# Rutherford gold foil experiment

This question may sound silly.
What actually I understood from this experiment is that the positively charged nucleus which is in the center is responsible for the bending and reflection of the alpha rays.

Here is my question:
Why cant there be any small holes in the gold foil which might have caused this kind of behavior?

• Why would they cause deflection of the $\alpha$ particles? Bear in mind that they did not appreciate that $\alpha$ particles might diffract when this experiment was done. – bon Feb 11 '16 at 13:56
• Does that mean alpha particles cannot be diffracted by surfaces and can pierce through all kinds of surfaces the same way.. – Aadhil RF Feb 11 '16 at 14:00
• I have never actually thought about this before. I would be interested to see if $\alpha$ particle diffraction is at all significant in this situation. I might look into the experiment a bit more later and do some calculations. $\alpha$ particles may still be diffracted by appropriate sized apertures if they have the right energy. It's a question of whether it's relevant here. Obviously in a historical context they didn't know about diffraction so they came to the only (correct) conclusion. – bon Feb 11 '16 at 14:07
• If you calculate the wavelength of an MeV alpha particle, you will find that diffraction is not in the cards at all. For neutron diffraction, at 1/4 the mass, you are down in the thermal regime (<<MeV) for diffraction. And, if surfaces were a real problem, then composition analysis by Rutherford Backscattering Spectrometry (RBS) would be significantly harder than it actually is. So, by simple physics you need to "hit" some entity in the solid that is heavy to be able to have elastic backscattering. Voids will not do at all - it has to be a nucleus. – Jon Custer Feb 11 '16 at 15:02
• "hit some" ...If the alpha particles are travelling at high speeds even hitting on the like charged particles(electrons) would reflect....Am i not right?? – Aadhil RF Feb 11 '16 at 15:10

Consider that to get diffraction effects you generally need the wavelength of the diffracting particle to be related to a length scale of importance in your sample. For the moment, take it to be something on the order of an inter-atomic spacing, roughly an Angstrom.

Taking an alpha particle at 3MeV (the ones originally used were more on the order of 5MeV, depending on the source used). The de Broglie wavelength is straightforward to calculate, and turns out to be 8E-15 meters, or 8E-5 Angstroms, 4+ orders of magnitude smaller than an inter-atomic spacing. So, one can rule out diffraction as a cause of energetic alpha particle scattering.

Now, plenty of folks do use neutron scattering to measure structure in materials. The trick is that they have to be very slow neutrons, or 'thermal' neutrons. Going through the de Broglie equation for a 25 meV neutron (millielectron Volt, or basically room temperature) you get about 1.8 Angstroms - which is right there with inter-atomic spacings. Now you have diffraction from solids!

So, energetic alpha particles are not diffracting off of anything related to crystal structure. They are interacting with a strong $1/r^{2}$ central force to give the observed differential cross section for scattering. And that force is centered on something heavy so as to result in backscattering. This shows the existence of the nucleus. (Another effect can be real interactions between nuclear energy levels and the alpha particle, but that is getting in to nuclear physics, a topic for another day.)

As a follow up to some of the comments - alpha particles do indeed interact with electrons in the sample, but their mass is so small that standard kinematics shows that an alpha will not backscatter off of an electron (unless it is highly relativistic - an alpha has a rest mass of about 3.6GeV, an electron has a rest mass of about 511keV).

Reflect means to bounce back, as in a ball bouncing off a wall. The average density of an atom is very low, so the observed reflection was startling... like throwing many billiard balls at a mass of fluffy cotton candy and every now and then a ball comes bouncing back!

The explanation offered was that there must be some "hard", dense object inside that fluff... the nucleus. Electrons are effectively spread out in their orbitals, and tend to act individually (bound by electromagnetic forces). An alpha particle, massing ~4*109 eV, could not be reflected by an electron massing ~5*105 eV -- that would be like bouncing a baseball off a ping-pong ball.

Since both alpha particle (He nucleus) and gold nucleus are positively charged, and the gold nucleus is held together by powerful nuclear forces (so all its particles' masses are effectively combined to ~2*1011 eV) , it explained the reflection. Since reflection occurred only rarely, it implied that the nucleus was a small, dense target.

• This doesn't actually answer the question, which is about whether $\alpha$ particles will diffract in this situation. – bon Feb 12 '16 at 10:09
• bouncing a baseball off a ping-pong ball.....why cant a fast moving baseball change its direction when hit by a ping-pong ball??? – Aadhil RF Feb 12 '16 at 12:44
• The baseball can change direction. However, for it to bounce backwards in the center-of-mass frame from an elastic collision requires that the mass of what it is bouncing off of has to be larger. Now, conversion from center-of-mass to the lab frame throws a bit of uncertainty in to the process, but not much. Consider this - for an electron to displace an atom in a crystal lattice (i.e. transfer ~5-10eV to the atom) requires a near 1MeV incident electron (which is relativistic). – Jon Custer Feb 12 '16 at 17:34