Review problem. A very slow neutron (with speed...

Review problem. A very slow neutron (with speed approximately equal to zero) can initiate the reaction $$ _{0}^{1} \mathbf{n}+\stackrel{10}{5} \mathbf{B} \rightarrow_{3}^{7} \mathbf{L i}+_{2}^{4} \mathbf{H} \mathbf{e} $$ The alpha particle moves away with speed $9.25 \times 10^{6} \mathrm{m} / \mathrm{s}$ . Calculate the kinetic energy of the lithium nucleus. Use nonrelativistic equations.

Review problem. A very slow neutron (with speed approximately equal to zero) can initiate the reaction
$$
_{0}^{1} \mathbf{n}+\stackrel{10}{5} \mathbf{B} \rightarrow_{3}^{7} \mathbf{L i}+_{2}^{4} \mathbf{H} \mathbf{e}
$$
The alpha particle moves away with speed $9.25 \times 10^{6} \mathrm{m} / \mathrm{s}$ . Calculate the kinetic energy of the lithium nucleus. Use nonrelativistic equations.

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Key Concepts

Conservation of Momentum

In any isolated system, including nuclear reactions, the total momentum before and after the reaction remains constant. When a neutron is absorbed by a nucleus, the momentum carried by the resulting particles must balance, allowing us to relate their individual momenta and thereby determine one particle's velocity or kinetic energy if the other’s values are known.

Non-relativistic Kinetic Energy

For particles moving much slower than the speed of light, classical mechanics applies. The kinetic energy in such cases is given by the formula KE = ½mv². This simplification is valid for many nuclear reaction scenarios where the products' speeds are low, allowing straightforward calculations without having to consider relativistic corrections.

Two-body Nuclear Reaction Kinematics

In reactions that yield two products, the conservation laws of momentum and energy govern how the total energy is partitioned between the products. With one product’s speed known, the momentum conservation can be used to determine the speed of the other particle, whose kinetic energy is then calculated using non-relativistic formulas. This approach is fundamental in analyzing the outcomes of nuclear reactions.

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