Question

The frequency of the series limit of the Balmer series of the hydrogen atoms of Rydberg’s constant R and velocity of light c is ______.

Options

• 4 Rc

• `4/"Rc"`

• Rc

• `"Rc"/4`

Answer 1

The frequency of the series limit of the Balmer series of the hydrogen atoms of Rydberg’s constant R and velocity of light c is `underlinebb("Rc"/4)`.

Explanation:

We know that the wavelength of the spectrum in a hydrogen atom is given as,

`1/lambda = R(1/n_1^2 - 1/n_2^2)`

For the series limit of the Balmer series, n₁ = 2 and n₂ = ∞

∴ `1/lambda = R[1/2^2 - 1/∞^2] ⇒ 1/lambda = R/4 ⇒ lambda = 4/R`

⇒ `c/f = 4/R`  [∵ c = fλ]

⇒ `f = (Rc)/4`