Question

Write balanced nuclear equations for the bombardment of (a) U-238 with a nucleus to produce Fm-249 and five neutrons. (b) Al-26 with an alpha particle to produce \(\mathrm{P}-30\). (c) Cu-63 with a nucleus producing \(\mathrm{Zn}-63\) and a neutron. (d) Al-27 with deuterium \(\left({ }_{1}^{2} \mathrm{H}\right)\) to produce an alpha particle and another nucleus. (c) Ar-40 with an unknown particle to produce \(\mathrm{K}-43\) and a proton. (d) a nucleus with a neutron to produce a proton and \(\mathrm{P}-31\).

Short answer

a) The balanced nuclear equation for U-238 producing Fm-249 and five neutrons is: U-238 + O-243 → Fm-249 + 5n b) The balanced nuclear equation for Al-26 with an alpha particle to produce P-30 is: Al-26 + He-4 → P-30 c) The balanced nuclear equation for Cu-63 with a nucleus producing Zn-63 and a neutron is: Cu-63 + H-1 → Zn-63 + n d) The balanced nuclear equation for Al-27 with deuterium to produce an alpha particle and another nucleus is: Al-27 + H-2 → He-4 + Mg-25 e) The balanced nuclear equation for Ar-40 with an unknown particle to produce K-43 and a proton is: Ar-40 + He-4 → K-43 + H-1 f) The balanced nuclear equation for a nucleus with a neutron to produce a proton and P-31 is: Si-31 + n → H-1 + P-31

Step-by-step solution

(a) U-238 produces Fm-249 and five neutrons

Initial particles: U-238 and a nucleus Final particles: Fm-249, and five neutrons To balance the mass numbers, we have: 238 + A = 249 + 5(1) A = 243 To balance the atomic numbers, we have: 92 + Z = 100 + 0 Z = 8 Thus, the initial nucleus has a mass number of 243 and an atomic number of 8, which is O-243. So the balanced nuclear equation is: \(\mathrm{U-}^{238}_{92}+\mathrm{O-}^{243}_{8} \to \mathrm{Fm-}^{249}_{100} + 5\mathrm{n}\)

(b) Al-26 with an alpha particle to produce P-30

Initial particles: Al-26, alpha particle Final particles: P-30 Balanced nuclear equation: \(\mathrm{Al-}^{26}_{13}+\mathrm{He-}^4_2 \to \mathrm{P-}^{30}_{15}\)

(c) Cu-63 with a nucleus producing Zn-63 and a neutron

Initial particles: Cu-63, a nucleus Final particles: Zn-63, neutron To balance the mass numbers, we have: 63 + A = 63 + 1 A = 1 To balance the atomic numbers, we have: 29 + Z = 30 + 0 Z = 1 Thus, the initial nucleus has a mass number of 1 and an atomic number of 1, which is H-1. So the balanced nuclear equation is: \(\mathrm{Cu-}^{63}_{29}+\mathrm{H-}^1_1 \to \mathrm{Zn-}^{63}_{30} + \mathrm{n}\)

(d) Al-27 with deuterium to produce an alpha particle and another nucleus

Initial particles: Al-27, deuterium Final particles: alpha particle, unknown nucleus To balance the mass numbers, we have: 27 + 2 = 4 + A A = 25 To balance the atomic numbers, we have: 13 + 1 = 2 + Z Z = 12 Thus, the final unknown nucleus has a mass number of 25 and an atomic number of 12, which is Mg-25. Balanced nuclear equation: \(\mathrm{Al-}^{27}_{13}+{ }_1^2\mathrm{H} \to \mathrm{He-}^4_2 + \mathrm{Mg-}^{25}_{12}\)

(e) Ar-40 with an unknown particle to produce K-43 and a proton

Initial particles: Ar-40, unknown particle Final particles: K-43, proton To balance the mass numbers, we have: 40 + A = 43 + 1 A = 4 To balance the atomic numbers, we have: 18 + Z = 19 + 1 Z = 2 Thus, the initial unknown particle has a mass number of 4 and an atomic number of 2, which is an alpha particle. Balanced nuclear equation: \(\mathrm{Ar-}^{40}_{18}+\mathrm{He-}^4_2 \to \mathrm{K-}^{43}_{19} + \mathrm{H-}^1_1\)

(f) a nucleus with a neutron to produce a proton and P-31

Initial particles: a nucleus, neutron Final particles: proton, P-31 To balance the mass numbers, we have: A + 1 = 1 + 31 A = 31 To balance the atomic numbers, we have: Z + 0 = 1 + 15 Z = 14 Thus, the initial nucleus has a mass number of 31 and an atomic number of 14, which is Si-31. Balanced nuclear equation: \(\mathrm{Si-}^{31}_{14}+\mathrm{n} \to \mathrm{H-}^1_1 + \mathrm{P-}^{31}_{15}\)

Key concepts

Nuclear Reactions

In physics, nuclear reactions are processes where two atomic nuclei or a nucleus and a subatomic particle, such as a neutron, collide to produce one or more new nuclei as well as other particles like protons, neutrons, or alpha particles. This transformation is governed by principles of conservation of mass-energy and momentum. Nuclear reactions are responsible for the tremendous amounts of energy produced in the core of stars, including our sun, through processes like nuclear fusion.

When writing balanced nuclear equations for such reactions, akin to chemical equations, we ensure that both mass numbers (the sum of protons and neutrons) and atomic numbers (the number of protons) balance on either side of the reaction. This reflects the conservation laws and provides a clear representation of the nuclear changes occurring during the reaction.

Neutron Bombardment

One type of induced nuclear reaction is neutron bombardment, where neutrons are used as projectiles to interact with nuclei. Neutrons, having no charge, can easily penetrate the nucleus and hence are notable for initiating nuclear reactions. These interactions might lead to a variety of transformations, like causing the nucleus to absorb the neutron and become unstable, thereby leading to nuclear decay, or triggering a nuclear fission reaction if the nucleus splits into smaller fragments.

For instance, neutron bombardment is frequently used in nuclear reactors, where the collision of neutrons with fissile material, such as uranium or plutonium, causes the nuclei to split and release energy. These reactions can also be used to create heavier elements, as neutrons are added and decay processes transform them into protons within the nucleus.

Nuclear Transmutation

The process where one chemical element or isotope is transformed into another is known as nuclear transmutation. This occurs during nuclear reactions when the number of protons in the nucleus changes. It can happen naturally, through radioactive decay, or can be induced artificially in the lab using accelerators or reactors.

For example, when we bombard a U-238 nucleus with a neutron and it captures the neutron, it may undergo a series of beta decays to become a completely different element – a process of transmutation. In the context of the provided solutions, when aluminum-27 is bombarded with deuterium, it transmutes to form an alpha particle and magnesium-25. All of these reactions not only showcase the conversion of one element to another but also exemplify the type of careful calculation needed to balance nuclear equations for both the mass and atomic numbers.