Quantum Chromodynamics

Practice

practice problem 1

The mass of the top quark is 172.6 GeV/c2; heavier than some atoms. Identify the heaviest element that is lighter than the top quark.

solution

The mass of subatomic particles is measured in electron volts while chemical elements are weighed in atomic mass units. This is a question about unit conversion.

mtop =  172.6 GeV/c2   103 MeV   1 u  = 185.294 u
1 GeV 931.494 MeV/c2

Now we need a periodic table. I have a nice one in this book. Find the greatest atomic mass less than 185.294 u. Tungsten satisfies this condition with a mass of 183.84 u. The next heavier element is rhenium at 186.21 u. This must be the answer. The top quark is heavier than an atom of every element up to element 74 — tungsten.


[magnify]

Well, that's almost right. We need to qualify this answer a bit. You may recall that the masses of the elements stated on a periodic table are averages. Atoms of any 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 and rhenium.

selected isotopes of tungsten (z = 74)   selected isotopes of rhenium (z = 75)
  mass (u)  half life abundance     mass (u)  half life abundance
182W 181.948202 stable 26.3%   182Re 181.951210 2.67 d  
183W 182.950220 1.1e17 y 14.3%   183Re 182.950817 70.0 d  
184W 183.950928 3e17 y 30.7%   184Re 183.952530 38.0 d  
185W 184.953416 75.1 d     185Re 184.952951 stable 37.4%
mass of the top quark = 185.294 u
186W 185.954357 stable 28.6%   186Re 185.954984 3.7183 d  
187W 186.957153 23.72 h     187Re 186.955744 4.35e10 y 62.6%
188W 187.958480 69.4 d     188Re 187.958106 17.005 h  
189W 188.961900 11.5 min     189Re 188.959219 24.3 h  

The mass of the top quark is more than most naturally ocurring tungsten atoms (roughly two thirds) and less than most naturally ocurring rhenium atoms (also roughly two thirds).

practice problem 2

What fraction of the mass of you and me, the air, earth, oceans, and everything else we deal with in ordinary life is due to the strong force?

solution

Protons have a rest mass of 938.272107 MeV/c2. Neutrons have a rest mass of 939.565439 MeV/c2. The rest masses of the up and down quarks are 2.01 MeV/c2 and 4.79 MeV/c2, respectively. This means that quarks make up …

2mu +1md  =  2(2.01 MeV/c2) + 2(4.79 MeV/c2)  =  8.81 MeV/c2  = 0.93896 … % of the mass of a proton
mp 938.272107 MeV/c2 938.272107 MeV/c2
      
1mu +2md  =  1(2.01 MeV/c2) + 2(4.79 MeV/c2)  =  11.59 MeV/c2  = 1.23354 … % of the mass of a neutron
mn 939.565439 MeV/c2 939.565439 MeV/c2

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 split the difference between the numbers calculated above, and let's agree to be reasonable in our precision. About 1% of the world around us is made of quarks. Everything else is made of fields.

practice problem 3

Write something.

solution

Answer it.

practice problem 4

Write something.

solution

Answer it.

The Physics Hypertextbook

  • No condition is permanent.