Energy in a Square Inch of Uranium-235: An Exploration of Nuclear Fission

The energy contained in uranium, a key element in nuclear power generation and weaponry, is influenced by the isotope and reaction involved. Uranium-235 (U-235) is the most frequently discussed isotope for generating nuclear energy.

Energy Density of U-235

U-235 releases approximately 200 million electron volts (MeV) per fission event. One MeV is about (1.6 times 10^{-13}) joules. Therefore, 200 MeV corresponds to roughly (3.2 times 10^{-11}) joules. This high energy output highlights the immense potential energy stored in uranium.

Mass of U-235

U-235 has a density of about 18.95 g/cm3. A square inch (in2) is approximately 6.45 cm2. Assuming a thickness of 1 cm, the volume of uranium in a square inch would be about 6.45 cm3. Thus, the mass of uranium in one square inch would be roughly:

[text{Mass} text{Density} times text{Volume} 18.95 , text{g/cm}^3 times 6.45 , text{cm}^3 approx 122.4 , text{g}]

Fission Events

The number of U-235 atoms in 122.4 g can be calculated using Avogadro's number (6.022 times 1023 atoms/mol) and the molar mass of U-235 (approximately 235 g/mol):

[text{Moles of U-235} frac{122.4 , text{g}}{235 , text{g/mol}} approx 0.520 , text{mol}][text{Number of atoms} 0.520 , text{mol} times 6.022 times 10^{23} , text{atoms/mol} approx 3.13 times 10^{23} , text{atoms}]

Assuming all U-235 atoms undergo fission, the total energy released would be:

[text{Total Energy} text{Number of atoms} times text{Energy per fission} approx 3.13 times 10^{23} times 3.2 times 10^{-11} , text{J} approx 1.00 times 10^{13} , text{J}]

This translates to approximately 10 trillion joules of energy if all U-235 undergoes fission. This is a vast amount of energy, far greater than that contained in conventional fuels.

Understanding Potential Energy and Forces

In physics, the concept of potential energy (U) is always related to a force (vec{F}) via the relation (vec{F} - abla U). This relationship is a convention that works well in Newtonian mechanics. The question of potential energy, however, is inherently arbitrary due to the fact that the smallest possible value (U_0) of a potential energy field is irrelevant, as different offsets do not change the force field.

For example, the force in a potential energy field (U) can be expressed as:

[vec{F'} - abla U' - abla (U U_0) - abla U]

This arbitrariness in potential energy values is a fundamental aspect of the concept, underscoring the importance of the gradient of potential energy rather than the absolute value of potential energy.

Understanding the enormous energy potential in a small volume of uranium-235 underscores the significance of nuclear science and technology. If you found this information useful, please support me by upvoting this answer and following my Space.