Question

Using \(Z\) to represent the atomic number and \(A\) to represent the mass number, give the general symbol for a nuclide of element X. Give also a specific example of the use of such symbolism.

Short answer

The general symbol for a nuclide can be represented as \[^A_ZX\], where X is the element symbol, A is the mass number, and Z is the atomic number. For example, Carbon-12, the most common isotope of carbon with 6 protons and 6 neutrons, can be represented as \[^{12}_6C\], where its atomic number (Z) is 6 and its mass number (A) is 12.

Step-by-step solution

Write the general symbol

The general symbol for a nuclide of element X can be written as X(A, Z), where X is the element symbol, A is the mass number, and Z is the atomic number. In a more commonly used notation, the mass number (A) is written as a superscript to the left, and the atomic number (Z) as a subscript to the left of the element symbol. So the representation becomes: \[^A_ZX\]

Provide a specific example

Let's take a specific example to illustrate the use of this symbolism. The most common isotope of carbon is Carbon-12, meaning it has 6 protons and 6 neutrons. Therefore, its atomic number (Z) is 6 and its mass number (A) is 12. Using the general symbol, this nuclide can be represented as: \[{}^{12}_6C\] This symbol indicates that this particular nuclide is the Carbon-12 isotope, with a mass number of 12 and an atomic number of 6.

Key concepts

Atomic Number

The atomic number, represented by the symbol \(Z\), is a fundamental property of an element. It tells us how many protons are in the nucleus of an atom of that element.
This is crucial because the number of protons determines the identity of the element and its position on the periodic table. For example:

• Hydrogen has an atomic number of 1, meaning it has 1 proton.
• Carbon's atomic number is 6, indicating 6 protons in its nucleus.
• Gold has an atomic number of 79, so it contains 79 protons.

Each element has its unique atomic number, which makes this value constant for any atom of that element, no matter how many neutrons or electrons it may have. Understanding the atomic number is key to identifying elements and their properties.

Mass Number

The mass number, denoted as \(A\), is the total number of protons and neutrons in the nucleus of an atom. It represents almost the entire mass of an atom, since electrons are significantly lighter.
Unlike the atomic number, which is fixed for each element, the mass number can vary. This is because atoms of the same element may have different numbers of neutrons. To calculate the mass number:

• Add the number of protons (atomic number, \(Z\)).
• Add the number of neutrons in the nucleus.

Use the formula: \(A = Z + \text{number of neutrons}\). This is why Carbon-12, the natural isotope of carbon with 6 protons and 6 neutrons, has a mass number of 12. Other isotopes like Carbon-14 have a mass number of 14, due to having 8 neutrons.

Isotopes

Isotopes are different forms of the same element, distinguished by their mass numbers. While the atomic number \(Z\) remains the same for isotopes of a given element (since they have the same number of protons), what changes is the number of neutrons.
This difference in neutron number affects the mass number \(A\). Here are some key points about isotopes:

• They have identical chemical properties because they consist of the same element.
• The physical properties, such as mass, may differ due to the neutron variance.
• Not all isotopes are stable; some may undergo radioactive decay.

A good example is carbon's isotopes: Carbon-12 is stable and makes up most of natural carbon, while Carbon-14 is radioactive and used in radiocarbon dating. Thus, understanding isotopes is essential for comprehending variations within elements and their applications in various scientific fields.