Question

The energy of an electron in a particular orbit of ${\mathrm{Li}}^{+2}$ is $-30.6\mathrm{eV}$. What is the energy of an electron in the same orbit of ${\mathrm{Be}}^{+3}$ ?

Answer 1

The energy of an electron in the same orbit of ${\mathrm{Be}}^{+3}$:

1. Using the formula, Energy of an electron in the first Bohr orbit, ${\mathrm{E}}_0=-13.6\mathrm{ev}$.
2. The energy of an electron in n^th orbit is-
   $E_n=E_0\times \frac{Z^2}{n^2}$
3. For single electron species energy of nth orbit $\mathrm{E}=-13.6\frac{{\mathrm{Z}}^2}{{\mathrm{n}}^2}\mathrm{eV}$ where Z = atomic no. of single-electron species, n = number of orbit.
4. For ${\mathrm{Li}}^{+2}$,
   $-30.6\mathrm{eV}=-13.6\frac{3^2}{{\mathrm{n}}^2}\mathrm{eV}$
   $n=2$
5. Hence, that particular orbit of ${\mathrm{Li}}^{+2}$ is 2^nd orbit.
6. Thus, the energy of an electron in the 2^nd orbit of $B{e}^{3+},E=$$-13.6\frac{4^2}{2^2}\mathrm{eV}$.
   $\mathrm{E}=-54.4\mathrm{eV}$
7. Finally, the energy of an electron in the same orbit of ${\mathrm{Be}}^{+3}$ is -54.4 eV.