It has been estimated that Earth has 9.1 ×10^11 kg of natural uranium that can be economically m

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It has been estimated that Earth has 9.1 ×10^11 kg of...

It has been estimated that Earth has $9.1 \times 10^{11} \mathrm{kg}$ of natural uranium that can be economically mined. Of this total, 0.70 percent is $^{235} \mathrm{U}$. If all the world's energy needs $\left(7.0 \times 10^{12} \mathrm{J} / \mathrm{s}\right)$ were supplied by $^{235} \mathrm{U}$ fission, how long would this supply last? Assume that $208 \mathrm{MeV}$ of energy is released per fission event and that the mass of $^{235} \mathrm{U}$ is about $3.9 \times 10^{-25} \mathrm{kg}$.

Key Concepts

Conversion of Mass to Number of Nuclei

Determining the number of nuclei available in a sample of nuclear fuel involves converting the mass of the fuel into the number of individual atoms based on the mass of a single nucleus. This concept is essential for scaling up the microscopic energy release per fission event to the energy obtainable from macroscopic quantities of fuel.

Energy Release per Fission Event and Unit Conversion

Each fission event releases a quantifiable amount of energy, often expressed in units such as mega electron volts (MeV). Converting this energy to joules is crucial for calculating the total energy that can be harnessed from a given mass of nuclear fuel, thus linking microscopic nuclear processes with macroscopic energy needs.

Power and Energy Supply Duration Calculation

To estimate how long a fuel supply will last, one must relate the total energy available from the fuel to the energy consumption rate (power). This involves calculating the total energy output from all fission events and then dividing by the global power demand, thereby converting a static resource quantity into a temporal availability measure.

Nuclear Fission

Nuclear fission is the process where a heavy nucleus splits into smaller nuclei, releasing a significant amount of energy in the process. This reaction is fundamental to nuclear power generation and is the principle behind nuclear reactors and atomic bombs, relying on the conversion of the nuclear binding energy into usable work or energy.

Isotopic Abundance

Isotopic abundance refers to the relative proportion of a particular isotope of an element found naturally. In the context of uranium, the percentage of uranium-235, which is fissile, is critical because it determines how much of the raw material can actually be used for energy production via fission.

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