When a star has exhausted its hydrogen fuel, it may fuse...

When a star has exhausted its hydrogen fuel, it may fuse other nuclear fuels. At temperatures above $1.0 \times 10^{8} \mathrm{K}$ , helium fusion can occur. Write the equations for the following processes. (a) Two alpha particles fuse to produce a nucleus $A$ and a gamma ray. What is nucleus $A ?$ (b) Nucleus $A$ absorbs an alpha particle to produce a nucleus $B$ and a gamma ray. What is nucleus $B ?(c)$ Find the total energy released in the reactions given in parts (a) and (b). Note: The mass of $_{4}^{8} \mathrm{Be}=8.005305 \mathrm{u} .$

When a star has exhausted its hydrogen fuel, it may fuse other nuclear fuels. At temperatures above $1.0 \times 10^{8} \mathrm{K}$ , helium fusion can occur. Write the equations for the following processes. (a) Two alpha particles fuse to produce a nucleus $A$ and a gamma ray. What is nucleus $A ?$ (b) Nucleus
$A$ absorbs an alpha particle to produce a nucleus $B$ and a gamma ray. What is nucleus $B ?(c)$ Find the total energy released in the reactions given in parts (a) and (b). Note: The mass of $_{4}^{8} \mathrm{Be}=8.005305 \mathrm{u} .$

Key Concepts

Stellar Nucleosynthesis

This concept involves the process by which elements are produced within stars through nuclear fusion reactions. It explains how stars generate energy and create heavier elements by fusing lighter nuclei, a fundamental process in astrophysics.

Alpha Particles

Alpha particles, which are helium nuclei composed of two protons and two neutrons, play a key role in nuclear fusion reactions. Their ability to overcome the Coulomb barrier at high temperatures allows them to participate in the synthesis of heavier elements in stellar environments.

Triple-Alpha Process

The triple-alpha process is an essential reaction in helium-burning stars where three alpha particles (helium nuclei) combine to form a carbon nucleus. This process typically involves the intermediate formation of a short-lived beryllium-8 nucleus, emphasizing the importance of sequential capture reactions in stellar nucleosynthesis.

Nuclear Reaction Equations

Writing nuclear reaction equations involves representing the reactants and products while ensuring the conservation of mass number and atomic number. These equations also include gamma rays when necessary to account for the energy released during the reaction.

Mass-Energy Equivalence and Q-value Calculation

In nuclear reactions, the difference in mass between reactants and products (the mass defect) is converted into energy, as described by Einstein’s equation E=mc². The Q-value, which quantifies this energy release or absorption, is fundamental for understanding the energetics of fusion reactions in stars.

Transcript

00:01 In this question, we are looking at how the star actually fuse undergo nuclear fusion.

00:09 And one of it that is possible is the fusion of alpha particles.

00:14 And of course, the alpha particle, after diffusion, you can undergo further fusion.

00:20 So we're going to look at what are the processes.

00:22 So we're given the first reaction is two alpha particles fusing together.

00:31 To form an unknown nucleus a along with a gamma ray.

00:39 So in order to identify what is the unknown nucleus a, we can use the conservation of our nuclear number, as well as the proton number.

00:51 So nuclear number is the number at the top, and proton number is the one that's below.

00:57 And the left -hand side, the total proton number, must be the same as the right -hand side.

01:01 So that's like the conservation of the proton number.

01:06 On the left hand side we see there's a total of 4.

01:08 So on the right we must have 4 as well.

01:10 Since gamma ray doesn't have any protons, it must have 4 protons.

01:15 Same for the nuclear number, this must be an 8.

01:18 Since left side inside we have 4 plus 4, which is 8.

01:22 Looking up the periodic table for an element with 4 protons, we see that this is actually beryllium.

01:28 So this is actually beryllium 8.

01:36 Now we are given that this beryllium 8 actually undergoes further absorption of a alpha particle.

01:47 It should be...

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