Calculate the quantity of energy produced per mole of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to produce Te-137 (atomic mass = 136.9253 amu) and Zr-97 (atomic mass = 96.910950 amu) (discussed in Problem 58).

검증된 단계별 안내

Identify the nuclear reaction: U-235 undergoes fission when it absorbs a neutron, resulting in the formation of Te-137, Zr-97, and additional neutrons.

Calculate the mass defect: Determine the difference in mass between the reactants (U-235 and a neutron) and the products (Te-137, Zr-97, and additional neutrons).

Convert the mass defect to energy: Use Einstein's equation, \( E = \Delta m c^2 \), where \( \Delta m \) is the mass defect and \( c \) is the speed of light, to find the energy released per fission event.

Determine the energy per mole: Multiply the energy per fission event by Avogadro's number (\( 6.022 \times 10^{23} \) mol\(^{-1}\)) to find the energy produced per mole of U-235.

Summarize the process: The energy produced per mole of U-235 is the result of converting the mass defect into energy, as described by Einstein's equation, and scaling it to a molar quantity using Avogadro's number.

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영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Nuclear Fission

Nuclear fission is a process in which a heavy nucleus, such as uranium-235, splits into two smaller nuclei, along with the release of energy and neutrons. This reaction can be initiated by the absorption of a neutron, leading to a chain reaction that can produce significant amounts of energy, which is the principle behind nuclear reactors and atomic bombs.

Mass-Energy Equivalence

Mass-energy equivalence, expressed by Einstein's equation E=mc², states that mass can be converted into energy and vice versa. In nuclear reactions, the mass of the products is often less than the mass of the reactants, and this 'missing' mass is converted into energy, which can be calculated to determine the energy released during fission.

Binding Energy

Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is a measure of the stability of a nucleus; higher binding energy indicates a more stable nucleus. In fission, the binding energy of the products is greater than that of the reactants, resulting in the release of energy during the reaction.