Question

Isotopes Are the following elements isotopes of each other? Explain. $$\begin{array}{l}{24} \\ {12}\end{array} \mathrm{Mg}, \begin{array}{c}{25} \\\ {12}\end{array} \mathrm{Mg}, \begin{array}{l}{26} \\ {12}\end{array} \mathrm{Mg}$$

Short answer

Yes, the elements \(\begin{array}{l}{24} \\\ {12}\end{array} \mathrm{Mg}\), \(\begin{array}{l}{25} \\\ {12}\end{array} \mathrm{Mg}\), and \(\begin{array}{l}{26} \\\ {12}\end{array}\mathrm{Mg}\) are isotopes of each other since they have the same atomic number (12) but different mass numbers (24, 25, and 26).

Step-by-step solution

Isotopes are the atoms of the same element that have the same number of protons (same atomic number) but a different number of neutrons (different mass number). #Step 2: Identify atomic number and mass number for each element#

In this case, we have three elements: \(1) \: \begin{array}{l}{24} \\\ {12}\end{array} \mathrm{Mg}\) \(2) \: \begin{array}{l}{25} \\\ {12}\end{array} \mathrm{Mg}\) \(3) \: \begin{array}{l}{26} \\\ {12}\end{array} \mathrm{Mg}\) The numbers on the top are the mass numbers (the total number of protons and neutrons) and the numbers on the bottom are the atomic numbers (the number of protons). #Step 3: Check if the elements are isotopes#

Since the atomic number (12) is the same for all three elements, this confirms that they are all Magnesium (Mg) atoms. Moreover, the mass numbers are different for each element (24, 25, and 26), which means they have different numbers of neutrons. #Step 4: Conclusion#

Therefore, all three elements \(\begin{array}{l}{24} \\\ {12}\end{array} \mathrm{Mg}\), \(\begin{array}{l}{25} \\\ {12}\end{array} \mathrm{Mg}\), and \(\begin{array}{l}{26} \\\ {12}\end{array}\mathrm{Mg}\) are isotopes of each other since they have the same atomic number (12) but different mass numbers (24, 25, and 26).

Key concepts

Atomic Number

The atomic number is a fundamental property of an element and indicates the number of protons in the nucleus of an atom. Elements are defined by the number of protons they possess, which also determines the element's position on the periodic table. For example, any atom with an atomic number of 12 is an atom of magnesium (Mg), irrespective of how many neutrons or electrons it has.

Protons carry a positive charge, and since atoms are electrically neutral, the atomic number also reveals the number of electrons in an uncharged atom. Understanding the atomic number is critical when determining if different atoms are isotopes of the same element - they must have the same atomic number, thus the same number of protons, to be considered isotopes.

Mass Number

The mass number of an atom is the total count of protons and neutrons in its nucleus. While the number of protons (atomic number) defines the type of element, the number of neutrons can vary within atoms of the same element, leading to different mass numbers.

To calculate the number of neutrons in an atom, you subtract the atomic number from the mass number:
Number of neutrons = Mass number - Atomic number.
This calculation is pivotal for identifying isotopes, as isotopes have the same number of protons but differ in the number of neutrons, giving them distinct mass numbers.

Neutrons

Neutrons are subatomic particles found in the nucleus of an atom alongside protons. Unlike protons, neutrons carry no electric charge; they are neutral. The main role of neutrons is to add mass to the atom and to help stabilize the nucleus. Since the number of neutrons can vary within atoms of the same element, different configurations, known as isotopes, can exist.

Isotopes have identical atomic numbers but different mass numbers because they have different numbers of neutrons. The varying numbers of neutrons contribute to the isotopes' distinct physical, and sometimes radioactive, properties while chemically, they behave similarly since they have the same number of protons and electrons.