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:

  1. The ground state energy of $H$-atom is $+13.6 eV$.

For second excited state, $n=2+1=3$

$$ \begin{gathered} \therefore E _3\left(He^{+}\right)=-13.6 \times \frac{Z^{2}}{n^{2}} eV \quad\left[\because \text { for } He^{+}, Z=2\right] \ =-13.6 \times \frac{2^{2}}{3^{2}} eV=-6.04 eV \end{gathered} $$



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