The ratio of kinetic energy of the electron for H-atom to that of He+ ion for \( n = 3 \) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{1}{4} \)
In the Bohr model the kinetic energy of the electron in orbit n of a hydrogen-like ion of atomic number Z is
\( \displaystyle K = 13.6\,\frac{Z^{2}}{n^{2}}\,\mathrm{eV} \)
For the same n the kinetic energy is proportional to Z2; hydrogen has Z = 1 and He+ has Z = 2.
\( \displaystyle \frac{K_{\mathrm{H}}}{K_{\mathrm{He^{+}}}} = \frac{1^{2}/3^{2}}{2^{2}/3^{2}} = \frac{1}{4} \)