The Bohr radius is given by a₀ = ₀ h^2 m e^2 . Determine the dimensions of the right-hand side.

Step-by-step solution

The dimensions of the physical quantities are: Permittivity of free space, [ ₀] = [M⁻¹ L⁻³ T^4 A^2] Planck's constant, [h] = [M L^2 T⁻¹] Mass, [m] = [M] Charge, [e] = [A T] Substituting these dimensions into the right-hand side of the given equation: [ RHS ] = [ ₀] [h]^2 [m] [e]^2 [ RHS ] = [M⁻¹ L⁻³ T^4 A^2] [M L^2 T⁻¹]^2 [M] [A T]^2 [ RHS ] = [M⁻¹ L⁻³ T^4 A^2] [M^2 L^4 T⁻²] [M A^2 T^2] [ RHS ] = [M L T^2 A^2] [M A^2 T^2] = [L] Alternatively, since a₀ represents the Bohr radius, its dimension must be that of length