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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. |
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Answer» 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` |
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