Question

Draw a diagram similar to that shown in Exercise \(21.2\) that illustrates the nuclear reaction \({ }_{83}^{211} \mathrm{Bi} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{81}^{207} \mathrm{Tl}\). [Section 21.2]

Short answer

To illustrate the nuclear reaction of Bismuth-211 transforming into Helium-4 and Thallium-207, the diagram can be drawn as follows: \[{}_{83}^{211}\mathrm{Bi} \longrightarrow{ }_{2}^{4}\mathrm{He} + {}_{81}^{207}\mathrm{Tl}\]

Step-by-step solution

Understanding the symbols

In this nuclear reaction, we have the following elements and isotopes involved: 1. Bismuth-211: \({}_{83}^{211}\mathrm{Bi}\) has an atomic number (Z) of 83 and mass number (A) of 211. 2. Helium-4: \({}_{2}^{4}\mathrm{He}\) has an atomic number (Z) of 2 and mass number (A) of 4. 3. Thallium-207: \({}_{81}^{207}\mathrm{Tl}\) has an atomic number (Z) of 81 and mass number (A) of 207. The arrow (\(\longrightarrow\)) is used to show the transformation from Bismuth-211 to Helium-4 and Thallium-207.

Drawing the diagram

To draw the diagram, follow these steps: 1. Write down the isotope of Bismuth-211 on the left side: \({}_{83}^{211}\mathrm{Bi}\). 2. Draw an arrow from Bismuth-211 to represent the nuclear reaction: \(\longrightarrow\). 3. Write down the isotopes of Helium-4 and Thallium-207 on the right side of the arrow, separated by a plus sign: \({}_{2}^{4}\mathrm{He} + {}_{81}^{207}\mathrm{Tl}\). Here is the final diagram showing the nuclear reaction: \[{}_{83}^{211}\mathrm{Bi} \longrightarrow{ }_{2}^{4}\mathrm{He} + {}_{81}^{207}\mathrm{Tl}\]

Key concepts

Nuclear Chemistry

Nuclear chemistry is a field of chemistry that deals with changes in the nucleus of atoms. Unlike chemical reactions which involve the electrons surrounding the nucleus and do not change the identity of an element, nuclear reactions cause an element to transform into a different element or isotope. This transformation can release or absorb a significant amount of energy, often in the form of radiation. For instance, the decay of radioactive isotopes is a natural nuclear process.

In nuclear reactions, we can observe transmutation as a heavier element breaks down into lighter elements or isotopes. The example given in the exercise, the decay of Bismuth-211 into Helium-4 and Thallium-207, is a classic illustration of nuclear transmutation through a process called alpha decay.

Isotopes

Isotopes are variants of a given chemical element that have the same number of protons but different numbers of neutrons in their nuclei, resulting in different mass numbers. Although isotopes of an element exhibit nearly identical chemical behavior, their nuclear properties can be quite distinct. This is why some isotopes are stable, while others are radioactive and decay over time.

For example, Bismuth-211 and Thallium-207, mentioned in the exercise, are isotopes of their respective elements. Isotopes are essential in various fields, including medicine, where radioactive isotopes are used for diagnostic imaging and treatment.

Alpha Decay

Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle, which consists of two protons and two neutrons. This means that the alpha particle is essentially a Helium-4 nucleus. When an alpha particle is emitted, the mass number of the original nucleus decreases by four units, and the atomic number decreases by two units, resulting in a new element or isotope.

In the depiction of \r\({}_{83}^{211}\mathrm{Bi} \longrightarrow { }_{2}^{4}\mathrm{He} + { }_{81}^{207}\mathrm{Tl}\), Bismuth-211 undergoes alpha decay to form Helium-4 and Thallium-207. It's important for students to understand that alpha decay is a common way heavy and unstable isotopes naturally stabilize themselves.

Atomic Number and Mass Number

The atomic number, represented by the letter Z, is the number of protons in an atom's nucleus and defines the identity of an element. For instance, all atoms of Bismuth have 83 protons, so its atomic number is 83. On the other hand, the mass number, represented by the letter A, is the total number of protons and neutrons in the nucleus. The mass number gives us information about the specific isotope of an element.

The sum of the mass numbers and atomic numbers before and after a nuclear reaction must be equal due to the law of conservation of mass and charge. When \r\({}_{83}^{211}\mathrm{Bi}\) decays, it produces \r\({}_{2}^{4}\mathrm{He}\) and \r\({}_{81}^{207}\mathrm{Tl}\), thus conserving both atomic and mass numbers through the process.