Question

Energy of an electron in the second orbit of hydrogen atom is $E _{2} .$ The energy of electron in the third orbit of $He ^{+}$will be

• A. $\frac{9}{16} E _{2}$
• B. $\frac{16}{9} E _{2}$
• C. $\frac{3}{16} E _{2}$
• D. $\frac{16}{3} E _{2}$

Answer 1

Answer: (B)

For $2^{\text {nd }}$ orbit of H-atom
$E _{2}=\frac{-13 \cdot 6}{2^{2}} eV$
For $3^{\text {rd }}$ orbit of $He ^{+}$
$E _{3}^{ He ^{+}} =\frac{-13 \cdot 6}{3^{2}} 2^{2}$
$=\frac{-13 \cdot 6}{4} \times \frac{4}{9} \times 2^{2} $
$= E _{2} \times \frac{16}{9}=\frac{16}{9} E _{2}$