De acuerdo con una estimación, existen 4.4 ×10^6 toneladas métricas de reservas de uranio mundia

De acuerdo con una estimación, existen 4.4 ×10^6 toneladas...

De acuerdo con una estimación, existen $4.4 \times 10^6$ toneladas métricas de reservas de uranio mundiales extraibles a $$\$ 130 / \mathrm{kg}$$ o menos. Alrededor de $0.7 \%$ del uranio que ocurren de manera natural es el isótopo fisionable ${ }^{25}$ U. a) Calcule la masa de ${ }^{250}$ U en esta reserva, en gramos. b) Encuentre el número de moles de ${ }^{285} \mathrm{U}$ y conviértela a un número de átomos. c) Suponiendo que de cada reacción se obtiene $208 \mathrm{MeV}$ y que toda esta energía se captura, calcule la energía total que se puede extraer de las reservas, en joules. d) Suponiendo que el consumo de potencia mundial es constante en $1.5 \times 10^{13} \mathrm{~J} / \mathrm{s}$, ddurante cuántos años las reservas de uranio podrian abastecer todas las necesidades de energía del mundo? e) ¿Qué conclusión se puede extraer?

Key Concepts

Isotopic Abundance

This concept involves understanding the natural occurrence of different isotopes in an element, particularly distinguishing between fissile and non-fissile isotopes. It is crucial when calculating the amount of a specific fissile isotope available within a given mass of material, which influences both the efficiency and feasibility of nuclear reactions for energy production.

Mole and Atomic Number Conversions

This concept involves converting mass into moles using the molar mass and then converting moles into number of atoms using Avogadro's number. These conversions are fundamental in chemistry and nuclear physics for quantifying substances at a microscopic level, allowing for the calculation of reaction yields based on the number of reactant particles present.

Unit Conversions

Unit conversion is a key mathematical tool used to switch between different measurement systems, such as converting mass from metric tons to grams or energy from electron volts to joules. This skill is essential for ensuring that calculations in nuclear physics and engineering maintain consistent units, thereby yielding correct quantitative results.

Nuclear Fission Energy Yield

This concept relates to the energy released during a nuclear fission reaction, typically expressed in mega electron volts (MeV) per reaction. Understanding the energy yield per reaction allows one to estimate the total energy that can be extracted from a given quantity of fissile material, which is critical in evaluating the potential of nuclear power as an energy source.

Energy Consumption Rate and Reserve Longevity

This concept involves comparing the total available extractable energy from nuclear reserves to the constant rate of energy consumption by society. It provides an estimation of how long the energy supply could last if it were the sole source of energy, and it is essential for discussions on energy sustainability and resource management in the context of global energy needs.

Transcript

00:01 Hello, and in this question here, we're told that the total mass of uranium in the world's, that is extractable in the earth surface, is equal to 4 .4 times 10 to the power of 9 kilograms.

00:17 Okay? and, well, we want to determine in the first part of the question, the mass of uranium, the amount of uranium 235, okay? so, the mass of uranium of uranium 235, okay? so the mass of, uranium 235 well that is equal to the percentage of uranium that is uranium 235 so that is equal to 0 .007 okay so that's so 0 .7 % is the percentage that is uranium 235 and writing 0 .7 % is a decimal it's equal to 0 .007 okay and we multiply by the total mass of uranium, which is 4 .4 times 10 to the power of 9.

01:08 So this gives the total mass of uranium 235 is equal to 3 .8, 3 .08 times 10 to the power of 10, sorry, times 10 to the power of 7 kilograms.

01:27 And we're asked to calculate the answer in grams.

01:30 So we just, that is equal to 10 to the power of 10 grams.

01:36 And that is the mass of uranium in grams, of uranium 235 in grams.

01:41 Now, in the next part of the question, we're asked to calculate how many moles of uranium this is equal to.

01:47 So one mole, so uranium has a mass of 235.

01:59 04439233u.

02:00 So this means that it has a mass of 235 .0 .04395 grams per mole.

02:09 Okay.

02:11 So we can divide this number here.

02:13 So this is the amount and when meant one mole waste.

02:17 So we can divide the total number of the total mass of uranium.

02:22 So the number of moles, okay, is equal to the mass of uranium 235 divided by the mass of a mole.

02:31 Okay? we can summon these two values, okay? and that gives the number of moles of uranium that's extractable in the earth surface is equal to 1 .3 times 10 to the power of 8 moles...

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