energy levels

Question

Energy of nth Bohr orbit in hydrogen-like ion (atomic number Z) scales as:

RankGuru · Accepted Answer

According to Bohr's model, the energy of an electron in the $n$-th orbit is given by $E_n = -\frac{m e^4 Z^2}{8 \epsilon_0^2 h^2 n^2}$. For hydrogen-like ions, this can be simplified to $E_n = -13.6 \frac{Z^2}{n^2} \, 	ext{eV}$. The negative sign indicates that the electron is bound to the nucleus. The energy is directly proportional to the square of the atomic number ($Z^2$) and inversely proportional to the square of the principal quantum number ($n^2$).

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