The wavelength of the first line of Lymasn series for hydrogen atom is equal

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The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number Z of hydrogen like ion is

Options

(a) 3
(b) 4
(c) 1
(d) 2

Correct Answer:

2

Explanation:

For first line of Lyman series of hydrogen
hc/λ₁ = Rhc (1/1² – 1/2²)
For second line of Balmer series of hydrogen like on
hc/λ₂ = Z²Rhc (1/2² – 1/4²)
By eq. λ₁ = λ₂
(1/1 – 1/2) = Z² (1/4 – 1/16) or Z = 2

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Topics: Atoms and Nuclei (136)
Subject: Physics (2479)

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