# Rutherfords experiment gold foil

I know there are many similar questions to this but didn't find one specifically like this please refer me to one if there is one already.

One component of his experimental set-up used gold foil, Au.

What change could have happened if he'd used Lithium foil instead what would be some observations he would've seen?

• The gist is that the deflection at any given angle would be vastly smaller. – MaxW May 24 at 6:40

Lithium will be oxidized in a moment, as it is very reactive and unstable on the air. Foil should be very thin, gold is very good to make thin foils.

Also, lithium has 2 stable isotopes. Which one do you mean?

• Litium $$\frac{7}{3}$$ – Ineedhelp May 24 at 8:54

There wouldn't have been large changes, the "angle spread" would have been different and the scattering probabilities.

If you want to know how exactly, you need to look up the differential cross section for electron lithium scattering. I can't guide you where to find it but it should certainly available somewhere

Aside of the pedantic issues of isotopes and oxidation, I guess what you're really asking is what would be different if we scattered alpha-particles off a much lighter nucleus.

The important aspect of the Rutherford Scattering Formula is that the scattering rate at any given angle $$\propto Z^2$$

So reducing the atomic number from 79 to 3 will reduce the rate by a factor of about 700. Since the rate is already quite low at the large angles where Rutherford scattering is notable, the effect would practically disappear.

From the gold foil experiment Rutherford was able to estimate the closest approach of an alpha to the gold nucleus by equating the initial kinetic energy of the alpha to the electric potential energy of the gold nucleus and alpha system at closet approach.
The experimental data was consistent with the theoretical predictions which were based on the assumption the only force between an alpha particle and a nucleus was the Coulomb repulsive force obeying the inverse square law.
The distance of closest approach gave an upper bound to the radius of the nucleus.

Soon after the gold foil experiment, other experiments were performed with other metal being used as targets and it was found that as the mass of a nucleus decreased scattering angles were more probable than for a target made of gold.
Again the assumption that the only force of interaction was the Coulomb repulsive force was seen to be valid because the experimental data agreed with the theoretic predictions except for large angle deflections.
The scattering angle increases as an alpha particle comes closer to a nucleus.
The departure of the experimental data from the theoretical predictions was thought to be be due to an alpha "touching" a nucleus with the result that there was a second force acting between an alpha and a nucleus.
Noting when experiment and theory did not agree enable an estimate to be made for the radius of a nucleus.

All other things being equal, using Lithium as a target would result in a greater probability of smaller angles of deflection and a greater probability of large angle deflections departing from theoretical predictions, based on the Coulomb force being the only force of interaction between an alpha and a nucleus, because for a given energy of alpha particles an alpha's nearest approach to a lithium nucleus is smaller than that for a gold nucleus.