# Homework Help: Atomic energy levels

1. Jan 7, 2006

### m00c0w

If an atom has a ground state energy level of -10.4eV then why is the ionisation energy 10.4 x 1.6 x 10^-19J ? Wouldn't that amount of energy just cause the electron to move to the highest energy level? I would have thought that the energy required to ionise the atom would be any value greater than 10.4eV? Please help!
Many thanks.

2. Jan 7, 2006

### frozen7

The ionization energy is from ground state to the infinity level.
So,
$$E = \frac {-13.6}{1^2}-\frac{-13.6}{\infty^2}$$
$$= -13.6eV$$

If my concept is not wrong, above should be the explanation.

3. Jan 7, 2006

### Hootenanny

Staff Emeritus
Energy levels are a measure of the potential energy between two particles. If two oppositly charge particles were an infinite distance apart they would have no attraction to each other and hence the potential energy between the two would be zero.

Now imagine a ball two meters above the surface of the earth. There is a potential energy due to gravity between the ball and the earth (mgh). Now bring the ball toa distance of one meter above the surface. The potential energyhas decrease. Therefore, when you have two bodies with an attractive force between them the potential energy between the two decrease with decreasing distance.

Treating the nucleus of an atom as a single particle, when the electron is an infinite distance from the nucleus, the potential energy is zero. However, if we were to bring the electron closer to the nucleus, its potential energy reduce, hence the negative energy levels.

So to ionise an atom (i.e. move the electron an infite distance from the nucleus) you have to make the potential energy zero. Therefore, you need to input an energy equal to that of the ground state.

Sorry if my prose is a bit awkward, but I hate writing. Hope it helped

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