Question

Radiation 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 transitions of helium ions as they absorbs energy from the radiation?

Answer 1

Energy of radiation (E) from the hydrogen atom is given by

`E = 13.6 (1/n_1^2 - 1/n_2^2 )`

Hydrogen atoms go through transition, n = 1 to n = 2.

The energy released is given by

`E = 13.6 (1/1-1/4)`

`= 13.6xx3/4 = 10.2  eV`
For He,

Atomic no, Z = 2

Let us check the energy required for the

transition in helium ions from n = 1 to n = 2.

`therefore` n₁ =1 to n₂ = 2

Energy (E₁) of this transition is given by

`E_1 = Z^2 13.6 (1/n_1^2 - 1/n_2^2)`

= `4xx13.6(1 - 1/4)`

= 40.8 eV

E₁ > E,

Hence, this transition of helium ions is not possible.

Let us check the energy required for the transition in helium ion from n = 1 to n = 3.
`therefore n_1 =1` to `n_2 = 3`

Energy (E₂) for this transition is given by
E₂ =`Z^2 xx 13.6 (1/n_2^2 - 1/n_1^2)`

= `4xx13.6xx(1/1- 1/9)`

= 48.3 eV

It is clear that E₂ > E.

Hence, this transition of helium ions is not possible.

Similarly, transition from n₁ = 1 to n₂ = 4 is also not possible.

Let us check the energy required for the transition in helium ion from n = 2 to n=3

∴ n₁ = 2 to n₂ = 3

Energy (E₃) for this transition is given by

`E_3 = 13.6xx4(1/4 - 1/9)`

= `(20xx13.6)/36 = 7.56  ev`

Let us check the energy required for the transition in helium ion from n = 2 to n = 3.

∴ n_​​1 = 2 to n₂ = 4

Energy (E_4) for this transition is given by

`E_4 = 13.6xx4 (1/4 - 1/16)`

`= 13.6xx3/4 = 10.2  eV`

We find that

E₃ < E

E₄ = E

Hence, possible transitions are from n = 2 to n = 3 and n = 2 to n = 4.