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. 4
B. 1
C. 2
D. 3

Answer

C

Explanation

Lyman series of H-atom we, can write
`(hc)/(lambda)=Rhc((1)/(1^(2))-(1)/(2^(2)))`
where, symbols hav their usual meaning. And for second line of Balmer series f H-like ion
`" " (hc)/(lambda)=Z^(2)Rhc((1)/(2^(2))-(1)/(4^(2)))`
Therefore ` ((1)/(2^(2))-(1)/(2^(2)))=Z^(2)((1)/(4)-(1)/(16))`
`" " (1-(1)/(4))=Z^(2)((1)/(4)-(1)/(16))rArrZ=2.19=2`