. h c k_B T : [h c] = [ M L ^2 T ⁻¹] [ L T ⁻¹] = [ M L ^3 T ⁻²] [k_B T] = Energy = [ M L ^2 T ⁻²] [ h c k_B T ] = [ M L ^3 T ⁻²] [ M L ^2 T ⁻²] = [ L ] (Matches IV) B. _s T^4 c : [ _s T^4] = Power per unit area = [ M L ^2 T ⁻³] [ L ^2] = [ M T ⁻³] [c] = [ L T ⁻¹] [ _s T^4 c ] = [ M T ⁻³] [ L T ⁻¹] = [ M L ⁻¹ T ⁻²] (Matches I) C. b k_B h : [b] = [ L K ] [k_B] = [ M L ^2 T ⁻² K ⁻¹] [b k_B] = [ M L ^3 T ⁻²] [h] = [ M L ^2 T ⁻¹] [ b k_B h ] = [ M L ^3