E.3 Radioactive Decay

conversions from kg to joules

E = mc²

conversion from u to joules

E = mc²

1 u = 1.661×10^-10 kg

binding energy

The energy required to separate an atomic nucleus completely into its constituent protons and neutrons.

Nucleus has a smaller mass than Nucleons separated

mass defect

the difference in mass between the mass of an object and the sum of the masses of its constituent particles

• binding energy

what is keeping the nucleus together

electric repulsion of protons strains the nucleus, but the residual strong force holds the nucleus together

to graph

y = force between nucleons (+ = repulsive, - = attractive_)

x = nucleon separation

evidence of strong force

• protons’ positive charge thus from Coulomb’s law repel each other, electrostatic force. however, neutrons allow for stability. This stability indicates the presence of strong force, binding protons, and neutrons to overcome electrostatic repulsion

• The mass deficit can be converted into binding energy from E = mc², showing the energy required to keep the nucleus together. The binding enegry per nucleon shows the strong force

if strong force did not exist nuclei of more than one proton would not exist electrostatic repulsion would exceed gravitational force

when does binding energy per nucleon peak

iron -56

strong force versus electrostatic repulsion

since the strong force is from short range, it does not act across the whole nuclei, which electrostatic force does.

Thus nuclei with greater nucleons require more neutrons than protons for stability. This is because neutrons provide equal amounts of strong force and additional spacing reducing electric force

Line of stability

neutron number, against the proton number graph. the line of stability reveals that for stable atoms more protons required at larger nucleus’s

Binding energy versus nucleons graph

Beyond 60 nucleons, Coulomb repulsion grows for heavier nuclei, but nuclear attraction remains the same

Binding energy from atomic mass units

multiply by MeV (931.5) rather than E = mc² which is joules, u is eV