(II) Calculate the total binding energy, and the binding energy per nucleon, for (a) ^63 Li, (b)

(II) Calculate the total binding energy, and the binding...

Key Concepts

Nuclear Mass Data

Nuclear mass data found in sources like Appendix B provide the precise mass measurements required for calculating the mass defect. These data are crucial as they enable the accurate determination of binding energies for various nuclei by providing the experimentally measured atomic masses.

Binding Energy per Nucleon

Binding energy per nucleon is obtained by dividing the total binding energy of a nucleus by its number of nucleons. This value provides insight into the average energy that binds each nucleon within the nucleus and is often used to compare the stability of different nuclei.

Binding Energy

Binding energy is the energy required to separate a nucleus into its individual protons and neutrons. It serves as a measure of the stability of a nucleus, with higher binding energy generally indicating a stronger, more stable nucleus due to the greater energy needed to overcome the nuclear forces holding it together.

Mass Defect

Mass defect is the difference between the sum of the individual masses of a nucleus's protons and neutrons and the actual measured mass of the nucleus. This deficit occurs because some of the mass of the nucleons is converted into binding energy when they combine to form the nucleus.

Mass–Energy Equivalence

Mass–energy equivalence, represented by Einstein’s equation E=mc², is the principle that mass can be converted into energy. In the context of binding energy, the mass defect is converted into energy, quantifying the binding energy that holds the nucleus together.

Transcript

00:01 In this question, we're working out the binding energy and the binding energy pernucleon for a lithium 6 and a lead 208 atom.

00:09 So we'll start the question with lithium 6, which has three protons and three neutrons.

00:19 So to find in binding energy, we add up the constituent parts, the masses of the constituent parts of the atom, and we take away the known mass for the atom.

00:29 And that gives us a mass difference.

00:31 We then convert this mass difference into a.

00:34 Mev, that gives us our binding energy.

00:36 And then to find binding energy per nucleon, we simply divide that number by the number of nucleons.

00:41 So for lithium 6, lithium 6 can be thought of as being made up of three hydrogen atoms, as that is three protons with an electron.

00:54 So three protons, and three neutrons.

00:59 So that's the constituent masses that make up a lithium atom.

01:03 From that we take away the known mass of lithium.

01:08 So i'll just put the numbers in here.

01:10 So the mass of hydrogen atom is 1 .007 -825, and that is in u, atomic mass units.

01:24 Then the mass of a neutron is 1 .008665.

01:33 And finally, the mass of the lithium atom is 6 .015 -121.

01:44 And these are all in u.

01:47 So let's just put that into the calculator and we will get our mass defect.

01:54 So three times 1 .007, 825 plus three times 1 .008 -665 minus 6 .0151.

02:09 And our mass defect is equal to 0 .03439u.

02:17 And then to convert from you to mega electron volts, we times by 931 .5.

02:25 So this answer times by 931 .5 is equal to 32 .0 m .v or 31 .99, however you want to write it.

02:43 So that is our binding energy for lithium.

02:45 And then to find our binding energy per nucleon, we simply do our binding energy, 32 .0, divided by the number of nucleons, which is this top number here, which is six.

02:57 And that gives us an answer of 5 .3m .v.

03:15 So that is part a.

03:17 Done.

03:18 I'll just now clear the board, and we can look at part b...

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