are alpha particles going to ruin bumper carts? Making them unsafe.

Question

Bumper cars are powered by a charged ceiling and floor. A pole on the bumper car connects these two charged surfaces to give the car current to run. The difference in voltage between the plates is typically around 48 V. The height difference between the ceiling and floor is 10ft. When radon in the ground decays it releases an alpha particle. Assuming the ceiling is negatively charged, the alpha particle could be accelerated towards the celling. It is not good for people to be hit with accelerated alpha particles. Mathematically show is this something we need to be concerned about?

Please and thank you

Answer 1

Hi Peyton,

When solving this and using facts about alpha particles, I found that is was actually safe.

We can treat the ceiling and the floor as each plate of a capacitor. The voltage between the plates is 48 V. Electric potential energy is given by U = q*V, where q is the charge of the alpha particle and V is the voltage. The charge of the alpha particle is q = +3.2 * 10^-19 C (an alpha particle has 2 protons, and each one has a charge of 1.6 * 10^-19), so

U = 3.2 * 10^-19 C * 48 V = 1.536 * 10^-17 J. To convert this to electron-Volts (eV), divide by 1.6 * 10^-19, so

U = 1.536 * 10^-17 J / (1.6 * 10^-19) = 96 eV (note that we could just have multiplied 2 * 48 to get this; the 2 is for the 2 protons in the alpha particle). While this is the potential energy, by Conservation of Energy, this number is also the maximum kinetic energy of the alpha particle.

The "typical" kinetic energy of an alpha particle is 5 MeV (5 million eV), which is considered harmless as it is easily absorbed by the skin. If 5 million eV is harmless, then 96 eV is definitely harmless.

Hope this helps! Please let me know if you have any questions.

Akshat Y.