A small atomic bomb releases energy equivalent to the...

A small atomic bomb releases energy equivalent to the detonation of 20,000 tons of TNT; a ton of TNT releases $4 \times 10^{9} \mathrm{J}$ of energy when exploded. Using $2 \times 10^{13} \mathrm{J} / \mathrm{mol}$ as the energy released by fission of $^{235} \mathrm{U},$ approximately what mass of $^{235} \mathrm{U}$ undergoes fission in this atomic bomb?

Key Concepts

Energy Unit Conversion

Energy unit conversion involves translating energy values between different measurement systems, such as converting tons of TNT into joules. This is essential for comparing the energy released from different sources, ensuring that all calculations are performed on a consistent energy scale.

Moles and Molar Mass in Nuclear Reactions

The concept of the mole and molar mass is crucial in nuclear reactions, as it allows for the conversion between the number of reacting atoms (or nuclei) and the measurable mass of the material. By knowing the energy released per mole and the molar mass of the substance, one can determine the mass of material that underwent the reaction.

TNT Equivalence

TNT equivalence is a method of quantifying the energy released in explosive events by comparing them to the energy released by a known amount of TNT. This concept allows for the conversion of explosive yields into standardized energy units (joules) so that different types of explosions can be compared directly.

Nuclear Fission Energy

Nuclear fission is the splitting of a heavy nucleus into lighter nuclei, accompanied by a large release of energy. The energy released per fission event is often given in terms of energy per mole, which provides a basis for calculating the total energy produced by fissioning a specific amount of material such as uranium-235.

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