Question

Let the series limit for Balmer series be 'λ₁' and the longest wavelength for Brackett series be 'λ₂'. Then λ₁ and λ₂ are related as ______.

Options

• λ₂ = 1.11 λ₁

• λ₁ = 0.09 λ₂

• λ₂ = 0.09 λ₁

• λ₁ = 1.11 λ₂

Answer 1

Let the series limit for Balmer series be 'λ₁' and the longest wavelength for Brackett series be 'λ₂'. Then λ₁ and λ₂ are related as λ₂ = 0.09 λ₁.

Explanation:

We know,

`1/lambda = "R"(1/2^2 - 1/"n"^2)` for Balmer series

`1/lambda = "R"(1/4^2 - 1/"n"^2)`  for Brackett series

Now, `1/lambda_1 = "R"/4`

`1/lambda_2 = "R"[1/16 - 1/25] = "R"[(25 - 16)/(16 xx 25)] = "9R"/(16 xx 25)`

∴ `lambda_1/lambda_2 = "R"/4 xx (16 xx 25)/"9R" = 100/9`

∴ `9/100 xx lambda_1 = lambda_2`

∴ λ₂ = 0.09 × λ₁