Calculate the amount of energy released or absorbed in the...

Calculate the amount of energy released or absorbed in the following reactions (express your answers in $\mathrm{MeV}$ ): (a) $^{12} \mathrm{C}+_{6}^{12} \mathrm{C} \rightarrow_{12}^{24} \mathrm{Mg}+\gamma$ (b) $^{12} \mathrm{C}+^{12} \mathrm{C} \rightarrow_{8}^{16} \mathrm{O}+2_{2}^{4} \mathrm{He}$ (c) $_{9}^{19} \mathrm{F}+_{1}^{1} \mathrm{H} \rightarrow_{8}^{16} \mathrm{O}+_{2}^{4} \mathrm{He}$ The mass of $^{12} \mathrm{C}$ is $12.0000 \mathrm{u}$, by definition, and the masses of $_{8}^{16} \mathrm{O},_{9}^{19} \mathrm{F},$ and $_{12}^{24} \mathrm{Mg}$ are $15.99491 \mathrm{u}$ $18.99840 \mathrm{u},$ and $23.98504 \mathrm{u}$, respectively. Are these reactions exothermic or endothermic?

Calculate the amount of energy released or absorbed in the following reactions (express your answers in $\mathrm{MeV}$ ):
(a) $^{12} \mathrm{C}+_{6}^{12} \mathrm{C} \rightarrow_{12}^{24} \mathrm{Mg}+\gamma$
(b) $^{12} \mathrm{C}+^{12} \mathrm{C} \rightarrow_{8}^{16} \mathrm{O}+2_{2}^{4} \mathrm{He}$
(c) $_{9}^{19} \mathrm{F}+_{1}^{1} \mathrm{H} \rightarrow_{8}^{16} \mathrm{O}+_{2}^{4} \mathrm{He}$
The mass of $^{12} \mathrm{C}$ is $12.0000 \mathrm{u}$, by definition, and the masses of $_{8}^{16} \mathrm{O},_{9}^{19} \mathrm{F},$ and $_{12}^{24} \mathrm{Mg}$ are $15.99491 \mathrm{u}$ $18.99840 \mathrm{u},$ and $23.98504 \mathrm{u}$, respectively. Are these reactions exothermic or endothermic?

Key Concepts

Mass-Energy Equivalence

This concept, defined by Einstein’s famous equation E=mc², relates a change in mass to a corresponding change in energy. In nuclear reactions, even a small difference in mass (mass defect) between reactants and products can result in a significant amount of energy being released or absorbed.

Mass Defect

The mass defect is the difference between the total mass of the reactants and the total mass of the products in a nuclear reaction. This difference arises because some mass is converted to energy (or vice versa) during the reaction, and it is the fundamental basis for the energy change in nuclear processes.

Q-Value Calculation

The Q-value of a nuclear reaction is a calculation that determines the net energy release or absorption. It is computed by taking the difference between the sum of the masses of the reactants and the sum of the masses of the products, and then converting this mass difference into energy using the mass-energy equivalence principle.

Atomic Mass Unit Conversion

In nuclear physics, atomic mass units (u) are often used to express masses, and these are converted into energy units (MeV) using a conversion factor, typically around 931.5 MeV per atomic mass unit (u). This conversion is essential when calculating the energy change in a nuclear reaction from mass differences.

Exothermic vs Endothermic Reactions

These terms describe whether a reaction releases or absorbs energy. In a nuclear reaction, if the products have less mass than the reactants (resulting in a positive Q-value), the reaction is exothermic, meaning it releases energy. Conversely, if the reactants have less mass than the products (resulting in a negative Q-value), the reaction is endothermic, meaning it absorbs energy.

Transcript

00:01 Question 19 asks to consider the induced nuclear reaction shown here.

00:06 It provides the atomic masses for each of these elements, and it asks to determine the energy in med released by the reaction.

00:14 So this is our situation.

00:16 This reaction, deuterium nitrogen produces carbon and helium.

00:21 So i'll type this one out, which is a little bit easier.

00:24 We know that the energy released in this reaction is simply given by the change in mass, multiplied by c squared.

00:38 So actually i represent this slightly differently.

00:42 We want to know, again, i did say the change in mass, so we should probably include change in mass, but also it's the absolute value of the difference in change in mass.

00:51 So that just means sometimes you'll need energy to compute this reaction, other times you'll have energy produced in this scenario.

00:58 So just to take that account, we just take in terms of absolute value.

01:02 And we have this expression.

01:05 So in order to solve for this, we look at the masses on, let's just say our reactant side, our product side, on the right hand side.

01:12 We take those masses, so we take, i'll write this out, so our delta mass we'll use is our mass of our final products minus our mass of our initial products.

01:25 And of course, we take the absolute value of that just so we have a positive mass quantity.

01:31 So continuing on, we add in this absolute value term, the mass is provided four hundred, us, so of the final terms.

01:39 Mass of carbon 12 is exactly 12...

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