If A represents Boltzmann constant, B represents Planck's constant and C represents speed of light in vacuum, then the quantity having the dimensions of A^4 B⁻³ C⁻² is

Step-by-step solution

Dimension of Boltzmann's constant A= J K = ML ^2 ~T ⁻² ~K ^1 = [ ML ^2 ~T ⁻² ~K ⁻¹ ] Dimension of Planck constant B= Js = [ ML ^2 ~T ⁻¹ ] Dimension of speed of light, C= [ LT ⁻¹ ] Desired dimension =A^4 B⁻³ C⁻² [ ML ^2 ~T ⁻² ~K ⁻¹ ]^4 [ ML ^2 ~T ⁻¹ ]⁻³ [ LT ⁻¹ ]⁻² [ M ^1 ~L ^0 ~T ⁻³ ~K ⁻⁴ ] Stefan constant ( ) is given by E= T^4 = E T^4 where, E= energy per unit area per unit time and T= absolute temperature. Dimension, = [ M L ^2 ~T ⁻² ] . [ L ^2 ][ T ] K ^4 ] = [ ML ^0 ~T ⁻³ ~K ⁻⁴ ] So, desired dimension is of St