An electron is moving in an orbit of circumference 14.92`Å` in `He^(+)` . Calculate
(a) Energy of electron in this orbit
(b) Ionisation Energy of `He^(+)`
(c ) Separation energy

Explanation

Circumference `=2pir_(n)`
`r_(n)=(14.92)/( 2 xx 3.14) ` ....(i)
`_(rn) = 0.529(n^(2))/( Z) ` ....(ii)
`implies( 14.92)/( 2 xx 3.14 ) = 0.529 (n^(2))/(2)`
`implies n^(2)=( 14.92 xx 2)/( 0.529 xx 2 xx 3.14)`
`impliesn^(2) = 9`
`implies n=3`
(a) Energy of `e^(-)` in this orbit
`E_(n)= - 13.6 (Z^(2))/( n^(2))eV`
`E_(3)= -13.6 (2^(2))/( 3^(2))eV`
`E_(3) = 13.6xx ( 4)/( 9) = -6.04 eV`
(b) Ionisation Energy
`I.E= E_(oo) -E_(1)`
`=0-(-13.6( 2^(2))/( 1^(2)))`
`= 54.4 eV`
(c ) Separation Energy
`E_("Separation") = E_(oo) - E_("excited")`
`E_("separation") = 0- E_("excited")`
`= 0-( - 6.04)`
`= 6.04eV`