The Atom

1. After acquiring a time machine, we decide to visit Rutherford to test his skills and knowledge. We break into his lab right before he conducts his scattering experiment, replacing his α-particles with single protons. Rutherford doesn't notice the switch—no one knows what protons are at this point in time and he's had a long day. What does he observe when he shoots these protons through gold?

2. Superman avoids Kryptonite like the plague because its radiation would strip him of his powers. Like other radioactive sources, the radioactive Kryptonite decays over time. If a sample of radioactive Kryptonite decays such that only 0.2 g of Kryptonite are left after 1 year with a 5 month half life, what's the initial quantity of radioactive Kryptonite?

3. Obtain a simplified expression for the energy of an electron orbiting the nucleus as a function of orbital level, n.

4. How much energy will be released by freeing an electron orbiting a nucleus at n = 2?

5. In #2 we learned that Kryptonite has a half life of 5 months. What's it's mean lifetime?

1. Answer: Exactly the same kind of results. Protons are positively charged, just like alpha particles. Some of them will breeze right past the nucleus. Others will hit the positive nucleus and be deflected at a large angle, while others will right shoot back at Mr. Rutherford at a 180-degree angle.

2. Answer: It's time to pull out the equation for radioactivity as a function of time with a half life, rather than the decay constant or mean lifetime, because of the information we were given. That would be , with N(1 yr) = 0.2 g, months and t = 12 months. Since the two numbers may be expressed as a ratio as well as the times we're not bound to use SI units. We find that N_o = 1.06 grams. As long as we don't forget the negative sign in the exponent we do, anyway.

3. Answer: This sounds like a job for eradicating all the constants in . The first constant is a₀ = 0.0529 nm = 5.29 × 10^-11 m. We need to stick to SI units if we want a sensible answer. The elementary charge is e =1.6 × 10^-19 C. Boltzmann's constant is . So, plugging everything in, we all the constants together produce -2.18 × 10^-19 J = -13.6 eV. The calculation of all these constants whittles the equation down to as our final expression and everyone is happy.

4. Answer:None. We learned earlier that negative energy means extra energy needs to be supplied to release a bound particle. So, actually, no energy will be released if you free an electron of level n = 2. Freeing an electron requires energy input.

One way to make this into a not-trick question would be to ask how much energy is needed to free an electron of n = 2. Then you can use the equation above, and get . The electron needs an amount greater than 3.4 eV to free it from the Coulomb force that draws it to the nucleus.

5. Answer:Ah, we need to find τ. Well that's found by , so τ = 7.2 months.

Particle Physics

1. A proton has a mass of and a charge of q = +1.6 × 10^-16 C. What properties does an anti-proton have?

2. All nucleons are composed of a combination of three up and down quarks. What three quarks make up the antiproton?

3. Check the conservation of baryon, lepton and electric charge in beta-plus (β⁺) decay.

4. What would happen if a proton collided with an anti-proton?

5. Thorium-232 is a common radioactive element naturally found in the continental upper crust of the Earth. Write down the products of this element as it alpha-decays to an isotope of radium (Ra).

1. Answer: An anti-proton has a a mass of and a charge of q = -1.6 × 10^-16 C.

2. Answer: Up quarks have a charge, and down ones have a charge. Let's try the following combinations and see what happens.

1. 
2. 
3. —Bingo!
4. 

Number 3 corresponds to the antiproton with a negative -e charge very well indeed. It goes against the grain that an antiproton doesn't have the exact opposite of the quarks of the proton, but opposite charge is essential, so there we have it.

3. Answer: First let's review the electrical charge:



One positive charge on the left side equals one positive charge on the right.

Next let's check the lepton charge:



The proton and neutrons aren't leptons, so their lepton numbers are zero. The positron's lepton charge (+1) cancels out the electron-neutrino's (–1), so once again, all's well.

And finally, let's check the baryon charge:



The positron and neutrino aren't baryons, so their baryon numbers are zero. The proton's baryon number on the left balances out the neutron's on the right.

Everyone is happy.

4. Answer: It would be easy to assume that two photons of energy 938 MeV would be created, corresponding to the rest mass of a proton. As far as we've learned in this unit, that would be correct, but what's the main difference between electrons and protons?

Electrons are elementary particles while protons are made of three quarks. So really, we'd need to analyze the interactions of the quarks within the proton and antiproton to answer this question. Yes, annihilation happens with energy released. However, if a quark annihilates with an anti-quark, we're left with a composite particle made of two quarks only. We haven't studied this family, but we'll just tell you they're called mesons.


5. Answer: Thorium's mass number is Z = 90 and its atomic mass number is A = 232. Its daughter nuclide will have an atomic mass number of A = 228 and a mass number of Z = 88. This means we can write the α-decay reaction as . We could add the emission of a gamma ray for good measure, if we like.