A physical quantity P has the dimensional formula [ L ⁻¹ T ⁻¹ K ⁻²] . Which of the following combinations of Stefan-Boltzmann constant ( ), Boltzmann constant ( k ) and Wien's displacement constant ( b ) has the same dimensions as P ?

Step-by-step solution

First, find the dimensional formulas of the given constants: Stefan-Boltzmann constant ( ): From E = A t T^4 , [ ] = [ M L ^2 T ⁻²] [ L ^2][ T ][ K ^4] = [ M T ⁻³ K ⁻⁴] Boltzmann constant ( k ): From E = k T , [k] = [ M L ^2 T ⁻²] [ K ] = [ M L ^2 T ⁻² K ⁻¹] Wien's displacement constant ( b ): From _ max T = b , [b] = [ L ][ K ] = [ L K ] Now, check the dimensions of the combination k⁻¹ b : [ k⁻¹ b] = [ ][b] [k] [ k⁻¹ b] = [ M T ⁻³ K ⁻⁴][ L K ] [ M L ^2 T ⁻² K ⁻¹] [ k⁻¹ b] = [ M L T ⁻³ K ⁻³] [ M L ^2 T ⁻² K ⁻¹] [ k