Question

The dimensions of Planck's constant are the same as the dimensions of

• A. Energy
• B. Frequency
• C. Linear Momentum
• D. Angular Momentum
• E. None of the above

Answer 1

Answer: (D)

Angular Momentum

Planck's constant, symbolized h, relates the energy in one quantum (photon) of electromagnetic radiation to the frequency of that radiation.

$h=\frac{E}{v}=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[T^{-1}\right]}=\left[M{L}^2{T}^{-1}\right]$

Angular momentum $=$ Moment of inertia $\times$ Angular velocity (Angular momentum)

$=\left[M{L}^2\right]\left[T^{-1}\right]=\left[M{L}^2{T}^{-1}\right]$

So, here we can see that both the Planck's constant and Angular momentum have the same dimensions.