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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?
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Solution
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.
∴ n1 = 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.
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