Atomic Structure - Result Question 4
####4. The ground state energy of hydrogen atom is $-13.6 eV$. The energy of second excited state of $He^{+}$ion in $eV$ is
(a) -54.4
(b) -3.4
(c) -6.04
(d) -27.2
(2019 Main, 10 Jan II)
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Answer:
Correct Answer: 4. (c)
Solution:
- The ground state energy of $H$-atom is $+13.6 eV$.
For second excited state, $n=2+1=3$
$$ \begin{gathered} \therefore E _3\left(He^{+}\right)=-13.6 \times \frac{Z^{2}}{n^{2}} eV \quad\left[\because \text { for } He^{+}, Z=2\right] \ =-13.6 \times \frac{2^{2}}{3^{2}} eV=-6.04 eV \end{gathered} $$
