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
- A.linear momentum
- B.angular momentum
- C.displacement
- D.torque
Correct answer
Explanation
The correct answer is B, angular momentum. Planck's constant has the dimensions [ML²T⁻¹], exactly those of angular momentum.
From E = hf, h = E / f. Energy has dimensions [ML²T⁻²] and frequency has [T⁻¹], so h has [ML²T⁻²] ÷ [T⁻¹] = [ML²T⁻¹], with the SI unit joule-second. Angular momentum is moment of inertia times angular velocity, or mass times velocity times distance, which also gives [ML²T⁻¹]. The link is not a coincidence: in Bohr's model the angular momentum of an electron is a whole-number multiple of h/2π. Planck's constant is about 6.626 × 10⁻³⁴ J s.
A is wrong: linear momentum, mass times velocity, has dimensions [MLT⁻¹].
C is wrong: displacement has dimensions of length only, [L].
D is wrong: torque has the dimensions of energy, [ML²T⁻²], not of energy times time.
Exam tip: Planck's constant and angular momentum share [ML²T⁻¹]; torque and work share [ML²T⁻²].
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