# Bohr's hydrogen model confusion

As per Bohr model for hydrogen atom,energy of $$n^{th}$$ electron orbital is given by $$\dfrac{-13.6}{n^2}$$ eV.

Energy of electron in the first orbit will be $$-13.6$$ eV and in second orbit will be $$-3.4$$ eV. For transition, the electron requires $$10.2$$ eV to be given. This will increase the potential energy of the electron but the potential energy of the nucleus should also increase as two oppositely charge particle separation increases.

From where does that nucleus acquire that energy?

A quick correction, the $$E=-13.6eV/n^2$$ is the total energy not the potential energy. The total energy is the sum of the kinetic energy $$T$$ and potential energy $$V$$, and the kinetic and potential energy are related by the virial theorem $$2T = -V$$.
The potential energy is that of the system, not just electron. The potential energy of two charges is just $$-q_1q_2/4\pi \epsilon_0 r$$, it isn't the sum of two terms.