Discussion
The dimensions of ratio of energy to Planck's constant are those of
Answer: C
Energy divided by Planck's constant has the dimensions of frequency.
From \(E = h\nu\), \(\frac{E}{h} = \nu\). Dimensionally, h is energy times time (J s), so
\[ \begin{aligned} \frac{[E]}{[h]} &= \frac{[\text{ML}^{2}\text{T}^{-2}]}{[\text{ML}^{2}\text{T}^{-1}]} \\ &= [\text{T}^{-1}] \end{aligned} \]
That is the dimension of frequency. Time is the reciprocal. Planck's constant itself has the same dimensions as angular momentum, which is why angular momentum is a natural trap, but the ratio E/h is not angular momentum. Velocity and linear momentum include length and mass, which cancel here.
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