Please solve the following questions. This is not an assignment, it will not be graded, and you do not need to submit your solutions to anyone. The questions are simply intended to help you practice for the exam.

These questions will not appear in the exam itself. Students who don't genuinely attempt to solve the questions on their own, and only memorize the solutions, will have a very hard time in the actual exam!

These questions are not multiple-choice, to encourage you to think of the answers on your own, but the questions in the actual exam will be multiple-choice.

If you need any clarifications for these questions, you can ask for them on the course Teams channel.

Question 1 Show/hide solution

How can we define mass precisely?

Solution: Either as resistance of the object to acceleration (inertial mass) or the strength of the object's gravitational field (gravitational mass)

Question 2 Show/hide solution

How are the two different definitions of mass related? Can an object have two different masses depending which definition is being used?

Solution: According the equivalence principle, the two definitions should always give the same value for an object's mass.

Question 3 Show/hide solution

How does the concept of energy explain why an object accelerated when it falls?

Solution: As the object falls, its gravitational potential energy (corresponding to its height) is converted to kinetic energy (corresponding to its speed). So if its height decreases, its speed increases.

Question 4 Show/hide solution

What is the meaning of Einstein's popular equation, E = mc²?

Solution: That there is a form of energy, called rest energy, which is proportional to the object's mass - just like, for example, its gravitational potential energy is proportional to its height.

Question 5 Show/hide solution

What is the structure of the atom?

Solution: It has a nucleus made of protons and neutrons, surrounded by a cloud of electrons.

Question 6 Show/hide solution

I have two different chemical elements. What can you say about the number of protons in the atoms of each element?

Solution: The number of protons (atomic number) is the thing that determines the type of element, so if the elements are different, the number of protons in their atoms must be different.

Question 7 Show/hide solution

How many protons are in a carbon atom?

Solution: Looking at the periodic table, the atomic number of carbon (C) is 6, so it has 6 protons.

Question 8 Show/hide solution

What do I get when I bind together 2 up quarks and 1 down quark?

Solution: A proton.

Question 9 Show/hide solution

What is the strong interaction? Which particle mediates it?

Solution: The strong interactions glues together the quarks inside protons and neutrons, and the protons and neutrons themselves inside the nucleus. It is mediated by the gluon.

Question 10 Show/hide solution

Is gravity described by the Standard Model?

Solution: No, the Standard Model only describes electromagnetism and the strong and weak interactions, but gravity is described by general relativity.

Question 11 Show/hide solution

What is the mass, charge, and spin of the photon?

Solution: Looking at the table of particles in the Standard Model, we see that it has no mass or charge, and its spin is 1.

Question 12 Show/hide solution

What is the mass, charge, spin, and generation number of the charm quark? Is it stable?

Solution: Looking at the table of particles in the Standard Model, we see that the charm quark's mass is ~1.28 GeV, its charge is 2/3, its spin is 1/2, and it is in the 2nd generation of matter. As it is in a higher generation of matter, it is unstable; only the particles in the first generation are stable.

Question 13 Show/hide solution

A particle has spin 3/2. What kind of particle is it?

Solution: Since it has half-integer spin, it is a fermion.

Question 14 Show/hide solution

Where, when, and how was the Higgs boson discovered?

Solution: It was discovered in 2012 in the Large Hadro Collider at CERN, by colliding together two protons with sufficiently high kinetic energy to create it.

Question 15 Show/hide solution

What is the difference between elementary, composite, and subatomic particles?

Solution: Elementary particles are not made of smaller particles. Composite particles are made of smaller particles. Subatomic particles can be either elementary or composite.

Question 16 Show/hide solution

What would be the charge of the antiparticle of a bottom quark?

Solution: Looking at the table of particles of the Standard Model, we see that the bottom quark has a charge of -1/3, so its antiparticle has an opposite charge of +1/3.

Question 17 Show/hide solution

What happens to the mass in an electron-positron annihilation?

Solution: It turns into kinetic energy of the two photons that are created.

Question 18 Show/hide solution

In one sentence, how is light produced inside stars?

Solution: Hydrogen is fused into helium, and since the final nucleus has less mass than the initial 4 nuclei, the rest energy due to the missing mass is released as the kinetic energy of the side-products of the reaction: neutrinos and photons.

Question 19 Show/hide solution

A star has a mass 3 times larger than the mass of our Sun. Which process dominates its nuclear fusion?

Solution: The CNO cycle.

Question 20 Show/hide solution

What is deuterium?

Solution: Recall that isotopes are atoms that have the same number of protons but a different number of neutrons. The most common isotope of hydrogen (¹H) has only 1 proton and no neutrons. Deuterium (²H) is an isotope of hydrogen which has not only 1 proton but also 1 neutron. It is less common, but still stable.

Question 21 Show/hide solution

Describe all the steps in the proton-proton chain.

Solution: In step 1, two protons (¹H) fuse into deuterium (²H), which is composed of 1 proton and 1 neutron. In this process, a neutrino and a positron are also released. In step 2, the deuterium fuses with another proton to produce ³He, an isotope of helium with two protons and one neutron. In this process, a photon is also released. These two steps happen TWICE, so that in the end we have a total of TWO ³He nuclei. These two nuclei then fuse into a single helium (⁴He) nucleus. In this process, two protons are also released.

Question 22 Show/hide solution

A positron is released in step 1 in the proton-proton chain, when one of the protons undergoes beta plus decay. Why can't an electron be released instead?

Solution: Because of conservation of electric charge. In step 1 we start with two protons, with a total charge of +2 (since each proton has a charge +1), and end with one deuterium (²H), which has only 1 proton and thus a total charge of +1. Since we started with +2, we must have another particle with charge +1, a positron, to conserve the original charge of +2. If this was an electron, then it would have charge -1 and the total charge would have been 0, which would violate conservation of charge.

Question 23 Show/hide solution

Which step in the proton-proton chain takes the most time, and why?

Solution: Step 1, because it is mediated by the weak interaction; since the interaction is so weak, it has a much smaller chance of happening.

Question 24 Show/hide solution

How many neutrons are in a helium-8 nucleus?

Solution: Helium has 2 protons, and 8 is the sum of protons + neutrons, so there must be 6 neutrons.

Question 25 Show/hide solution

Why are two single protons produced in step 3 of the proton-proton chain, in addition to the ⁴He nucleus?

Solution: Because the step started with two ³He nuclei, each one containing 2 protons, for a total of 4 protons. 2 of these protons fuse into ⁴He, but the other two don't, so they remain as single protons.

Question 26 Show/hide solution

In the process of creating one ⁴He nucleus via the proton-proton chain, how many photos are emitted in total? And how many of these are due to antimatter annihilation?

Solution: 6 photons are emitted in total. Out of them, 4 are due to electron-positron annihilation.

Question 27 Show/hide solution

What portion of the initial rest energy is converted to kinetic energy in the proton-proton chain?

Solution: Approximately 0.7%.

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