Question

Though the common isotope of aluminum has a mass number of \(27,\) isotopes of aluminum have been isolated (or prepared in nuclear reactors) with mass numbers of \(24,25,26,28,29,\) and \(30 .\) How many neutrons are present in each of these isotopes? Why are they all considered aluminum atoms, even though they differ greatly in mass? Write the atomic symbol for each isotope.

Short answer

The aluminum isotopes have the following number of neutrons: 11, 12, 13, 15, 16, and 17. They are all considered aluminum atoms because they all have the same number of protons (13) in their nucleus, which determines the element's identity. The atomic symbols for the isotopes are \(_{13}^{24}Al\), \(_{13}^{25}Al\), \(_{13}^{26}Al\), \(_{13}^{28}Al\), \(_{13}^{29}Al\), and \(_{13}^{30}Al\).

Step-by-step solution

1. Recall the concept of isotopes and the definition of mass number

An element can have various isotopes, which are atoms of the same element but have different numbers of neutrons in their nucleus. The mass number (A) is the sum of the number of protons (Z) and the number of neutrons (N) in the nucleus of an atom. So, the mass number (A) = number of protons (Z) + number of neutrons (N)

2. Find the atomic number of aluminum

Aluminum has an atomic number (Z) of 13, which means it has 13 protons in its nucleus. This piece of information is vital because the atomic number determines the element's identity. All aluminum atoms have 13 protons, regardless of the number of neutrons, so they all belong to the same element but different isotopes.

3. Determine the number of neutrons for each isotope

Using the mass number (A) of each isotope and the fact that aluminum has an atomic number (Z) of 13, we can calculate the number of neutrons (N) for each isotope. To find the number of neutrons (N) in each isotope: N = A - Z Let's perform the calculation for each isotope: Isotope 1: Mass number A = 24 N = 24 - 13 N = 11 Isotope 2: Mass number A = 25 N = 25 - 13 N = 12 Isotope 3: Mass number A = 26 N = 26 - 13 N = 13 Isotope 4: Mass number A = 28 N = 28 - 13 N = 15 Isotope 5: Mass number A = 29 N = 29 - 13 N = 16 Isotope 6: Mass number A = 30 N = 30 - 13 N = 17

4. Write the atomic symbol for each isotope

Now that we have calculated the number of neutrons for each isotope, we can write the atomic symbol for each. The atomic symbol includes the element's symbol, atomic number (Z), and mass number (A). Format: \(_Z^A X\), where X is the element symbol. Isotope 1: \(_{13}^{24}Al\) Isotope 2: \(_{13}^{25}Al\) Isotope 3: \(_{13}^{26}Al\) Isotope 4: \(_{13}^{28}Al\) Isotope 5: \(_{13}^{29}Al\) Isotope 6: \(_{13}^{30}Al\)

5. Explain why all isotopes are considered to be aluminum atoms, even with differing masses

All isotopes of an element have the same number of protons, which is the atomic number. The unique number of protons in an atom's nucleus determines its identity. In the case of aluminum, all of its isotopes have 13 protons in their nucleus, so they are all considered aluminum atoms. Their differing mass numbers are due to the varying numbers of neutrons in their nuclei, which doesn't affect their chemical characteristics.

Key concepts

Understanding Atomic Number

The atomic number of an element is a fundamental property that defines the element's identity. It tells us the number of protons in the nucleus of an atom. Protons are positively charged particles, and their number remains constant across all isotopes of a given element. This is why, despite varying in mass, all isotopes of aluminum are classified as aluminum atoms—they all contain 13 protons. In essence, the atomic number is like an ID number for elements on the periodic table, making it indispensable in chemistry.
For example, every aluminum atom has an atomic number of 13, regardless of the number of neutrons or electrons it may have. This is why aluminum with 13 protons will always be aluminum, whether it's the most common isotope with a mass number of 27 or a less common one with a mass number of, say, 26 or 30.

Mass Number and Its Role

When we refer to the mass number, we're talking about the total count of protons and neutrons in an atom's nucleus. It's symbolized by the letter 'A.' Since the atomic number (Z) gives us the number of protons, and protons and neutrons collectively make up the nucleus's mass, the mass number becomes an important factor in distinguishing different isotopes of an element.
Here's how it works: For each isotope of aluminum, the mass number changes because the number of neutrons varies. Yet, since the atomic number (number of protons) remains constant at 13, these different mass numbers reflect only the difference in neutrons. The greater the mass number, the more neutrons an isotope has. As a characteristic example, aluminum isotopes with mass numbers from 24 to 30 illustrate this variety: though they all retain 13 protons (and thus their 'aluminum' identity), the neutrons fluctuate, giving each isotope its unique mass.

Calculating Neutrons in Isotopes

Determining the number of neutrons in an isotope is straightforward with a simple formula: Neutrons (N) = Mass number (A) - Atomic number (Z). Since the atomic number is equal to the number of protons, and the mass number is the sum of protons and neutrons, subtracting the atomic number from the mass number leaves us with the number of neutrons.
Let's apply this: For an aluminum isotope with a mass number of 27, the calculation would be 27 (mass number) - 13 (atomic number), resulting in 14 neutrons. Proceeding with this method for each isotope of aluminum we have:

• For mass number 24: 24 - 13 = 11 neutrons
• For mass number 25: 25 - 13 = 12 neutrons
• For mass number 26: 26 - 13 = 13 neutrons
• For mass number 28: 28 - 13 = 15 neutrons
• For mass number 29: 29 - 13 = 16 neutrons
• For mass number 30: 30 - 13 = 17 neutrons

This neutron calculation not only aids in identifying isotopes but also underscores the variety within a single element, providing insight into the structure and properties of atoms.