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) = RZ^(2) ((1)/(n_(1)^(2))- (1)/(n_(2)^(2)))`
Given `therefore R(1)^(2) (1- (1)/(4))= RZ^(2) [(1)/(4)- (1)/(16)]`
`rArr (3)/(4)= (3Z^(2))/(16) rArr Z= 2`