The change in mass when 1 proton and 1 neutron, initially at rest, bind together can be explained in terms of the γ-ray energy and the kinetic energy of recoil.
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できた重陽子の静止質量は、結合前の質量の和の何％か？
箱全体から初めの空箱の質量を引くと、結合前の核子の質量の和の何％か？
The equations explain the phenomenon
1The protons and neutrons in an atomic nucleus are counted.A=Z+N……
2The deuteron's mass is compared with the sum of the proton and neutron masses.Δm=mp+mn − Md……
3The mass difference Δm is converted into a rest energy difference.ΔE=Δm c²……
4Conservation of energy relates the states before and immediately after binding.(mp + mn) c²=Md c²+B……
5Rearranging the energy conservation equation gives the deuteron's mass ratio.Mdmp + mn=1 − B(mp + mn) c²≒99.88%……
6The total mass is calculated when the energy remains in the box.Mtotal=Md+Bc²=mp+mn……
The following sections cover nuclear reactions, radioactive decay, and elementary particles.
7The electrostatic force between protons is estimated.F=k e²r²≒231 N……
8The binding energy per nucleon is compared across nuclei.Maximum BA≒8.8 MeV……
9Formulate the radioactive decay lawdNdt=−λ N……
10Solve the decay equation and find the half-lifeN=N₀ (12)t/T……
11Classify the types of radiation238U→234Th+4He……
12A heavy atomic nucleus splits.235U+n→2 atomic nuclei+2〜3 n+200 MeV……
The following section examines the internal structure of nucleons. Their valence quark compositions are taken as experimentally established properties and are not derived from the equations in the previous step.
13Look inside nucleonsValence quark composition:The proton p has the composition uud、The neutron n has the composition udd……
What this chapter has shown
The energy of the stationary nucleons before binding is divided between the rest energy of the resulting atomic nucleus and the energy released. By E=mc², the nucleus's rest mass is smaller than the sum of the nucleon masses by the released energy divided by c².
99.88 %Deuteron mass/sum of masses before binding
If the γ-ray and recoil energies also remain inside the box, the mass of the entire box − the initial mass of the empty box is 100% of the sum before binding.
In everyday lifeIn the Sun, reactions that form helium nuclei from hydrogen nuclei release energy corresponding to the difference in rest mass before and after the reaction.
An atomic nucleus is lighter than its constituent particles because the nucleons release energy as they bind together, reducing the rest mass accordingly. If the released energy remains within the system, the total mass is unchanged from before binding. The average binding energy for 1 nucleon is greatest near iron, and both nuclear fusion and nuclear fission release energy by producing nuclei closer to this region. Although individual nuclei decay randomly, 1 at a time, the average number remaining follows a definite curve determined by the half-life. The forces encountered in high-school physics are understood here in terms of 4 fundamental forces: gravity, the electromagnetic force, the strong force, and the weak force.