Modern Physics 1 Question 5
4. $A He^{+}$ion is in its first excited state. Its ionisation energy is
(Main 2019, 9 April II)
(a) $54.40 eV$
(b) $13.60 eV$
(c) $48.36 eV$
(d) $6.04 eV$
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Solution:
- Energy of a hydrogen atom like ion by Bohr’s model is $E _n=-13.6 \frac{Z^{2}}{n^{2}}$
where, $Z$ =atomic number
and $n=$ principal quantum number.
For a $He^{+}$ion in first excited state,
$n=2, \quad Z=2$
$\therefore \quad E _2=-13.6 \times \frac{4}{4}=-13.6 eV$
So, it’s ionisation energy $=-\left(E _2\right)=13.6 eV$.
