Find the average binding energy per nucleon of (a) 12^24 Mg and (b) ^8537 Rb

Name: Problem 11, Chapter 29: College Physics
Uploaded: 2020-03-24T05:35:42-08:00
Duration: 6 min 52 s
Channel: Lisa Tarman
Description: Find the average binding energy per nucleon of (a) 12^24 Mg and (b) ^8537 Rb

Find the average binding energy per nucleon of (a) 12^24 Mg...

Key Concepts

Nuclear Binding Energy

Nuclear binding energy is the energy required to disassemble a nucleus of an atom into its individual nucleons (protons and neutrons). It represents the stability of the nucleus, as a larger binding energy implies a more tightly bound and stable nucleus. This energy arises due to the strong nuclear force overcoming the electrostatic repulsion between protons.

Binding Energy per Nucleon

The binding energy per nucleon is a measure of the average energy that would be needed to remove a nucleon from the nucleus. It is calculated by dividing the total binding energy of the nucleus by the number of nucleons present. This parameter is important in understanding the overall stability and energy release in nuclear reactions, such as fusion and fission.

Mass Defect

The mass defect is the difference between the sum of the individual masses of the protons and neutrons and the actual mass of the nucleus. This missing mass has been converted into binding energy, as described by Einstein's equation, E=mc². The mass defect is a crucial concept for calculating the nuclear binding energy.

Atomic Nucleus Structure

The structure of the atomic nucleus consists of protons and neutrons, collectively known as nucleons. The number of nucleons determines the mass number, while the number of protons determines the element. Understanding the arrangement and interactions of these nucleons is essential for analyzing nuclear properties, including binding energy and stability.

Transcript

00:01 In number 11, we're asked to find the binding energy per nucleon for this magnesium and this ribidium.

00:08 So the binding energy, that's the energy that takes the whole, the atom together.

00:15 If you would add up the mass of all the pieces and then compare it to the mass of the whole thing, there's a little bit of mass missing, and that is the mass that's the binding energy.

00:26 So i'm looking for this missing mass.

00:31 And if i add up the mass of all the protons, plus the mass of all the neutrons, and then subtract the mass of the atom as a whole, i'm going to call that mass total.

00:48 That would be the part of the mass that is the binding energy.

00:56 These aren't that hard, they're just tedious.

01:01 So for this magnesium, my atomic number is 12, so i have 12 protons.

01:05 So here i'm going to just put 12 times the mass of a proton.

01:12 And this will be in atomic mass units, so in u's.

01:17 So 1 .007 -825 plus the mass of my neutrons, and you can tell if my mass number is 24, i subtract, and you can tell them must also be 12 neutrons.

01:36 So 12 times the mass of a neutron.

01:46 1 .008665 and i subtract the mass of the whole thing.

01:55 For the mass of the whole thing, if you look in appendix b in the back of the book, so i looked up magnesium 24 and that was 23 .985 -042.

02:23 So i do this math and i find out that the missing mass is 0 .212838, and that is u's atomic mass units.

02:40 So that's the mass.

02:41 I'm going to convert that to its energy.

02:44 So i'm going to just do my conversion factor here.

02:47 I know that one atomic mass unit is the same as 931 .5 mega electron volts.

03:00 So i get my binding energy is 198 .259 mega electron volts.

03:26 But i may ask to find the binding energy per nucleon...