Radition coming from transition n = 2 to n =1 of hydrogen atoms falls on helium ions in n =1 and n =2 states. What are the possible transit ions of helium ions as they absorb energy from the radition ?

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Solution

From trasitions n = 2 to n = 1

E = 13.6 $(\frac{1}{1} - \frac{1}{4})$

= $13.6 \times \frac{3}{4} = 10.2 e V$

Let the transitions possible on He

n = 1 to 2

$E_{1} = 4 \times 13.6 (1 - \frac{1}{4})$

= 40.8 e V

$E_{1} > E,$ Hence it is not possible

n = 1 to n = 3

$E_{2} = 4 \times 13.6 (1 - \frac{1}{9})$

= 48.3 e V

$E_{2} > E .$ Hence impossible

Similary, n = 1 to n = 4

is also not possible

n = 2 to n =3

$E_{3} = 13.6 \times 4 (\frac{1}{4} - \frac{1}{9})$

= $\frac{20 \times 13.6}{36} = 7.56 e V$

As $E_{3} < E a n d E_{4} = E$

Hence $E_{3}$ and $E_{4}$ can be possible

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