Question

Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on He⁺ ions in n = 1 and n = 2 states. The possible transition of helium ions as they absorb energy from the radiation is ______.

विकल्प

• n = 2 → n = 3

• n = 1 → n = 4

• n = 2 → n = 5

• n = 2 → n = 4

Answer 1

Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on He⁺ ions in n = 1 and n = 2 states. The possible transition of helium ions as they absorb energy from the radiation is n = 2 → n = 4.

Explanation:

Given: The incident radiation is from the transition n_i = 2 to n_f = 1 of hydrogen atoms, and it is incident on He⁺ ions in states n = 1 and n = 2.

To find: He⁺ ion transitions are possible.

Radiation energy emitted by hydrogen atoms (Z = 1): 

E = `13.6(Z)^2(1/n_f^2 - 1/n_i^2)eV`

E = `13.6(1/1 - 1/4)` = 10.2 eV

Electron energy levels in the He⁺ (Z = 2) ion:

`E_n = (13.6(Z^2))/n^2`

E₁ = -54.4 eV, E₂ = -13.6 eV,

E₃ = -6.04 eV, E₄ = -3.4 eV

We can see:

E₂ - E₄ ≈ E.

A He⁺ ion will undergo the transition n = 2 → n = 4 as a result of a photon with energy E = 10.2 eV.