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 ______.

1. Linear impulse
2. Angular impulse
3. Linear momentum
4. Angular momentum

Answer 1

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).