Identify the pair of physical quantities which have different dimensions:

We need to identify the pair of physical quantities that have different dimensions.

Option A: Wave number and Rydberg's constant

Wave number $$k = \frac{1}{\lambda}$$, so its dimension is $$[L^{-1}]$$.

Rydberg's constant $$R$$ also has dimension $$[L^{-1}]$$ (it appears in $$\frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$$).

Both have the same dimensions.

Option B: Stress and Coefficient of elasticity

Stress $$= \frac{F}{A}$$, dimension $$= [ML^{-1}T^{-2}]$$.

Coefficient of elasticity (Young's modulus) $$= \frac{\text{Stress}}{\text{Strain}}$$. Since strain is dimensionless, its dimension is also $$[ML^{-1}T^{-2}]$$.

Both have the same dimensions.

Option C: Coercivity and Magnetisation

Both coercivity and magnetisation have the dimension of magnetic field intensity $$H$$, which is $$[AL^{-1}]$$.

Both have the same dimensions.

Option D: Specific heat capacity and Latent heat

Specific heat capacity $$c = \frac{Q}{m \Delta T}$$, dimension $$= \frac{[ML^2T^{-2}]}{[M][K]} = [L^2T^{-2}K^{-1}]$$.

Latent heat $$L = \frac{Q}{m}$$, dimension $$= \frac{[ML^2T^{-2}]}{[M]} = [L^2T^{-2}]$$.

These have different dimensions — specific heat capacity has an extra factor of $$K^{-1}$$.

Therefore, the correct answer is Option D.