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Problem 87 Hard Difficulty

One of the simplest fusion reactions involves the production of deuterium, $_{1}^{2} \mathrm{H}(2.014102 \mathrm{u}),$ from a neutron and a proton. Write the complete fusion reaction and find the amount of energy released.

Answer

$\frac{1}{1} p+\frac{1}{0} n \rightarrow \frac{2}{1} H$
$-2.2244 \mathrm{MeV}$

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Top Physics 103 Educators
Elyse G.

Cornell University

LB
Liev B.

Numerade Educator

Farnaz M.

Simon Fraser University

Aspen F.

University of Sheffield

Video Transcript

for this question were asked to write out the fusion reaction of a proton and a neutron to form deteriorate and then were asked to find the energy released from this fusion. So this is the fusion reaction. We have a proton which has one atomic mass and one for the atomic number, and neutron, which has one mass number but zero for the atomic number, since it doesn't have a charge. And since we need to conserve the mass number in the atomic number, there's 21 plus one is two for the mass number, so deuterium has two and 1.0 is one. So deuterium has won for the atomic number. So this is our equation. So find the energy released. We need to find the mass deference deficit MD. So the mass deficit comes from taking the mass of the final product. We can call this imps of age which were given immunity of atomic units. In the beginning of the question, we're told that this is equal to 2.14102 atomic units. We subtract from that the mass of the objects that were fused together to make that object so the mass of the proton in atomic units and then also subtract the mass of the neutron and atomic units. These are just constant, so you can look them up. But the mass of the proton is equal to 1.6 exceeding 1.7852 And that of the neutron is 1.8665 atomic units. So carrying out this operation, we find that the mass deficit is equal to zero 0.2 three a atomic units so we can convert that to units of energy units of MTV. So the energy is equal to the mass deficit, since energy and mass are interchangeable. According to Einstein's equation, the energy is equal to the mass deficit m sub d multiplied by the conversion between MTV and atomic units, which is 931 0.49 MTV for everyone atomic unit. So taking her mass deficit value and multiplying it by this conversion factor, we find that the energy that is released here is 2.2 to maybe making box that in as our solution as well as the energy equation cause I was the other part of the solution were asked to find so he can box this in as well.

University of Kansas
Top Physics 103 Educators
Elyse G.

Cornell University

LB
Liev B.

Numerade Educator

Farnaz M.

Simon Fraser University

Aspen F.

University of Sheffield