Question

If the frequency of the revolution of electron in ground state of H atom is f,then the frequency of revolution of 2 nd electron in Li++ ion is
A) f/2
B) 3f
C) f
D) f/3

Answer 1

Given : If the frequency of the revolution of electron in ground state of H atom is f.

To find : The frequency of revolution of 2nd electron in Li⁺⁺ ion.

solution : frequency, f = velocity of electron/path length of one revolution

⇒v/2πr

we know, velocity of electron, v ∝ Z/n

and radius of nth orbit, r ∝ n²/Z

so frequency, f ∝ (Z/n)/(n²/Z) = Z²/n³

i.e., f₁/f₂ =(Z₁/Z₂)²(n₂/n₁)³

⇒f/f₂ = (1/3)² × (3/1)³

⇒f/f₂ = 3

⇒f₂ = f/3

Therefore the frequency of revolution of 2nd electron in Li⁺⁺ ion is f/3.