The energy of a photon is given by E = hν, where ν is the frequency of radiation. Use this equation to get the dimensional formula of ‘h’.

To find the dimensional formula of Planck's constant (h), let's start with the given equation:

E = hν

Where:

E is the energy of the photon
h is Planck's constant
ν is the frequency of the radiation
Now, let's analyze the dimensions of each term.

Energy (E): The dimension of energy is given by the formula for kinetic energy or potential energy:

[E] = [M L² T⁻²]

(where M is mass, L is length, and T is time).

Frequency (ν): Frequency is the number of cycles per unit time, so the dimension of frequency is:

[ν] = T⁻¹

Now, substituting the dimensions of energy (E) and frequency (ν) into the equation E = hν:

[M L² T⁻²] = [h] × [T⁻¹]

To isolate the dimension of h, we divide both sides of the equation by T⁻¹:

[h] = [M L² T⁻²] × T

[h] = [M L² T⁻¹]

Thus, the dimensional formula of Planck's constant (h) is:

[M L² T⁻¹]