Imagine removing one electron from $He^4$ and $He^3$. Their energy levels,as worked out on the basis of the Bohr model,will be very close. Explain why?

(N/A) Both ${ }_{2} He^{3}$ and ${ }_{2} He^{4}$ are isotopes of helium.
When one electron is removed from each,they both become hydrogen-like ions $(He^+)$ with a single electron.
The energy levels of a hydrogen-like ion are given by the formula $E_n = -\frac{Z^2 R_y}{n^2}$,where $Z$ is the atomic number and $R_y$ is the Rydberg constant.
Since both isotopes have the same atomic number $Z = 2$,their energy levels are identical in the ideal Bohr model.
However,the slight difference in mass between the nuclei of $He^3$ and $He^4$ leads to a very small difference in the reduced mass of the electron-nucleus system,which is why their energy levels are very close but not perfectly identical.