The Famous Scattering Experiment From Ernest Rutherford

The famous scattering experiment by Ernest Rutherford (1871-1937) experimentally confirmed the thesis of a very small, almost point-like atomic nucleus.

In 1897 Rutherford recognized that the ionizing radiation from uranium consists of several types of particles. In 1902 he hypothesized that chemical elements change to lower atomic number elements through radioactive decay. In 1903 he differentiated radioactivity into alpha radiation, beta radiation and gamma radiation according to their increasing penetrating power and introduced the concept of half-life. This work was awarded the 1908 Nobel Prize in Chemistry.

His best-known contribution to atomic physics is Rutherford's atomic model, which he derived in 1911 from his experiments on scattering alpha particles on gold foil. Rutherford extended Thomson's atomic model, which assumed a uniform distribution of mass.

In his scattering experiment, Rutherford aimed an alpha emitter at a thin gold foil. According to Thomson's atomic model, all alpha particles should pass through the gold foil without being deflected. However, if the atom has a very small, almost point-like nucleus, as Rutherford suspected, then in rare cases the alpha particles would have to be strongly deflected. He also derived the associated formula for the probability of being distracted, the famous scatter formula. Accordingly, the probability of a deflection by the angle phi decreases by a factor of 1/sin^4(phi/2).

The following parts are required for this experiment:

• a vacuum pump link
• Possibly a pressure sensor to check the internal pressure, but this isn't absolutely necessary
• a robust metal housing (don't forget: If the inner pressure is nearly 0 mbar, then there is a force/weight of 10N/1 kg on each cm²!). I got mine from the company bopla link
• a BPX61 photodiode whose protective glass must be carefully removed! ebay
• an amplifier circuit with the TLC272, which must be mounted inside the vacuum chamber/metal housing
• a circuit using the LM386 to drive a speaker and the counter
• an electronic counter to measure the count rate link
• an alpha emitter Americium-241. These you can find in older smoke detectors based on ionization. But be very careful and don't touch the emitter or even scratch on it!!!
• Gold leaf ebay

The electronics consist of two circuits, a first amplifier with the TLC272 and a second amplifier with the LM386. You will also need a counter for the count rate. I made a counter by myself using an arduino and a 8 digit display. Don't forget to connect the metal housing with GND of the first amplifier. Otherwise you will have a lot of noise in your signal!

The parts you will need:

• 2x 9V batteries
• foil capacitors with 1x 1.5 µF, 2x 100 nF, 1x 22 pF, 1x 470 nF, 1x 150 pF, 1x 47 nF
• electrolytic capacitors with 2x 10 µF, 1x 47µF and 1x 100 µF
• 1/4W resistors with 1x 270 kohm, 1x 470 kohm, 1x 4.7 Mohm, 1x 1kohm, 1x 330 kohm, 1x 1.2 kohm, 1x 10 ohm and 1x 1Mohm
• a small piezo speaker/buzzer
• a photodiode BPX61 with removed glass cover
• 1x LM386 audio amplifier
• 1x TLC272 operatrional amplifier

The experiment is actually quite simple. A certain angle is set between the alpha emitter, gold foil and photodiode. Then you close the metal housing and turn on the vacuum pump. The count rate is then determined in counts per minute. The final vacuum pressure should be at least around 5 mbar or lower. At a pressure of 1 bar, the alpha rays only travel a few centimetres. But if the pressure drops to 5 mbar, for example, the alpha particles can travel around 200 times further than in air. You can check the pulses coming from the amplifier with an oscilloscope. You should be able to see nice single pulses.

Caution: For angles > 10°, the counting rate drops very sharply and is sometimes only 0.1 cpm! Of course, the vacuum pump has to be switched off again for each new angle and the metal housing has to be opened. At the end you get a graph that shows the count rate as a function of the scattering angle phi.

The experiment can also be simulated with EXCEL by calculating the deflection of the positively charged alpha particles on the nucleus, which is also positively charged. As can be seen, for a significant deflection, the distance of the incident alpha particle must be in the range of 0.05 pm (1 pm = 10^-12 m) or smaller. The entire atom has a diameter of around 10^-10 m. By comparing the diameter of 10^-10 m to the distance of less than 5*10^-14 m required for a deflection, you can see why deflection of the alpha particle is so rare.

Here you can find among other things the EXCEL-file: Link

So it is possible to repeat this famous physics experiment with relatively simple means. But there is a much easier way. All you need is a metal ball and a wine glass with a foot that curves upwards. If you let the ball roll against the glass, it will be deflected due to the curvature like the alpha particles in the Rutherford experiment. In most cases, the bullet is only slightly deflected. But it happens again and again that the ball is deflected more strongly or even scattered back.

If you are interested in more exciting physics experiments, here is my homepage and my YouTube channel:

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