Chemistry

The Bohr model treats the electron as orbiting the nucleus in a stable state where the electric force provides exactly the centripetal force needed. For $\mathrm{He}^+$, the key is that the nuclear charge is $Z = 2$, which strengthens the attraction and pulls the electron faster than in hydrogen. Set up the force balance equation and use the Bohr quantization condition ($mvr = n\hbar$) to solve for velocity without needing the radius explicitly.

The Bohr model treats the electron as orbiting the nucleus in a stable state where the electric force provides exactly the centripetal force needed. For $\mathrm{He}^+$, the key is that the nuclear charge is $Z = 2$, which strengthens the attraction and pulls the electron faster than in hydrogen. Set up the force balance equation and use the Bohr quantization condition ($mvr = n\hbar$) to solve for velocity without needing the radius explicitly.