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Question:

What would be the maximum wavelength for the Brackett series of the hydrogen spectrum?

74483˚A

40519˚A

22790˚A

18753˚A

Solution:

Wavelength: 1/λ = R(1/n₁² - 1/n₂²)Z²
where, R = 109737.3 cm⁻¹; For hydrogen spectrum, Z = 1
For maximum wavelength of Brackett series, n₁ = 4 and n₂ = 5
∴ 1/λₘ = 109737.3 × (1/4² - 1/5²) × 1² cm⁻¹;
λₘ = 0.00040519 cm = 40519 Å