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:

  1. 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 $=-\left(E _2\right)=13.6 eV$.



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