Dimensional Formula of Planck’s Constant

In the above formula,

To derive the dimensional formula of Planck’s constant (ℎ), we’ll use the formula

Energy[E]= Plank’s constant (h) × Frequency(ν) ….(1)

The dimensional formula for energy (E) is given by the below formula

E = [ML²T^-2]

Dimensional Formula of Frequency is given as

Frequency = 1/T = [T^-1]

Now, let’s substitute the dimensional formulas of Energy and Frequency in equation (1), we get

ML²T^-2 = [h] × [T^-1]

Now, isolate the dimensional formula of ℎ by rearranging the equation:

h = [ML²T^-2] / [T^-1]

After simplifying,

[h] = ML²T^-1

So, the derived dimensional formula for Planck’s constant (ℎ) is ML²T^-1.