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. 1S
C. 2
D. 3

Answer

C

Explanation

Lyman series for H-ion
`(hc)/(lamda)=Rhc((1)/(1^(2))-(1)/(2^(2)))`
and for H-like ion `(hc)/(lamda)=Z^(2)Rhc((1)/(2^(2))-(1)/(4^(2)))`
`therefore ((1)/(1^(2))-(1)/(2^(2)))=Z^(2)((1)/(4)-(1)/(16))`
`(1-(1)/(4))=Z^(2)((1)/(4)-(1)/(16))`
Z=2