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

Answer

D

Explanation

For the first line of Lyman series for hydrogen atom
`(hc)/(lambda_(1))=Rhc((1)/(1^(2))-(1)/(2^(2)))`
For the second line of Balmer series for a hydrogen like ion
`(hc)/(lambda_(2))=Z^(2)Rhc((1)/(2^(2))-(1)/(4^(2)))`
according to question `lambda_(1)=lambda_(2)`
`rArr ((1)/(1)-(1)/(2))=Z^(2)((1)/(4)-(1)/(16))`
`:.Z=2`