Question

The dimensions of Planck constant equals to that of

• A. energy
• B. momentum
• C. angular momentum
• D. power

Answer 1

The Correct Option is C

The Planck constant is a fundamental constant in physics that is pivotal in the formulation of quantum mechanics. Its dimensions play a crucial role in understanding the physics of very small particles like electrons and photons.

Let's explore the dimensions of the Planck constant and compare them to those of the given options.

1. The Planck constant (h) is defined in terms of energy (E) and frequency (v) through the relation:

   E = hv

   We can express energy in terms of mass (M), length (L), and time (T):

   [E] = [M][L]^2[T]^{-2}

   The frequency (v) is the reciprocal of time, thus:

   [v] = [T]^{-1}

   Plugging these into the equation, the dimensions of the Planck constant (h) are:

   [h] = [E][v]^{-1} = [M][L]^2[T]^{-2}[T] = [M][L]^2[T]^{-1}

2. Now let's compare this with the dimensions of angular momentum. Angular momentum (L) in physics is given by:

   L = I\omega (where I is the moment of inertia and \omega is angular velocity)

   Moment of inertia, I, has dimensions:

   [I] = [M][L]^2

   Angular velocity (\omega) has dimensions:

   [\omega] = [T]^{-1}

   Thus, the dimensions of angular momentum are:

   [L] = [M][L]^2[T]^{-1}

As we can see, the dimensions of the Planck constant ([M][L]^2[T]^{-1}) match exactly with those of angular momentum, confirming that the Planck constant has the same dimensions as angular momentum.

Conclusion: The Planck constant equals the dimension of angular momentum.