The dimensions of Planck constant $h$ are equivalent to those of which of the following?

Solution

1. The energy of a photon is given by $E=hf$, where $f$ is frequency.
2. Rearranging gives $h=E/f$.
3. Since frequency has dimensions of $T^{-1}$, the dimensions of $h$ are $[M{L}^2{T}^{-2}]/[T^{-1}]=[M{L}^2{T}^{-1}]$.
4. Angular momentum $L=mvr$ has dimensions $[M][L{T}^{-1}][L]=[M{L}^2{T}^{-1}]$.
5. Hence the answer is (C).