Question

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

Short answer

In the given Aluminum isotopes, \({ }_{13}^{27}\mathrm{Al}\) has 13 protons and 14 neutrons, \({ }_{13}^{28}\mathrm{Al}\) has 13 protons and 15 neutrons, and \({ }_{13}^{29}\mathrm{Al}\) has 13 protons and 16 neutrons.

Step-by-step solution

Identify the atomic number (protons) and atomic mass number for each isotope

Here are the atomic numbers and atomic mass numbers for each isotope: - \({ }_{13}^{27}\mathrm{Al}\): Atomic number (\(Z\)) = 13, Atomic mass number (\(A\)) = 27 - \({ }_{13}^{28}\mathrm{Al}\): Atomic number (\(Z\)) = 13, Atomic mass number (\(A\)) = 28 - \({ }_{13}^{29}\mathrm{Al}\): Atomic number (\(Z\)) = 13, Atomic mass number (\(A\)) = 29

Calculate the number of neutrons for each isotope

To calculate the number of neutrons in each isotope, we need to subtract the atomic number (\(Z\), protons) from the atomic mass number (\(A\)): 1. \({ }_{13}^{27}\mathrm{Al}\): Number of neutrons = \(A - Z = 27 - 13 = 14\) 2. \({ }_{13}^{28}\mathrm{Al}\): Number of neutrons = \(A - Z = 28 - 13 = 15\) 3. \({ }_{13}^{29}\mathrm{Al}\): Number of neutrons = \(A - Z = 29 - 13 = 16\)

Present the results

Now, we can present the number of protons and neutrons in each isotope: - \({ }_{13}^{27}\mathrm{Al}\): 13 protons and 14 neutrons - \({ }_{13}^{28}\mathrm{Al}\): 13 protons and 15 neutrons - \({ }_{13}^{29}\mathrm{Al}\): 13 protons and 16 neutrons

Key concepts

Atomic number

The atomic number is a fundamental aspect of an element's identity. It is represented by the symbol \(Z\). This number tells us how many protons are in the nucleus of an atom of the element. For aluminum, the atomic number is always 13, because every aluminum atom has 13 protons.

• The atomic number determines the type of element. Every element is defined by its atomic number.
• It's key in the periodic table, which is arranged by increasing atomic number.

It's important to note that the atomic number is not affected by the number of neutrons or electrons an atom has. Even in different isotopes, the atomic number remains the same. For example, aluminum isotopes such as \({ }_{13}^{27}\mathrm{Al}\), \({ }_{13}^{28}\mathrm{Al}\), and \({ }_{13}^{29}\mathrm{Al}\) all share the atomic number 13, with 13 protons. This atomic number ensures these isotopes are still aluminum, despite differences in neutron count and atomic mass.

Atomic mass

The atomic mass, or atomic mass number, is denoted by the symbol \(A\). This value is the total number of protons and neutrons in an atom's nucleus. It is a critical factor in distinguishing different isotopes of the same element.

• Each isotope of an element has a unique atomic mass number.
• Atomic mass reflects both the protons (atomic number) and neutrons present in the atom's nucleus.

For example, aluminum isotopes have the same number of protons (13), but they have different atomic masses because they differ in their number of neutrons:- \({ }_{13}^{27}\mathrm{Al}\): Atomic mass number = 27- \({ }_{13}^{28}\mathrm{Al}\): Atomic mass number = 28- \({ }_{13}^{29}\mathrm{Al}\): Atomic mass number = 29These differences in atomic mass numbers reflect the unique identities of each isotope, impacting their physical and chemical properties subtly.

Neutrons

Neutrons are neutrally charged particles residing in an atom's nucleus alongside protons. Unlike protons, neutrons do not affect the atomic number but do contribute to the atomic mass number of an atom. The number of neutrons in an atom can vary, leading to the formation of isotopes.

• Calculating neutrons: \( \text{Number of Neutrons} = A - Z \)
• Neutrons stabilize the nucleus by offsetting the electrostatic repulsion between protons.
• Isotopes: Atoms of the same element with the same number of protons but different numbers of neutrons.

To understand this better, let's revisit the aluminum isotopes:- For \({ }_{13}^{27}\mathrm{Al}\), there are \(27 - 13 = 14\) neutrons.- For \({ }_{13}^{28}\mathrm{Al}\), there are \(28 - 13 = 15\) neutrons.- For \({ }_{13}^{29}\mathrm{Al}\), there are \(29 - 13 = 16\) neutrons.Thus, while these isotopes of aluminum have the same atomic number and number of protons, the different numbers of neutrons result in different atomic masses, giving each isotope its unique identity.