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## Homework Statement

Estimate the energy of an electron in a hydrogen atom and hence deduce an approximate formula for the ionization energy of hydrogen. How accurate is your formula?

## Homework Equations

Don't know but it is in the field of quantum mechanics

## The Attempt at a Solution

Ionisation Energy is energy required to remove an electron.

Electrostatic Potential (energy per unit charge) V=q/(4πε_0 r)= e/(4πε_0 r)

For a Bohr atom (Z=1), energy required to remove an electron from the atom with a nucleus of charge e and a radius r0 is the Electrostatic Potential Energy:

PE=qV = e^2/(4πε_0 r)×1/e

=(1.6×10^(-19))/(4π×8.85×10^(-12)×10^(-15) )

=1.4MeV

The equation estimates the distance of the electron from the proton in the nucleus as a precise value – this is not the case. An electron’s position is given by a wave-function probability density and it is in effect occupying the whole of the atom at once.

IS ANY OF THIS RIGHT?