# Video: Recalling the Rutherford alpha Scattering Experiment

In the Rutherford alpha scattering experiment, which of the following statements about the deflection of alpha particles is correct? [A] Most alpha particles are deflected by more than 45°. [B] alpha particles are never deflected by more than 90°. [C] alpha particles are never deflected by less than 45°. [D] alpha particles are never deflected by more than 45°. [E] Most alpha particles are negligibly deflected.

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### Video Transcript

In the Rutherford 𝛼 scattering experiment, which of the following statements about the deflection of 𝛼 particles is correct? a) Most 𝛼 particles are deflected by more than 45 degrees. b) 𝛼 particles are never deflected by more than 90 degrees. c) 𝛼 particles are never deflected by less than 45 degrees. d) 𝛼 particles are never deflected by more than 45 degrees. e) Most 𝛼 particles are negligibly deflected.

To assess these statements, we’ll need to understand the setup and conclusions of the Rutherford 𝛼 scattering experiment, which was performed in the early 20th century by two of Ernest Rutherford’s students. Schematically, the experimental setup consists of an 𝛼 particle source that shoots a beam of 𝛼 particles at a target. The target consists of a thin layer of gold foil. And surrounding the target is a screen. The 𝛼 particles enter through a hole in the side of the screen, hit the target, and scatter. Some travel straight through, some off to the side, and some even back towards the original source.

The trajectory of the 𝛼 particles is determined when they collide with the screen, resulting in a flash of light, which is then observed with the eye. And the trajectories are recorded as angles around the circle. The Rutherford scattering experiment was originally conceived to test the current model of the atom at the time, the plum pudding model. In this model, the atom, the basic building block of matter, is assumed to consist of two parts with an analogy brought to plum pudding. The atom consists of small, negatively charged electrons embedded in a large, positively charged background, where the electrons are the plums and the background is the pudding.

In a more modern iteration, we might liken the electrons to the chocolate and the positive charge to the dough in a chocolate chip cookie. The plum pudding model also predicts that 𝛼 particles, which at the time they knew only to be subatomic and positively charged but which we now know are really helium nuclei, that is, two protons and two neutrons carrying a charge of plus two, should either pass straight through the atom or get minorly deflected. Either way, no 𝛼 particle should be deflected to a significant angle. And certainly no 𝛼 particle should bounce back off of the atom.

So those doing the experiment expected to see trajectories with little to no change. That is, all the 𝛼 particles would hit the screen right around zero degrees. And they were not expecting anything with any significant deflection and certainly nothing with a deflection greater than 90 degrees. We should note that several small deflections accumulated across hitting several atoms could build up to a large deflection. So to eliminate the probability of this happening, the experimenters used very thin target so 𝛼 particles would only hit one or two atoms as they passed through.

The observations made, however, did not conform to the predictions of the plum pudding model. Most of the 𝛼 particles that passed through the target clustered on the screen around zero as expected. However, several 𝛼 particles had large deflections, approaching and exceeding 45 degrees. A few even had deflections all the way back towards the source, certainly not within the predictions of the plum pudding model. Already, just by knowing the observations of the Rutherford scattering experiment, we can see that the correct choice is e: most 𝛼 particles are negligibly deflected. This is because most of the 𝛼 particles hit the screen around zero degrees which means that their trajectory is negligibly changed, while only a few hit the screen farther out or even all the way back towards the source.

Say we didn’t remember what observations were made, we could have still guessed the correct answer by recalling the conclusions reached as a result of the experiment. The unexpectedly large deflections of the 𝛼 particles suggested that the plum pudding model of the atom was not correct. Instead, it was suggested that atoms consist of a small, positively charged nucleus orbited at a distance by electrons. The hard, positively charged nucleus accounted for the deflection of 𝛼 particles to all angles. The electrons orbiting far out account for the fact that the volume of an atom is much larger than the volume of its nucleus. A corollary of these two conclusions is that an atom is mostly empty space.

From these conclusions, we have enough information to figure out the answer to the question. The 𝛼 particle is a helium nucleus. So it’s much smaller than the nuclei of the gold atoms making up the foil. In this new model, there are three ways that the 𝛼 particle can interact with the atom. If the 𝛼 particle arrives at the atom straight on or very near straight on, it will be deflected right back, similar to throwing a ball against a wall. If the 𝛼 particle arrives at the nucleus at a glancing angle, it will pass by and get deflected somewhat. Finally, the 𝛼 particle could miss the nucleus entirely and pass through the mostly empty space, that is, the atom.

In this case, the 𝛼 particle doesn’t deflect at all, since it doesn’t interact with the nucleus. Using this, we can immediately see that choices b, c, and d are not true. Since with a small hard nucleus, 𝛼 particles can be deflected at any angle. Specifically, trajectories that totally missed the nucleus deflect by zero degrees, which is certainly less than 45 degrees. And c is not true. And head-on trajectories that bounce straight back towards the source deflect by more than 90 degrees. So b and d are also not true. To choose between a and e, we recall that one of the conclusions of the Rutherford scattering experiment is that atoms are mostly empty space.

Therefore, most incoming 𝛼 particle trajectories completely miss the nucleus and don’t interact with it at all and therefore don’t deflect. On the other hand, even among the minority of 𝛼 particle trajectories that do interact with the nucleus, only a small portion of those actually pass close enough to deflect by more than 45 degrees. So since only a few trajectories for 𝛼 particles meet the conditions to deflect by more than 45 degrees. But most of the trajectories pass through empty space and so would be negligibly deflected. We again conclude e: most 𝛼 particles are negligibly deflected. And this time, we worked out the answer from the conclusions reached in the Rutherford scattering experiment rather than directly knowing the observations.