Calculate the amount of energy released per gram of hydrogen...

Calculate the amount of energy released per gram of hydrogen nuclei reacted for the following reaction. The atomic masses are $_{1}^{1} \mathrm{H}, \quad 1.00782$ u; $_{1}^{2} \mathrm{H}, \quad 2.01410 \quad \mathrm{u} ;$ and an electron, $5.4858 \times 10^{-4}$ u. (Hint: Think carefully about how to account for the electron mass.) $$ _{1}^{1} \mathrm{H}+_{1}^{1} \mathrm{H} \longrightarrow_{1}^{2} \mathrm{H}+_{+1}^{0} \mathrm{e} $$

Calculate the amount of energy released per gram of hydrogen nuclei reacted for the following reaction. The atomic masses are $_{1}^{1} \mathrm{H}, \quad 1.00782$ u; $_{1}^{2} \mathrm{H}, \quad 2.01410 \quad \mathrm{u} ;$ and an electron, $5.4858 \times 10^{-4}$ u. (Hint: Think carefully about how to account for the electron mass.)
$$
_{1}^{1} \mathrm{H}+_{1}^{1} \mathrm{H} \longrightarrow_{1}^{2} \mathrm{H}+_{+1}^{0} \mathrm{e}
$$

Key Concepts

Electron Mass Considerations

In nuclear reactions involving electrons, it is crucial to account for the electron mass accurately. Despite being relatively small compared to nuclear masses, the electron mass can affect the overall mass balance and, ultimately, the precise calculation of energy release in high-precision nuclear energy computations.

Nuclear Reaction Energetics

Nuclear reaction energetics studies the energy changes during nuclear processes, primarily focusing on how differences in binding energy among nuclei lead to energy release or absorption. This concept is central to understanding the dynamics and stability of nuclear reactions.

Energy Conversion

Energy conversion in nuclear reactions involves changing the units of the mass defect into energy. Typically, the conversion factor 1 atomic mass unit (u) ? 931.5 MeV is used. This conversion is essential to quantify the energy released from the mass difference occurring in the reaction.

Mass Defect

Mass defect is the difference in mass between the reactants and the products in a nuclear reaction. This loss in mass, when converted using Einstein’s equation (E=mc²), represents the energy released in the reaction. It forms the fundamental concept behind calculating the energy yield of nuclear processes.

Transcript

00:01 In this problem, we're talking about the mass defect of hydrogen nuclei.

00:06 And this is important because this has a direct application.

00:10 This could be seen as the reaction that occurs in the sun.

00:13 This is hydrogen nuclei reacting.

00:16 So the way that we're going to figure this out is that we're going to use the famous equation, e equals mc squared.

00:23 The only difference is, in this case, we're going to have e equals a delta mc squared.

00:28 So what does that mean? we have to find the mass defect, the change in mass in this overall reaction that we're given.

00:37 And in this reaction, just to review it, we're given two hydrogen nuclei that's going to form two hydrogen nuclei plus a positron.

00:49 So how do we find the mass defect to plug into our equation? well, this is actually a lot of calculation to do.

00:55 We're going to get the delta m equals the mass of our two hydrogen nuclei plus our positron minus two times the mass of our one hydrogen nuclei.

01:09 So you can, another way to think about this is that this is just the mass of the products minus the mass of the reactants.

01:16 Okay, so now let's start this calculation.

01:19 Delta m is going to be equal to 2 .01410 minus 2 times 1 .0 .0 .0.

01:26 0 .0782 minus 5 .485 .08 times 10 to the negative fourth.

01:35 Okay.

01:37 So now we're going to simplify this.

01:38 Delta m equals negative 4 .4 -284 times 10 to the negative 4th.

01:44 This is an amus per nucleus.

01:47 And then we can convert it into kilograms per nucleus...