A hydrogen-like atom with atomic number $Z$ is in an excited state of principal quantum number $n$. It emits a photon of wavelength $\lambda$ when it transitions to the ground state. If the recoil momentum of the atom is $p$, what is the expression for $Z$ in terms of $\lambda$, $p$, and Rydberg constant $R$?

1. A.$Z=\sqrt{\frac{h}{\lambda R(1-1/n^2)}}$
2. B.$Z=\sqrt{\frac{p}{hR(1-1/n^2)}}$
3. C.$Z=\sqrt{\frac{p\lambda }{hR(1-1/n^2)}}$
4. D.$Z=\sqrt{\frac{h\lambda }{pR(1-1/n^2)}}$