The values of the masses in the reaction p+ ^19 F →α+ ^16 O have been determined by a mass spect

The values of the masses in the reaction p+ ^19 F →α+ ^16 O...

Key Concepts

Nuclear Reaction Q-value

The Q-value of a nuclear reaction is defined as the net amount of energy released (or absorbed) during the reaction, which is determined by the mass defect. It is calculated by taking the difference in mass between the reactants and products and converting that mass difference into energy using Einstein’s E=mc² and the appropriate conversion factors. A positive Q-value indicates that the reaction is exothermic, releasing energy into the system.

Conversion Factors

Conversion factors are necessary to translate the mass defect into useful energy units. In nuclear physics, atomic mass units (u) are commonly used, and one atomic mass unit is equivalent to approximately 1.660539 × 10?²? kilograms. Additionally, the conversion factor where 1 u is equivalent to roughly 931.494 MeV/c² is used to directly convert a mass difference in atomic mass units into an energy value in mega-electron volts (MeV).

Mass Defect

Mass defect refers to the difference between the total mass of the reactants and the total mass of the products in a nuclear reaction. It arises because some of the mass is converted into energy during the reaction in accordance with mass-energy equivalence. In general, if the total mass of the products is less than that of the reactants, the reaction releases energy, and this missing mass is termed the mass defect.

Einstein's Equation E=mc^2

Einstein's equation, E=mc^2, establishes the relationship between mass and energy, stating that mass can be converted into energy and vice versa. In the context of nuclear reactions, this equation is used to calculate the energy released when a mass defect occurs. The mass difference multiplied by the square of the speed of light gives the amount of energy liberated.

Transcript

00:01 In this problem, we have a particle reaction, proton interacting with fluorine, giving us an alpha particle and oxygen.

00:11 Our particle is actually a helium nucleus.

00:13 We're given the masses of the participants in all this before and after.

00:20 And we're asked, what is the energy released in this? and in these types of problems, we usually define the quantity q as the energy release.

00:30 That's a very common notation.

00:32 And this.

00:34 And i'm going to assume that all four are moving.

00:39 Most likely, though, probably the fluorine is at rest, and the proton comes with some kinetic energy and hits it and causes this.

00:47 Not really important.

00:49 The q is defined as the kinetic energy after, as what it was before.

00:56 So this would be alpha plus k oxygen, minus k proton, let's play floreen.

01:06 That's its definition, really.

01:08 That's his definition.

01:10 Energy release.

01:13 Certainly if this number if what's afterward is greater than what's before, then it's energy release.

01:20 Now, let's look at how we can, this still doesn't help as you say, well, but you didn't, nothing's setting the problem about any type of kinetic energies.

01:29 You don't even, like you said yourself, you don't know what's moving, what's not moving, but we do know the masses.

01:34 So now let's look at energy conservation.

01:37 So that's for the sake of argument, like i said, we'll be writing out every term.

01:43 There's the kinetic energy for the proton, the rest energy, kinetic energy for the fluorine, plus its rest energy, and that's equal to the kinetic energy of the alpha particle, plus the rest energy of the alpha particle, and the same for the, that's the for the oxygen.

02:17 And there's our expression.

02:18 Now let's bring all the terms, let's bring all the terms with mass on the left, everything else, onto the right.

02:25 And i'm going to factor out the c squared.

02:28 Mp plus mf minus.

02:34 And we're going to have the m alpha.

02:37 And let me put parentheses here, m alpha, minus or plus m oxygen.

02:49 And this would be multiplied by c squared.

02:52 And this leaves us with k alpha, because k -oxygen minus proton and minus, but if actually the plus with the parentheses, plus the k -4ene.

03:08 But what is this? this is q.

03:13 So we can find q by looking at the mass difference.

03:17 So what this will tell me is, if q is positive, that means that means a sum of the rest mass.

03:27 I had more rest mass initially than i had afterward.

03:31 Some of the rest mass, initial rest mass, was converted into connect energy.

03:37 That's what's telling me.

03:39 Larger amount here, lesser amount after, and that gives me the energy that's released.

03:51 And so now it's just a matter of punching in our numbers, but that's the meaning of it.

03:56 You know, these q values, q values have a lot of uses.

04:00 Because if you're looking at maybe just a decay, you know, this concept of looking at the masses.

04:08 If you're looking at, say, an object that is just sitting there at rest, can it actually end up, can it actually decay? if the rest mass afterward is less, then the answer is it could.

04:22 But if the rest mass afterward is more, how can that be? where can the, where the new rest mass, extra rest mass come from? that would require then that it had to be, had to have something interact with it with kinetic energy.

04:36 So the kinetic energy was what's called a threshold connect energy brought that reaction to pass.

04:46 So you have, that'd be a conversion then of kinetic energy to rest mass.

04:54 This is actually rest mass to conversion converted to kinetic energy...

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