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$\bullet$ In a hypothetical nuclear-fusion reactor, two deuteriumnuclei combine or "fuse" to form one helium nucleus. Themass of a deuterium nucleus, expressed in atomic mass units(u), is 2.0136 u; that of a helium nucleus is 4.0015 u.$\left(1 \mathrm{u}=1.661 \times 10^{-27} \mathrm{kg} .\right)$ (a) How much energy is releasedwhen 1.0 $\mathrm{kg}$ of deuterium undergoes fusion? (b) The annualconsumption of electrical energy in the United States is on theorder of $1.0 \times 10^{19} \mathrm{J} .$ How much deuterium must react to pro-duce this much energy?

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17421 $\mathrm{kg}$

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

Simon Fraser University

University of Sheffield

University of Winnipeg

Lectures

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

03:18

Sir Isaac Newton described the law of universal gravitation in his work "Philosophiæ Naturalis Principia Mathematica" (1687). The law states that every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

03:50

In a hypothetical nuclear …

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In a hypothetical nuclear-…

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The fusion of two deuteriu…

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E MMH The fusion of two de…

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At illustrates one way to …

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In one type of fusion reac…

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Consider a fusion reaction…

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One of the promising react…

all right and part of this problem. We want to know how much energy Khun b released from converting a kilogram of deuterium into helium. So the first thing we need to do is we need to figure out how many dude Iran's there are in one kilogram and were given that one. Dude, Iran has a ah atomic mass of 2.136 atomic mass units. And the conversion for this two kilograms is 1.661 times 10 to the negative 27. And this comes out to 2.99 um, times 10 to the 26. Then if we if this gets converted to helium, we end up with half the number of helium atoms because it takes to do drones to form one helium. So this is the number of peeling nuclear weekend, and the mass associated without many nuclei is gonna be this number times the way of a single one. And we were given that their masses for point oo 15 atomic last units and again, we want to convert this two kilograms. Oh, no. This comes out to 0.993 65 kilograms. So the amount that we lost in the reaction is one minus that, and we multiply this by C squared to get 5.7 times tended 14 Jules and in part B. We want to figure out, um, how many kilograms it would take. Two power. The U. S. So that's tender. The 19 Jules divided by a 5.7 times 10 to the 14 Jules per kilogram. And this equals 1.8 times 10 to the four kilograms, which is not very much at all.

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