Problem 16 - University Physics with Modern Physics

Question

What particle \((\alpha\) particle, electron, or positron) is emitted in the following radioactive decays? (a) \(_{14}^{27} \mathrm{Si} \rightarrow_{13}^{27} \mathrm{Al}\) (b) \(^{238} \mathrm{U} \rightarrow_{90}^{234} \mathrm{Th} ;\) (c) \(_{33}^{74} \mathrm{As} \rightarrow_{34}^{74} \mathrm{Se}\)

Step-by-Step Solution

Answer

(a) Positron, (b) Alpha particle, (c) Electron

Step 1: Understand the Process

Radioactive decay is a process where an unstable atom loses energy by emitting radiation. The type of particle emitted determines the decay process: alpha decay emits an alpha particle, beta decay emits an electron or a positron.

Step 2: Analyze (a) Silicon to Aluminum Decay

In the decay \(_{14}^{27} \mathrm{Si} \rightarrow_{13}^{27} \mathrm{Al}\),we see that the atomic number decreases by 1 while the mass number remains the same. This indicates the emission of a positron, which is characteristic of \(\beta^+\) (beta plus) decay.

Step 3: Analyze (b) Uranium to Thorium Decay

In the decay \(^{238} \mathrm{U} \rightarrow_{90}^{234} \mathrm{Th}\),the atomic number decreases by 2 and the mass number decreases by 4, indicating the emission of an alpha particle (\(_{2}^{4}\mathrm{He}\)).

Step 4: Analyze (c) Arsenic to Selenium Decay

In the decay \(_{33}^{74} \mathrm{As} \rightarrow_{34}^{74} \mathrm{Se}\),the atomic number increases by 1 whereas the mass number stays the same, signifying the emission of an electron (beta particle), characteristic of \(\beta^-\) decay.

Key Concepts

Alpha Decay

Alpha decay is a fundamental concept in nuclear physics, where an unstable nucleus emits an alpha particle to become a more stable nucleus. An alpha particle is composed of two protons and two neutrons, identical to a helium nucleus \((_{2}^{4}\mathrm{He})\). This process results in a decrease in the atomic number by 2 and the mass number by 4.

For example, when uranium-238 undergoes alpha decay, it transforms into thorium-234. The equation is as follows: \[_{92}^{238}\mathrm{U} \rightarrow _{90}^{234}\mathrm{Th} + _{2}^{4}\mathrm{He} \]

• The nucleus of uranium loses two protons and two neutrons.
• This decreases the atomic number from 92 to 90.
• The mass number decreases from 238 to 234.

Alpha decay generally occurs in heavy elements where the strong nuclear force struggles to hold a large nucleus together. Understanding alpha decay helps in studying radioactive materials and predicting how they will change over time.

Beta Decay

Beta decay is another type of radioactive decay involving the emission of a beta particle, which can either be an electron or a positron. It occurs in two forms, beta minus (\(\beta^-\)) decay and beta plus (\(\beta^+\)) decay.

In beta minus decay, a neutron within the nucleus is converted into a proton and an electron. The electron is ejected from the atom, leaving the nucleus with an increased atomic number by 1, while the mass number remains unchanged. For instance, arsenic-74 decays to selenium-74 as shown below: \[_{33}^{74}\mathrm{As} \rightarrow _{34}^{74}\mathrm{Se} + \beta^- \]

• The atomic number increases from 33 to 34, adding one proton.
• Mass number remains constant.
• An electron is emitted as a beta particle.

In beta plus decay, a proton is converted into a neutron and a positron, with the positron being expelled from the atom. This decreases the atomic number by 1, with again no change to the mass number. For example, silicon-27 decays into aluminum-27: \[_{14}^{27}\mathrm{Si} \rightarrow _{13}^{27}\mathrm{Al} + \beta^+ \]

• Silicon loses a proton and emits a positron.
• The atomic number decreases to 13.

Beta decay plays a crucial role in the management of nuclear reactions, providing insight into the mechanisms of nuclear changes.

Nuclear Physics

Nuclear physics is a branch of physics that studies the components and behavior of atomic nuclei. It encompasses the understanding of radioactive decay, nuclear reactions, and radiation.

Key processes in nuclear physics include:

• Alpha decay, where a nucleus emits an alpha particle diminishing its atomic number by 2.
• Beta decay, involving the transformation of neutrons to protons or vice versa through the emission of electrons or positrons.

Nuclear physics is integral to a variety of applications, such as:

• Energy production through nuclear reactors, utilizing fission and sometimes fusion.
• Medical treatments like radiation therapy, relying on radioactive isotopes.
• Industrial applications including radiographic inspection of materials.

By studying nuclear physics, scientists can better understand the forces that hold the nucleus together and develop technologies in various fields, from energy to medicine.