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Question
Photon is quantum of radiation with energy E = h ν where ν is frequency and h is Planck’s constant. The dimensions of h are the same as that of ______.
- Linear impulse
- Angular impulse
- Linear momentum
- Angular momentum
Solution
b. Angular impulse
d. Angular momentum
Explanation:
We know that the energy of radiation, E = hv. So, we have to compare / with dimensional formula of each option.
`[h] = ([E])/([v]) = ("Force" xx "Displacement")/"Frequency"`
= `([ML^2T^-2])/([T^-1]) = [ML^2T^-1]`
a. Dimension of linear impulse
`[I] = [Ft] = [MLT^-2][T] = [MLT-1]`
where t is the time interval.
b. Dimension of angular impulse
`[J] = [Iω] = [ML^2][T^-1] = [ML^2T^-1]`
c. Dimension of linear momentum
`[P] = [mv] = [M][LT^-1] = [MLT^-1]`
d. Dimension of angular momentum
`[L] = [mvr] = [M][LT^-1][L] = [ML^2T^-1]`
Hence, the dimension of angular impulse and angular momentum is the same as Planck's constant (h).
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