Energy of an electron in a one-electron system can be calculated as
`E_(n) = (-2.18 xx 10^(-18) Z^(2))/(n^(2))`
Which of the following correctly states the relationship between the n=2 level of `He^(+)` atom (Z=2) and n=2 level of `Li^(2+)` ion (Z=3)?

Options

A. `E_(He^(+)) = (9)/(4)E_(Li^(2+))`
B. `E_(He^(+)) = (4)/(9) E_(Li^(2+))`
C. `E_(He^(+)) = (9)/(2)E_(Li^(2+))`
D. `E_(He^(+)) = (2)/(9)E_(Li^(2+))`

Answer

B

Explanation

`E_(He^(+)) = (K(2)^(2))/((2)^(2)) = k`
`E_(Li^(2+)) = (K(3)^(2))/((2)^(2)) = (9)/(4)K`
`rArr E_(He^(+)) = (4)/(9) E_(Li^(2+))`