Question

A mixture, of hydrogen (H) and singly ionised helium (He⁺), has the H and He⁺ ions excited to their respective first excited states. Due to collosions, H atoms transfer their entire excitation energy to the He⁺ ion. Applying Bohr’s model, the quantum number, n, of the finally populated state of He⁺ ions, is

(1) 2

(2) 3

(3) 4

(4) 5

Answer 1

Correct option :  (3)

Explanation :

Excitation energy gained by the H–atom, in the first excited state (i.e. n = 2), is 

E₂ – E₁ = (13.6 – 3.4) eV = 10.2 eV

For He⁺ ion, (z = 2); therefore, its energy, in an, excited state (n = n), is

∴ The energy, of He⁺ ion, is the first excited state (i.e., n = 2), is E'₂ = -13.6 eV

The energy E", of the He⁺ ion, after collosion with H–atoms; 

E" - E'₂ + 10.2 Ev = - 3.4 eV

Let n be the quantum number of state, corresponding to an energy of –3.4 eV, in the He⁺ ion. Then