Atomic Structure 1 Question 4
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4. The ground state energy of hydrogen atom is $-13.6 \mathrm{eV}$. The energy of second excited state of $\mathrm{He}^{+}$ion in $\mathrm{eV}$ is
======= ####4. The ground state energy of hydrogen atom is $-13.6 \mathrm{eV}$. The energy of second excited state of $\mathrm{He}^{+}$ion in $\mathrm{eV}$ is
3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed (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 $\mathrm{H}$-atom is $+13.6 \mathrm{eV}$.
For second excited state, $n=2+1=3$
$$ \begin{gathered} \therefore E_{3}\left(\mathrm{He}^{+}\right)=-13.6 \times \frac{\mathrm{Z}^{2}}{n^{2}} \mathrm{eV} \quad\left[\because \text { for } \mathrm{He}^{+}, Z=2\right] \ =-13.6 \times \frac{2^{2}}{3^{2}} \mathrm{eV}=-6.04 \mathrm{eV} \end{gathered} $$
