A force F is modelled by the equation F = e^ - x^2 k T , where x is distance, k is the Boltzmann constant, and T is absolute temperature. The dimensional formula of the constant is :

Step-by-step solution

The argument of an exponential function must be dimensionless. Therefore, [ x^2 k T ] = [M^0 L^0 T^0] The term k T represents thermal energy, so its dimensional formula is [M L^2 T⁻²] . Substituting the dimensions of x and k T : [L^2] [ ] [M L^2 T⁻²] = 1 [ ] = [L^2] [M L^2 T⁻²] = [M⁻¹ T^2] The exponential term is dimensionless, so the dimensions of F must equal the dimensions of . [F] = [ ] [ ] [ ] = [ ] [F] = [M⁻¹ T^2] [M L T⁻²] = [M⁻² L⁻¹ T^4] Answer: [M⁻² L⁻¹ T^4]