Atomic Structure Result Question 4
4. The ground state energy of hydrogen atom is $-13.6$ eV . The energy of second excited state of $\mathrm{He} {+}$ ion in eV is
(2019 Main, 10 Jan II)
(a) $-54.4$
(b) $-3.4$
(c) $-6.04$
(d) $-27.2$
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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(\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} $
BETA
