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Question
Calculate the energy required for the process
\[\ce{He^+_{(g)} -> He^{2+}_{(g)} + e^-}\]
The ionization energy for the H atom in the ground state is 2.18 ×10–18 J atom–1
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Solution
Energy associated with hydrogen-like species is given by,
`"E"_"n" = - 2.18 xx 10^(-18) ("Z"^2/"n"^2)"J"`
For ground state of hydrogen atom,
`triangle "E" = "E"_oo - "E"_1`
`= 0 - [-2.18 xx 10^(-18) {(1)^2/(1)^2}]`J
`triangle "E" =2.18 xx 10^(-18) "J"`
For the given process,
\[\ce{He^+_{(g)} -> He^{2+}_{(g)} + e^-}\]
An electron is removed from n = 1 to n = ∞.
`triangle "E" = "E"_oo - "E"_1`
`= 0-[-2.18 xx 10^(-18) {(2)^2/(1)^2}]`
`triangle "E" = 8.72 xx 10^(-18)` J
∴ The energy required for the process is `8.72 xx 10^(-18)`J
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