Quantum Chromodynamics
Practice
practice problem 1
solution
The mass of subatomic particles is measured in electronvolts while chemical elements are weighed in atomic mass units. This is a question about unit conversion.
mtop = | 172.69 GeV/c2 | 103 MeV | 1 u | ||
1 | GeV | 931.494 MeV/c2 |
mtop = 185.390 u
Now we need a periodic table. I have a nice one in this book. Find the elements that are around 186 u.
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It looks like the top quark is heavier than an atom of every element up to element 75 — rhenium. This is the pretty good answer. However…
You may recall that the masses stated on a periodic table are averages. Atoms of every element can be found with a variety of masses. These variations are called isotopes. Here's a fragment of the table of isotopes for tungsten, rhenium, and osmium with the top quark slipped in.
tungsten (z = 74) | rhenium (z = 75) | osmium (z = 76) | ||||||
---|---|---|---|---|---|---|---|---|
182W | 181.948 206 u | 26.3% | 182Re | 181.951 211 u | 182Os | 181.952 186 u | ||
183W | 182.950 225 u | 14.3% | 183Re | 182.950 821 u | 183Os | 182.953 110 u | ||
184W | 183.950 933 u | 30.7% | 184Re | 183.952 524 u | 184Os | 183.952 491 u | 0.02% | |
185W | 184.953 421 u | 185Re | 184.952 956u | 37.4% | 185Os | 184.954 043 u | ||
mass of the top quark = 185.390 u | ||||||||
186W | 185.954 362 u | 28.6% | 186Re | 185.954 987 u | 186Os | 185.953 838 u | 1.58% | |
187W | 186.957 158 u | 187Re | 186.955 751 u | 62.6% | 187Os | 186.955 748 u | 1.60% | |
188W | 187.958 487 u | 188Re | 187.958 112 u | 188Os | 187.955 836 u | 13.3% | ||
189W | 188.961 912 u | 189Re | 188.959 228 u | 189Os | 188.958 145 u | 16.1% | ||
190W | 189.963 180 u | 190Re | 189.961 816 u | 190Os | 189.958 445 u | 26.4% | ||
191W | n/a | 191Re | 190.963 124 u | 191Os | 190.960 928 u | |||
192W | n/a | 192Re | 191.965 960 u | 192Os | 191.961 479 u | 41.0% |
The top quark is heavier than most naturally ocurring tungsten atoms, lighter than most naturally ocurring rhenium atoms, and lighter than nearly all naturally ocurring osmium atoms. This is the pedantic answer to this question.
practice problem 2
solution
Protons have a mass of 938.272 MeV/c2. Neutrons have a mass of 939.565 MeV/c2. The masses of the up and down quarks are 2.3 MeV/c2 and 4.8 MeV/c2, respectively. This means that quarks make up…
2mu +1md | = | 2(2.3 MeV/c2) + 1(4.8 MeV/c2) |
mp | 938.272 MeV/c2 | |
2mu +1md | = | 9.4 MeV/c2 |
mp | 938.272 MeV/c2 | |
2mu +1md | = | 1.00% of the mass of a proton |
mp | ||
1mu +2md | = | 1(2.3 MeV/c2) + 2(4.8 MeV/c2) |
mn | 939.565 MeV/c2 | |
1mu +2md | = | 11.9 MeV/c2 |
mn | 939.565 MeV/c2 | |
1mu +2md | = | 1.27% of the mass of a neutron |
mn |
Most of the universe is hydrogen, but the Earth is more than just hydrogen. There's oxygen, silicon, carbon, aluminum, and more. These elements are made of nuclei that are roughly half protons and half neutrons. I can't tell you anything better than that. Let's agree to be reasonable in our precision.
The strong force is responsible for nearly 99 per cent of the mass we deal with in our everyday lives.
practice problem 3
- What combination(s) of quarks will produce a sigma baryon with a charge of −1e?
- What combination(s) of quarks will produce a sigma baryon with a charge of +0e?
- What combination(s) of quarks will produce a sigma baryon with a charge of +1e?
- What combination(s) of quarks will produce a sigma baryon with a charge of +2e?
solution
uu | ud | dd | |
---|---|---|---|
s | uus (+⅔ e)(+⅔ e)(−⅓ e) +1 e |
uds (+⅔ e)(−⅓ e)(−⅓ e) +0 e |
dds (−⅓ e)(−⅓ e)(−⅓ e) −1 e |
c | uuc (+⅔ e)(+⅔ e)(+⅔ e) +2 e |
udc (+⅔ e)(−⅓ e)(+⅔ e) +1 e |
ddc (−⅓ e)(−⅓ e)(+⅔ e) +0 e |
b | uub (+⅔ e)(+⅔ e)(−⅓ e) +1 e |
udb (+⅔ e)(−⅓ e)(−⅓ e) +0 e |
ddb (−⅓ e)(−⅓ e)(−⅓ e) −1 e |
- There are two sigma baryons with a charge of −1 e
dds (Σ−), ddb (Σ−b)
- There are three sigma baryons with a charge of 0 e
uds (Σ0), ddc (Σ0c), udb (Σ0b)
- There are three sigma baryons with a charge of +1 e
uus (Σ+), udc (Σ+c), uub (Σ+b)
- There is one sigma baryon with a charge of +2 e
uuc (Σ++c)
practice problem 4
- the electrostatic force between them. (About how big is this?)
- the gravitational force between them. (About how big is this?)
Please comment on these values.
- Why is the nuclear force between nucleons called the strong nuclear force?
- Why is the gravitational force often described as weak?
solution
Answer it.