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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

1. 3
2. 4
3. 1
4. 2

Correct answer: 2

Solution

The wavelength of the first line of the Lyman series for hydrogen corresponds to a transition from n=2 to n=1. For the second line of the Balmer series, the transition is from n=4 to n=2. Using the Rydberg formula and equating the wavelengths, the atomic number Z of the hydrogen-like ion is found to be 2.

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