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

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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