Question

The frequencies for series limit of Balmer and Paschen series respectively are 'v₁' and 'v₃'. If frequency of first line of Balmer series is 'v₂' then the relation between 'v₁', 'v₂' and 'v₃' is ______.

Options

• v₁ - v₂ = v₃

• v₁ + v₃ = v₂

• v₁ + v₂ = v₃

• v₁ - v₃ = 2v₁

Answer 1

The frequencies for series limit of Balmer and Paschen series respectively are 'v₁' and 'v₃'. If frequency of first line of Balmer series is 'v₂' then the relation between 'v₁', 'v₂' and 'v₃' is v₁ - v₂ = v₃.

Explanation:

Using v = nλ, `1/lambda="n"/"v"`

⇒ `1/lambda="R"(1/"n"_1^2-1/"n"_2^2)` 

⇒ v = Rc`(1/"n"_1^2-1/"n"_2^2)` 

∴ v₂ Rc`(1/2^2-1/"3"^2)` 

= Rc`(1/4-1/9)`   ...(i)

v₁ = Rc`(1/2^2)="Rc"/4`

v₃ = Rc`(1/3^2)="Rc"/9`

⇒ v₁ - v₃ = Rc`(1/4-1/9)`    ...(ii)

From eqs. (i) and (ii),

v₁ - v₃ = v₂ ⇒ v₁ - v₂ = v₃