The energy, E, of a photon can be expressed as E=hf where f is the frequency and h is Planck's constant. The dimensions of h are the same as that of

The energy of a photon is given by E = hf. To find the dimensions of Planck's constant (h), we rearrange the formula to h = E/f. Energy (E) has the dimensional formula [ML"T⁻"], and frequency (f), being the reciprocal of time, has the dimension [T⁻!]. Dividing these yields the dimensions for h as [ML"T⁻!]. Angular momentum (L) is defined as the product of linear momentum (mv) and radius (r), resulting in dimensions [M][LT⁻!][L] = [ML"T⁻!]. Thus, Planck's constant and angular momentum share the same dimensions. In contrast, linear momentum is [MLT⁻!], torque is [ML"T⁻"], and displacement is [L]. The unit for both h and angular momentum is Joule-seconds (J!s).

Sources

1. [1] https://www.sciencedirect.com/topics/mathematics/angular-momentum