Atomic Structure Result Question 50-1
Passage Based Questions
The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $S_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state $S_2$. The state $S_2$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.
50. Energy of the state $S_1$ in units of the hydrogen atom ground state energy is
(2010)
(a) $0.75$
(b) $1.50$
(c) $2.25$
(d) $4.50$
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Answer:
Correct Answer: 50. ( c )
Solution:
- Ground state energy of electron in $H$ -atom $\left(E_{\mathrm{H}}\right)$
$ E_{\mathrm{H}}=\dfrac{k Z^2}{n^2}=k(Z=1, n=1) $
For $S_1$ state of $\mathrm{Li}^{2+}$,
$ E=\dfrac{k(3)^2}{2^2}=\dfrac{9}{4} k=2.25 k $
BETA
