Question

Aluminum exists in several isotopic forms, includ\(\operatorname{ing}_{13}^{27} \mathrm{Al}, \underset{13}{28} \mathrm{Al},\) and \(_{13}^{29} \mathrm{Al} .\) Indicate the number of protons and the number of neutrons in each of these isotopes.

Short answer

In the isotopes \(_{13}^{27}\mathrm{Al}\), \(_{13}^{28}\mathrm{Al}\), and \(_{13}^{29}\mathrm{Al}\), all have 13 protons. The number of neutrons in each isotope are 14, 15, and 16 respectively.

Step-by-step solution

Identify numbers in the isotopic notation

Isotope notation is written as: \[ _{\text{X}}^{\text{A}}\text{Z} \] Where: - X: Number of protons/Atomic number - A: Atomic Mass Number (Number of Protons + Number of Neutrons) - Z: Element Symbol Let's apply this rule to the isotopes given. For \(_{13}^{27}\mathrm{Al}\): - Number of protons (X) = 13 - Atomic Mass Number (A) = 27 For \(_{13}^{28}\mathrm{Al}\): - Number of protons (X) = 13 - Atomic Mass Number (A) = 28 For \(_{13}^{29}\mathrm{Al}\): - Number of protons (X) = 13 - Atomic Mass Number (A) = 29

Calculating the number of neutrons

Knowing the number of protons and the Atomic Mass Number, we can calculate the number of neutrons in each isotope by subtracting the number of protons from the Atomic Mass Number. For \(_{13}^{27}\mathrm{Al}\): - Number of neutrons = 27 - 13 = 14 For \(_{13}^{28}\mathrm{Al}\): - Number of neutrons = 28 - 13 = 15 For \(_{13}^{29}\mathrm{Al}\): - Number of neutrons = 29 - 13 = 16

Results

- The number of protons and neutrons in \(_{13}^{27}\mathrm{Al}\) is 13 and 14 respectively. - The number of protons and neutrons in \(_{13}^{28}\mathrm{Al}\) is 13 and 15 respectively. - The number of protons and neutrons in \(_{13}^{29}\mathrm{Al}\) is 13 and 16 respectively.

Key concepts

Protons

Protons are subatomic particles that reside in the nucleus of an atom. They are incredibly significant as they define the type of element an atom belongs to. The number of protons in an atom's nucleus is known as the atomic number, which is unique to each element. This means every aluminum atom will have 13 protons.

• The positive charge of a proton balances the negative charge of an electron.
• Protons and neutrons together form the nucleus of an atom.
• Knowing the number of protons helps in identifying the element's position on the periodic table.

Remember that protons are constant for each element regardless of isotopic variations. That's why in isotopes like \(_{13}^{27}\mathrm{Al}\), \(_{13}^{28}\mathrm{Al}\), and \(_{13}^{29}\mathrm{Al}\), the proton count remains 13.

Neutrons

Neutrons are neutral particles found in the nucleus of an atom. Unlike protons, they have no charge, but they contribute significantly to the mass of an atom. Neutrons play a pivotal role in stabilizing the nucleus.

• Neutron number can vary within atoms of the same element, creating isotopes.
• Isotopes have the same number of protons but different numbers of neutrons.
• The difference in neutron count in isotopes affects properties like atomic mass and stability, not chemical behavior.

For example, in aluminum isotopes:

• In \(_{13}^{27}\mathrm{Al}\), there are 14 neutrons.
• In \(_{13}^{28}\mathrm{Al}\), there are 15 neutrons.
• In \(_{13}^{29}\mathrm{Al}\), there are 16 neutrons.

These varying numbers of neutrons help in understanding the different isotopic forms of the same element.

Atomic Mass Number

The atomic mass number, often simply called mass number, represents the total number of protons and neutrons in an atom's nucleus. It provides an approximate mass of the atom.

• Calculated as: Number of Protons + Number of Neutrons.
• Affects the isotopic properties of elements.
• Commonly used in writing isotope notation.

This number differs in an element's isotopes due to changes in the neutron count. For instance:

• The atomic mass number for \(_{13}^{27}\mathrm{Al}\) is 27 (13 protons + 14 neutrons).
• The atomic mass number for \(_{13}^{28}\mathrm{Al}\) is 28 (13 protons + 15 neutrons).
• The atomic mass number for \(_{13}^{29}\mathrm{Al}\) is 29 (13 protons + 16 neutrons).

Understanding the atomic mass number helps explain how isotopes vary and how they are represented in scientific terms.