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Problem 10 Medium Difficulty

According to one estimate, there are $4.4 \times 10^{6}$ metric tons of world uranium reserves extractable at $\$ 130 / \mathrm{kg}$ or less. About 0.70$\%$ of naturally occurring uranium is the fissionable isotope 235 $\mathrm{U}$ . (a) Calculate the mass of $^{2355} \mathrm{U}$ in this reserve in grams. (b) Find the number of moles of 235 $\mathrm{U}$ and convert to a number of atoms. (c) Assuming 208 MeV is obtained from each reaction and all this energy is captured, calculate the total energy that can be extracted from the reserve in joules. (d) Assuming world power consumption to be constant at $1.5 \times 10^{13} \mathrm{J} / \mathrm{s},$ how many years could the uranium reserves provide for all the world's energy needs using conventional reactors that don't generate nuclear fuel? (e) What conclusions can be drawn?

Answer

a) $3.1 \times 10^{7} \mathrm{kg}$
b) $7.8 \times 10^{31}$ atoms
c) $2.6 \times 10^{21} \mathrm{J}$
d) 5.5$\mathrm{yrs}$
e) The energy provided by fission would not be sufficient to sustain the world's energy needs

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Top Physics 103 Educators
Elyse G.

Cornell University

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Video Transcript

for the first polities question to find out why Steam ass off. You're in you to be five. In our reserves, you're given debts. A total of 4.4 step out of six metric tons off. Ah, uranium to tree uranium. Sorry, naturally occurring uranium. And out off this metric tons 20.7% is how I still talk to treat five, which we can use for you coefficient. Right. So you mess will be close to this 4.4 metric tons What you play by. It's your 0.7% all right. And you want to convert from metric tons to S I units, which is k g or I don't grams all cagey. So one ton, one metric ton is actually tended poetry k g so we can cover this tonnes into cagey by multiplying by 10 to poetry you should get one time Send polo seven kitschy. Next we want to find what is the number of atoms in this total mess off? Union 25. So number off your immune to five phantoms. We take the mess which is 3.1 times in post seven kilograms. Me divide by D mass off each individual atom. So the mess off a uranium to refire term is 235 you where you wasted atomic mass units. So we're gonna convert that into K G by multiplying by 1.66 times 10 Part ministry seven k g poor right? So we should get the number off atoms to be 7.8 times 10 31 and we assume that's all of these attorneys can on a coefficient. So they told him of energy that can be captured, Right? Told So Toto will be the number off, you know, 235 multiplied by the energy released, pull efficient and energy release. Proficient is given as 200 feet MTV. And since you're dealing with a very large number, we can convert it into juice by multiplying by 1.6 times 10 part Minnesota teen juice per m e v. So this will give us in terms off juice and on set should be to play six times and protein one juice. Finally, given that the consumption rates off energy for the whoa, we assume it to be 1.5 time tent about the teen juice per second going to find out how long that this amount off energy can last us. So t time that ah can't lost it would be closed toe the taught energy divide by D energy consumption rate, which is 1.5 times 10 part 13 jokes per second. So these in terms off juice and you will get the answer in terms off seconds, which is a very lunch number 2.6 to fight by. Fine, get what points of it. Tree first tent puff eight seconds. Now converting this into a smaller unit. I mean, a larger unit in terms off years. And today that we divide by the number of seconds in a year that IHS treat point 156% poll seven seconds per year. We get about 5.5 years now. This is a very, very short amount time Only this tells us that she fisher in the loneliness not enough to sustain the world's energy needs, at least at this particular price off 130 or less per kilogram. If you're in you and like the, you have to either source for other forms off energy. Oh, it to keep, uh, the energy consumption at this particular devil

National University of Singapore
Top Physics 103 Educators
Elyse G.

Cornell University

Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Farnaz M.

Other Schools