Question

Write equations for the following nuclear reactions. (a) bombardment of \(^{238} \mathrm{U}\) with \(\alpha\) particles to produce \(^{239} \mathrm{Pu}\) (b) bombardment of tritium ( \(^{3} \mathrm{H}\) ) with \(_{1}^{2} \mathrm{H}\) to produce \(^{4} \mathrm{He}\) (c) bombardment of \(^{33} \mathrm{S}\) with neutrons to produce \(^{33} \mathrm{P}\).

Short answer

The nuclear reactions are: (a) \(^{238}_{92} \mathrm{U} + ^{4}_{2} \mathrm{He} \rightarrow ^{239}_{94} \mathrm{Pu} + ^{1}_{0}n\),(b) \(^{3}_{1} \mathrm{H} + _{1}^{2} \mathrm{H} \rightarrow ^{4}_{2} \mathrm{He} + ^{1}_{0}n\),(c) \(^{33}_{16} \mathrm{S} + ^{1}_{0}n \rightarrow ^{33}_{15} \mathrm{P} + ^{-1}_{0}e\).

Step-by-step solution

Write Equation for Reaction a

For the reaction \(^{238} \mathrm{U} + \alpha \rightarrow ^{239} \mathrm{Pu} + ?\), An alpha particle has an atomic number of 2 and a mass of 4. To make the atomic numbers and masses balance, the particle produced should have an atomic number of 2 and a mass of 3. Thus, the product of the reaction is a neutron \(^{1}_{0}n\), so the reaction is \(^{238}_{92} \mathrm{U} + ^{4}_{2} \mathrm{He} \rightarrow ^{239}_{94} \mathrm{Pu} + ^{1}_{0}n\)

Write Equation for Reaction b

Consider the reaction \(^{3} \mathrm{H} + _{1}^{2} \mathrm{H} \rightarrow ^{4} \mathrm{He} + ?\). The missing particle must have an atomic number of 0 and a mass number of 1 to make the atomic numbers and masses balance, which is a neutron \(^{1}_{0}n\). So the reaction is \(^{3}_{1} \mathrm{H} + _{1}^{2} \mathrm{H} \rightarrow ^{4}_{2} \mathrm{He} + ^{1}_{0}n\)

Write Equation for Reaction c

For the reaction \(^{33} \mathrm{S} + neutron \rightarrow ^{33} \mathrm{P} + ?\), because the atomic numbers and masses must balance, the missing particle would essentially be an electron \(^{-1}_{0}e\) So the reaction is \(^{33}_{16} \mathrm{S} + ^{1}_{0}n \rightarrow ^{33}_{15} \mathrm{P} + ^{-1}_{0}e\)

Key concepts

Alpha Particle Bombardment

Alpha particle bombardment plays a crucial role in nuclear reactions. An alpha particle is essentially the nucleus of a helium atom, denoted as \[ _{2}^{4} ext{He} \] which means it has a mass number of 4 and an atomic number of 2. When a nucleus is bombarded with alpha particles, it can transform into a new element because of the rearrangement and addition of those nucleons -- protons and neutrons. In the exercise given, an example of such bombardment is when \[ _{92}^{238} ext{U} + _{2}^{4} ext{He} \] produces \[ _{94}^{239} ext{Pu} \]. This reaction is known for producing Plutonium-239 from Uranium-238. Alpha particles penetrate into the uranium nucleus, adding two protons and two neutrons. In this process, a neutron is also released to ensure balance in the reaction. Understanding alpha particle bombardment is critical as it underpins processes such as nuclear synthesis and formation of transuranic elements.

Neutron Production

Neutron production occurs in various nuclear reactions and is vital for maintaining balance in these equations. When you bombard a nucleus, neutrons are often part of the released particles, carrying away energy and momentum to stabilize the newly formed nucleus.To illustrate this in the problem at hand, consider Reaction B: \[ _{1}^{3} ext{H} + _{1}^{2} ext{H} \rightarrow _{2}^{4} ext{He} + _{0}^{1}n \].In this reaction, deuterium and tritium combine to form helium-4 and a neutron. The neutron produced is essential not just for balance but also for facilitating further nuclear interactions. Neutrons themselves do not carry any charge, allowing them to move and penetrate other atomic nuclei with relative ease in processes like nuclear fission and fusion.In the realm of nuclear physics, controlling neutron production is crucial in applications like nuclear reactors and atomic bomb reactions, where the number of neutrons produced can significantly influence the rate of the reaction.

Balancing Nuclear Equations

Balancing nuclear equations is a fundamental skill in understanding nuclear reactions. It ensures the conservation of both mass and atomic numbers, crucial for maintaining equilibrium in nuclear reactions. A balanced nuclear reaction means the sum of atomic numbers (protons in the nuclei) and mass numbers (total nucleons) on both sides of the equation should be equal. To achieve this, we take into account not only the main products but also any additional particles released or absorbed.Consider Reaction C from the original exercise: \[ _{16}^{33} ext{S} + _{0}^{1}n \rightarrow _{15}^{33} ext{P} + _{-1}^{0}e \].Here, sulfur is converted into phosphorus upon neutron bombardment, and to keep the equation balanced, an electron (or beta particle) is emitted. The roles of different particles ensure all balances are satisfied. • **Atomic number:** Conserved by ensuring the sum of protons on both sides is equivalent.• **Mass number:** Conserved by ensuring the total number of nucleons remains unchanged.Balancing nuclear equations demands careful attention, perfecting your understanding of different particles involved, and acknowledging the laws of conservation.