# Ionization energy of hydrogen

## 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???

## Answers and Replies

Matterwave
Science Advisor
Gold Member
1.4MeV is about 100,000 times too large.

I think it's because your radius appears to be 100,000 times too small.

You are right that this semi-classical model of the electron is wrong, but you can get a good estimate of the ionization energy using this. And I think that's what the question asks.