The wavelength of spectral line obtained in the spectrum of Li²⁺ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is

The wavelength of spectral line obtained in the spectrum of Li2+ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is

Q. The wavelength of spectral line obtained in the spectrum of Li²⁺ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is

(A) 1.14 × 10⁻⁶ cm

(B) 2.28 × 10⁻⁶ cm

(D) 2.28 × 10⁻⁷ cm

Correct Answer: 1.14 × 10⁻⁶ cm

Explanation

Let the two energy levels be n₁ and n₂.

Given:

n₁ + n₂ = 4 n₁ − n₂ = 2

Solving the above equations:

n₁ = 3 n₂ = 1

For hydrogen-like ions, the wavelength is given by:

1 / λ = R Z² (1 / n₂² − 1 / n₁²)

For Li²⁺, atomic number Z = 3.

Substituting values:

1 / λ = R × 9 (1 / 1² − 1 / 3²)

1 / λ = R × 9 (1 − 1/9)

1 / λ = R × 9 × 8/9 1 / λ = 8R

Using R = 1.097 × 10⁵ cm⁻¹,

1 / λ = 8 × 1.097 × 10⁵ 1 / λ = 8.776 × 10⁵ cm⁻¹

λ = 1 / (8.776 × 10⁵) λ ≈ 1.14 × 10⁻⁶ cm

Hence, the wavelength of the spectral line is 1.14 × 10⁻⁶ cm.

Explanation

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