Calculate the binding energy in J/nucleon of the deuterium nucleus whose mass is 2.0135 u.

Name: Problem 54, Chapter 21: Chemistry The Molecular Nature of Matter
Uploaded: 2022-02-03T06:23:54-08:00
Duration: 6 min 6 s
Channel: Sandra Lundell
Description: Calculate the binding energy in J/nucleon of the deuterium nucleus whose mass is 2.0135 u.

step 1 First, we need to understand what deuterium is. Deuterium is the isotope, healy, or hydrogen, 2.

Calculate the binding energy in J/nucleon of the deuterium...

Key Concepts

Atomic Mass Unit (u)

The atomic mass unit is a standard unit of mass used to express the masses of atoms and nuclei. It provides a convenient scale for comparing nuclear masses and is crucial for converting mass differences into energy values.

Binding Energy

Binding energy is the energy required to separate a nucleus into its individual protons and neutrons. It represents the strength of the nuclear forces that hold the nucleons together in the nucleus and is a key indicator of nuclear stability.

Mass Defect

Mass defect is the difference between the mass of a fully assembled nucleus and the sum of the masses of its constituent protons and neutrons. This missing mass has been converted into binding energy according to Einstein's mass-energy equivalence principle.

Energy-Mass Equivalence

Energy-mass equivalence is a principle articulated by Einstein’s famous equation E = mc², which shows that mass can be converted into energy. In the context of nuclear physics, it allows the calculation of binding energy from the observed mass defect.

Binding Energy Per Nucleon

Binding energy per nucleon is the total binding energy divided by the number of nucleons in the nucleus. It offers a measure of the average binding strength each nucleon experiences in the nucleus, which is useful for assessing nuclear stability.

Transcript

00:01 First, we need to understand what deuterium is.

00:05 Deuterium is the isotope, healy, or hydrogen, 2.

00:14 Where that 2 represents one proton and one neutron.

00:20 All right.

00:21 And we're just doing the nucleus.

00:23 So what we're going to end up needing to do is solve einstein's equation, e equals mc squared, and then dividing it by the number of nucleus.

00:35 Now, nucleons is just a generic term for protons and neutrons.

00:42 So deuterium has two nucleons.

00:47 And since they wanted the energy per nucleon, we'll divide by two at the end.

00:50 Okay.

00:51 So first up, in order to solve e equals mc squared, we need to get our delta m.

01:01 Delta m is called the mass defect.

01:04 Essentially, when protons and neutrons come together to form a nuclear, there's a large amount of energy that has to be used in order to hold the nucleus together.

01:13 Now, that energy has to come from somewhere.

01:17 And what einstein figured out was that energy was coming from mass that was being essentially destroyed and converted into energy.

01:27 So our change in mass we're going to find is that if we were to add one proton and one neutron together, which should be the mass of the nucleus of deuterium, that's not what we get.

01:42 The real value is 2 .035.

01:44 That is not what you get when you add a proton and a neutron.

01:47 So to get delta m, right? we start by adding together our nucleons.

01:54 So one proton, i have the masses of protons listed here.

01:59 You can get them off of, you can search from online.

02:02 Usually they're in like the front cover or the back cover of your textbook.

02:05 One proton is 1 .1 .00727.

02:16 647 amus, or atomic mass units, and then one neutron, 1 .008665 amus.

02:25 And yes, you do want to use all of the decimal points that you can for this, because there's a very subtle change in mass.

02:32 So if you just cut it off at one or two decimal points, you're not going to see it.

02:37 Okay, and from that, we're going to subtract the value that they gave us for it, which was the 2 .0135 amuse.

02:46 Plug that into your calculator and you should get a value of 0 .00244147 amus.

02:59 All right.

03:01 So that is the change in mass.

03:02 That's how much mass went missing when the nucleus formed.

03:06 Now, before we plug it into e equals mc squared, we need different units than that.

03:12 We actually need it to be in kilograms...

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