Question

What is the dimensional formula of Planck's constant?

Answer 1

Step 1: Definition

Planck's constant is being utilized just to describe a particle as well as wave phenomena on such an atomic scale. These are some of the causes for the creation of quantum mechanics seems to be Planck's constant.

1. Planck's constant would be a basic constant equivalent to the energy of an electromagnetic radiation's quantum split by its own frequency.
2. Planck's constant is denoted by “h”.
3. The value of h is $6.6260715\times {10}^{-34}\mathrm{J}.\mathrm{s}$

Step 2: Planck's constant

We know the formula, $\mathrm{E}=\mathrm{h\nu }$

$\mathrm{Planck}\text{'}\mathrm{s}\mathrm{constant}\left(\mathrm{h}\right)=\frac{\mathrm{Energy}\left(\mathrm{E}\right)}{\mathrm{Frequency}}$

The dimensional formula of energy is:

$\left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$ …(equation $1$)

The dimensional formula of frequency is:

$\left[{\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^{-1}\right]$ …(equation $2$)

By substituting the equation $1$ and $2$ in the above formula we get,

$\mathrm{Placnk}\text{'}\mathrm{s}\mathrm{constant}\left(\mathrm{h}\right)=\frac{\left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]}{\left[{\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^{-1}\right]}=\left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-1}\right]$

Therefore, the dimensional formula of Planck's constant is $\left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-1}\right]$.