NEET2026PhysicsUnits and DimensionsActual
Consider that _s , k_B , b represent Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of _s k_B⁻¹b is :
Options
- A[ L ⁻¹ T ⁻¹ K ⁻⁴]
- B[ L ⁻¹ T ⁻¹ K ⁻²]
- C[ L ⁻¹ K ⁻²]
- D[ L ⁻¹ T ⁻¹ K ⁻³]
Correct answer
B. [ L ⁻¹ T ⁻¹ K ⁻²]
Step-by-step solution
The dimensional formula for the Stefan-Boltzmann constant _s is obtained from the relation E = _s A t T^4 , where E is energy, A is area, t is time, and T is temperature: [ _s] = [ M L ^2 T ⁻²] [ L ^2][ T ][ K ^4] = [ M T ⁻³ K ⁻⁴] The dimensional formula for the Boltzmann constant k_B is obtained from E = k_B T : [k_B] = [ M L ^2 T ⁻²] [ K ] = [ M L ^2 T ⁻² K ⁻¹] The dimensional formula for Wien's displacement constant b is obtained from _ max T = b : [b] = [ L ][ K ] = [ L K ] Now, substituting these dimensions in