It is estimated that the energy released in the atomic-bomb...

It is estimated that the energy released in the atomic-bomb explosion at Hiroshima was about $7.6 \times 10^{13} \mathrm{~J}$, equivalent to 20,000 tons of TNT. If an average of $200 \mathrm{MeV}$ was released per fission, and if all fissions were by neutron capture in $\mathrm{U}^{235}$, find the number of $\mathrm{U}^{225}$ atoms fissioned and the mass of $\mathrm{U}^{23 s}$ consumed. If 20 percent of the $\mathrm{U}^{23 \mathrm{~s}}$ atoms fissioned, what mass of $\mathrm{U}^{235}$ was needed for the bomb?

Key Concepts

Energy Unit Conversion

This concept involves converting energy units from electron volts (eV) to joules (J). It is essential in nuclear physics to relate the energy released per event (in MeV) to the total energy output (in joules) by using the conversion factor (1 eV = 1.602×10?¹? J).

Energy Yield per Fission

In nuclear fission reactions, a fixed amount of energy is released when a nucleus splits. Here, the average energy release of 200 MeV per fission event serves as a basis to calculate how many fission events are needed to produce a given total energy, linking the microscopic processes to macroscopic energy amounts.

Nuclear Fission Process

Nuclear fission is the splitting of a heavy atomic nucleus into lighter nuclei, accompanied by the release of a large amount of energy. This process, often initiated by neutron absorption in fissile materials like U-235, underpins the operation of atomic bombs and nuclear reactors.

Atomic Mass and Mole Calculations

This concept connects the count of individual atoms to their total mass by using the molar mass and Avogadro's number. It enables one to calculate the mass of material consumed in a reaction by determining the number of atoms involved in nuclear fission.

Reaction Efficiency and Critical Mass

In real-world nuclear reactions, not all the fuel undergoes fission. The efficiency—represented here by a 20% fissioned fraction—must be considered to compute the actual mass of fissile material required. This concept is critical in understanding how a partial yield affects the design and required amount of nuclear material in applications like bombs or reactors.

Please give Ace some feedback