Energy of an electron in the 2nd orbit of hydrogen atom is E and the energy of electron in 3rd orbit of He+ will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (16 ÷ 9) E
In the Bohr model of a hydrogen-like ion, the energy of the electron in the nth orbit is proportional to \( Z^{2}/n^{2} \).
\( \displaystyle E_n = -13.6\,\frac{Z^{2}}{n^{2}}\,\mathrm{eV} \)
\( \displaystyle E = E_{\mathrm{H}}(n = 2) = -13.6 \times \frac{1^{2}}{2^{2}}\,\mathrm{eV} = -3.4\,\mathrm{eV} \)
\( \displaystyle E_{\mathrm{He^{+}}}(n = 3) = -13.6 \times \frac{2^{2}}{3^{2}}\,\mathrm{eV} \approx -6.04\,\mathrm{eV} \)
\( \displaystyle \frac{E_{\mathrm{He^{+}}}}{E} = \frac{2^{2}/3^{2}}{1^{2}/2^{2}} = \frac{16}{9} \)
So the energy in the third orbit of He+ is \( \frac{16}{9}E \).