Question

Calculate the ratio of wavelength of first spectral line of lyman and balmer series of hydrogen spectra

Answer 1

First line of the Balmer Series, n₂ = 2 and n₁ = 3

∵ $\frac{1}{\lambda} = R_H (\frac{1}{(n_1)^2} - \frac{1}{(n_2)^2} )$

⇒ 1/λ = R(1/4 - 1/9)

∴ λ = 1/R × 36/5

⇒ λ = 911 × 10⁻¹⁰ × 36/5 m.

λ = 6559.2 × 10⁻¹⁰ m.

For Lymen Series,

n₂ = 2 , n₁ = 1

∴ $\frac{1}{\lambda} = R_H (\frac{1}{(n_1)^2} - \frac{1}{(n_2)^2} )$

⇒ 1/λ = R(1/1 - 1/2)

λ = 1/R(2)

⇒ λ = 911 × 2 × 10⁻¹⁰ m.

⇒ λ = 1822× 10⁻¹⁰ m.

Ratio of wavelength = 6559.2 × 10⁻¹⁰/1822 × 10⁻¹⁰

= 6559.2/1822

= 18/5

Hope it helps.

Answer 2

Explanation:

Ratio of wavelength = 6559.2 × 10⁻¹⁰/1822 × 10⁻¹⁰

Ratio of wavelength = 18/5