A helium atom consists of two electrons orbiting round a nucleus of charge Z=2. But the electrons do not see the full charge Z=2 of the nucleus. Each electron sees the nucleus slightly screened by the other electron so that the effective charge `Z_(eff)` seen by each electron is less than 2. The ionisation potential for a He atom in its ground state is measured experimentally to be 24.46 eV. Estimate the effective charge of the nucleus as seen by each electron in the helium ground state.

Explanation

It is known that ground state energy of hydrogen atom =-13.6eV
Energy of each electron in He ground state
`=-Z_(eff)^2xx13.6eV`
`:.` ground state energy of He atom
`=2(-Z_(eff)^2)xx13.6eV=-Z_(eff)^2xx27.2eV`
In `He^(+)` ground state, Z=2 and there is no screening because there is only one electron.
`:.` Energy of `He^(+)` ground state
`=-4xx13.6eV`
`-5.44eV`
`:.` Ionisation potential
`=[-54.4+Z_(eff)^2xx27.2],`
the exptal value of which is 24.46V
`:. -54.4+Z_(eff)^2xx27.2=24.46V,`
which gives `Z_(eff)=1.70`