Calcule la energía de enlace por nucleón de los núcleos siguientes: (a) 7^14 N (masa nuclear,

Calcule la energía de enlace por nucleón de los núcleos...

Key Concepts

Nuclear Binding Energy

Nuclear binding energy is the energy required to disassemble a nucleus into its individual protons and neutrons. It represents the result of the attractive strong force that holds nucleons together within the nucleus and is a direct indicator of the nucleus's stability.

Mass Defect

Mass defect refers to the difference between the sum of the individual masses of protons and neutrons and the measured mass of the nucleus. This 'missing' mass has been converted into binding energy due to the mass-energy equivalence principle.

Binding Energy per Nucleon

Binding energy per nucleon is the total nuclear binding energy divided by the number of nucleons in the nucleus. It is a useful metric for comparing the stability of different nuclei: higher values typically indicate more stable nuclei.

Mass-Energy Equivalence

Mass-energy equivalence, encapsulated in Einstein's equation E=mc², establishes that mass and energy are interchangeable. This principle allows the conversion of the mass defect into binding energy, thereby quantifying the energy that holds the nucleus together.

Atomic and Nuclear Mass Considerations

When calculating nuclear binding energy, it's important to recognize the difference between nuclear masses (which exclude the mass of electrons) and atomic masses (which include electrons). Accurate calculations require using the appropriate mass values or making adjustments when necessary.

Transcript

00:02 To solve this problem, we need to find the binding energy per nucleon for several different isotopes.

00:08 We're going to start with this nitrogen 14 isotope.

00:11 To find the binding energy first, not just binding energy per nucleon, but binding energy, what we're going to do is need to find the mass defect.

00:17 That is the difference in mass between the calculated mass of adding up all the protons and neutrons and the experimental mass that we find in the lab.

00:25 So first, to calculate the mass, what we're going to do is we're going to figure out that there are seven protons, because it's nitrogen.

00:33 And for each of these protons, we are going to add 1 .007 -825 amu, because that's the mass of a proton.

00:43 Now, there's also seven neutrons in this case, and we're going to add 1 .00665 amus for each neutron, because each neutron is a little bit heavier than each proton.

00:56 When you calculate this all out, multiply each one this by seven, and then you're going to add them together, you're going to find a calculation.

01:02 You're going to calculated mass for this nitrogen isotope to be 14 .11543 amu.

01:12 Now this is interesting because this is actually slightly different than what we find in a lab.

01:16 Experimentally we determine the mass of this to be 13 .999m .2 3 amu.

01:25 Now the difference between these two mass is what we call the mass defect.

01:28 It's the energy that is lost to hold the nucleons together to make them stable.

01:34 So that energy can be converted, this mass difference can be converted into energy using einstein's equation e equals mc squared.

01:41 But first we need to figure out this defect at 0 .116 -196 amu.

01:50 Now this is in amus.

01:52 To use einstein's equation, it has to be in kilograms.

01:55 So we need to convert from amus to kilograms.

01:58 Use just a little bit of dimensional analysis where we have 6 .022 times 10 to the 23rd amu.

02:07 Atomic mass units is equal to 1 gram.

02:10 And it needs to be in kilograms.

02:11 So we're going to multiply this by 1 ,000 kilograms on our, or 1 ,000 grams on the bottom to get one kilogram on top.

02:19 When you convert through all of this, it's going to lead us to having 1 .92953 times 10 to negative 28 kilograms.

02:28 Now we can use this in e equals mc squared, we can plug in this amount of kilograms in here and it'll tell us the amount of energy that this mass was converted into, this mass defect.

02:42 So we do that.

02:43 And for mass, i'll be there and for speed of light, i'm going to use 2 .998 times 10 to the 8 meters per second.

02:52 Now, since this is going to be squared where units are going to be kilograms times meters per second squared, which is actually what you get for joules.

02:59 So when you multiply this mass times the speed of light squared, you are going to end up with an energy that is equal to 1 .734 times 10 to the negative 11 joules.

03:16 Now this is jewels for the whole isotope.

03:18 If you want to answer the problem, we need to divide by the number of nucleons, which happens to be 14 in this case.

03:24 So this is going to tell us what is the average amount of energy that is binding this nucleus together per nucleon.

03:33 And we're going to end up with a simple answer of 1 .239 times 10 to the negative 12 joules per nucleon.

03:44 All right, so this is the answer to the first part.

03:46 Now there were two other isotopes that we need to talk about...

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