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. 2
B. 3
C. 4
D. 1

Answer

A

Explanation

`(1)/(lamda_(1))=R((1)/(1^(2))-(1)/(2^(2)))=(3R)/(4)`
`(1)/(lamda_(s))=R((1)/(1^(2))-(1)/(4^(2))=(3R)/(16)Z^(2)`
`lamda_(1)=lamda_(2) implies Z^(2)=4 implies Z=2`