A hydrogen like ion having wavelength difference between first Balmer and Lyman series equal 593 Å has Z equal to

Options

A. 2
B. 3
C. 4
D. 1

Answer

B

Explanation

As, `(1)/(lamda)=RZ^(2)[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]`
`implies Delta lamda=(1)/(RZ^(2)((1)/(4)-(1)/(9)))-(1)/(RZ^(2)((1)/(1)-(1)/(4)))`
`implies 593=(36)/(5RZ^(2))-(4)/(3RZ^(2))`
`implies Z^(2)=(88)/(15Delta lamda)`
`=(88)/(15(1.097xx10^(7))(593xx10^(-10)))=9`
`implies Z=3`