In the relation E = e^ - z k_B T , E is energy, z is distance, k_B is the Boltzmann constant and T is temperature. The dimensional formula of h (where h is Planck's constant) is the same as that of :

Step-by-step solution

According to the principle of homogeneity of dimensions, the exponent z k_B T must be dimensionless. [ z k_B T ] = [ M ^0 L ^0 T ^0] The dimensional formula for k_B T (thermal energy) is [ M L ^2 T ⁻²] . Therefore, [ ] = [k_B T] [z] = [ M L ^2 T ⁻²] [ L ] = [ M L T ⁻²] From the given relation, the dimension of E is the same as that of . [ ] = [ ] [E] = [ M L T ⁻²] [ M L ^2 T ⁻²] = [ L ⁻¹] The dimensional formula of Planck's constant h is [ M L ^2 T ⁻¹] . Now, finding the dimension of h : [ h] = [ L ⁻¹] [ M L ^2 T ⁻