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The missing mass that holds nuclei together

Science · Matter & Materials · ages 17-18

Name ______________________ Date ____________

Binding energy per nucleon gives the exact energy needed to remove any particular nucleon from a nucleus.
Circle one: True False
What is the mass defect of a nucleus?
- Whole nucleus minus separate nucleons
- Protons minus neutrons
- Separate nucleons minus whole nucleus
Which listed nucleus lies near the maximum of the binding-energy-per-nucleon curve?
- Hydrogen-2
- Iron-56
- Uranium-238
Use the stated rounded total of 28.3 MeV for helium-4's binding energy. Divide it among its 4 nucleons to find the binding energy per nucleon in MeV. Give the unrounded quotient.
Answer: ______________
A deuteron contains one proton and one neutron. Use rounded nuclear masses in MeV/c squared: proton 938.28, neutron 939.57, deuteron 1875.61. Find its binding energy in MeV.
Answer: ______________
A heavy nucleus splits. All products together contain the same protons and neutrons as the parent, but have greater total binding energy. What is the net energy change?
- Energy is released
- Energy is absorbed
- Energy is unchanged
Helium-4 has binding energy 28.3 MeV. Each deuteron has binding energy 2.24 MeV. For breakup into two deuterons, what energy input is needed to account for the increase in total rest mass? Round to one decimal place.
- 28.3 MeV must be supplied
- 23.8 MeV must be supplied
- 23.8 MeV would be released
Mia compares fusion reactions with unchanged total protons and neutrons. Each option gives the nucleon-weighted average binding energy before and after. Which change releases energy?
- From 8 to 7 MeV per nucleon
- From 7 to 6 MeV per nucleon
- From 2 to 6 MeV per nucleon

Answer key

For grown-ups. Fold this page away before handing over the rest.

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False · Binding energy per nucleon is an average found by dividing the complete binding energy by nucleon count. A particular nucleon's removal energy can differ.
Separate nucleons minus whole nucleus · The free parts weigh more, and the difference is the defect.
Iron-56 · Iron-56 lies near the maximum in the iron and nickel region. It is not the unique highest point.
7.075 · Divide the total binding energy by the nucleon count: 28.3 divided by 4 is 7.075 MeV.
2.24 · The mass defect is 938.28 + 939.57 - 1875.61 = 2.24 MeV/c squared. Multiplying by c squared gives binding energy 2.24 MeV.
Energy is released · For unchanged nucleons, greater total binding energy means lower total rest mass. The decrease in rest-mass energy is released.
23.8 MeV must be supplied · The deuterons retain 2 × 2.24 = 4.48 MeV of binding energy. The decrease is 28.3 - 4.48 = 23.82 MeV, so 23.8 MeV must be supplied.
From 2 to 6 MeV per nucleon · With total nucleon count unchanged, a larger weighted average means greater total binding energy. Only the change from 2 to 6 MeV per nucleon increases it.