1. We compare dimensions of each pair.

A pair has different dimensions only if their dimensional formulas are not the same.

2. Option A: Wave number and Rydberg's constant

• Wave number = number of waves per unit length $[\text{wave number}] = L^{-1}$
• Rydberg's constant appears in $\frac{1}{\lambda} = R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$ so $[R] = L^{-1}$

So both have same dimensions.

3. Option B: Stress and Coefficient of elasticity

• Stress = force/area $[\text{stress}] = \frac{[F]}{[A]} = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2}$
• Coefficient of elasticity (modulus of elasticity) = stress/strain

Since strain is dimensionless, $[\text{coefficient of elasticity}] = [\text{stress}] = ML^{-1}T^{-2}$

So both have same dimensions.

4. Option C: Coercivity and Magnetisation

• Magnetisation $M$ has unit magnetic dipole moment per unit volume. Its SI unit is $A/m$.
• Coercivity $H_c$ is magnetic field intensity required to reduce magnetisation to zero. Its SI unit is also $A/m$.

Hence, $[\text{coercivity}] = [\text{magnetisation}]$

So both have same dimensions.

5. Option D: Specific heat capacity and Latent heat

• Specific heat capacity: $c = \frac{Q}{m\,\Delta T}$ So, $[c] = \frac{ML^2T^{-2}}{M\Theta} = L^2T^{-2}\Theta^{-1}$

• Latent heat (specific latent heat): $L = \frac{Q}{m}$ So, $[L] = \frac{ML^2T^{-2}}{M} = L^2T^{-2}$

These are different because specific heat capacity contains $\Theta^{-1}$, while latent heat does not.

6. Conclusion

The pair having different dimensions is: $\boxed{\text{D: Specific heat capacity and Latent heat}}$