Discussion
The dimensions of Planck's constant are the same as those of
Answer: D
Planck's constant has the dimensions of angular momentum.
From \(E = h\nu\), \(h = \frac{E}{\nu}\), so its unit is J s and its dimensions are \([ML^{2}T^{-2}] \times [T] = [ML^{2}T^{-1}]\). Angular momentum \(L = mvr\) has dimensions \([M][LT^{-1}][L] = [ML^{2}T^{-1}]\), the same.
Energy is \([ML^{2}T^{-2}]\), power \([ML^{2}T^{-3}]\), angular frequency \([T^{-1}]\) and linear momentum \([MLT^{-1}]\); none matches. Bohr's rule \(mvr = \frac{nh}{2\pi}\) is a reminder that \(h\) and angular momentum share units.
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