Problem 57 - Chemistry An Atoms First Approach

Question

An element's most stable ion has a \(2+\) charge. If the ion of element \(\mathrm{X}\) has a mass number of 230 and has 86 electrons, what is the identity of the element, and how many neutrons does it have?

Step-by-Step Solution

Answer

The element is Radium (Ra), which has an atomic number of 88 and 142 neutrons.

Step 1: Determine the number of protons

Since we know that the ion of the element has a 2+ charge and has 86 electrons, we can determine the number of protons in the element. In a neutral atom, the number of protons equals the number of electrons. Since the ion has a 2+ charge, this means it has lost 2 electrons. So, the neutral atom would have 86+2 = 88 electrons, which indicates that there are 88 protons.

Step 2: Identify the element

Now that we know there are 88 protons in the element, we can use the periodic table to find the identity of the element. The atomic number (number of protons) is what identifies an element. In the periodic table, the element with atomic number 88 is Radium (Ra). So, the identity of the element is Radium.

Step 3: Find the number of neutrons

To find the number of neutrons in the element, we can use the mass number and the atomic number. The mass number is the sum of the number of protons (atomic number) and the number of neutrons. In this case, we have: Mass number = Number of protons + Number of neutrons 230 = 88 + Number of neutrons By solving for the number of neutrons, we get: Number of neutrons = 230 - 88 = 142 So, Radium has 142 neutrons.

Key Concepts

Atomic Number

The atomic number is a fundamental characteristic of an element and is essential in determining its identity. It is denoted as the number of protons present in the nucleus of an atom. Since each element has a unique number of protons, the atomic number serves as a unique identifier for that element on the periodic table.

For instance, when looking at an element's most stable ion with a charge, as in our exercise with element X that has a 2+ charge, understanding the atomic number becomes vital. The exercise provides valuable insight that, if a neutral atom normally has the same number of protons and electrons, an ion with a 2+ charge would mean it has two electrons less than protons. This is how we inferred that the atomic number of element X, with 86 electrons in its ionized state, is 88, since the number of protons must equal the number of electrons in a neutral state.

Protons and Electrons

The balance of protons and electrons defines the charge of an atom. Protons have a positive charge whereas electrons carry a negative charge. In a neutral atom, the number of protons is equal to the number of electrons, resulting in a balanced charge.

When an atom has more or fewer electrons compared to protons, it becomes an ion. For example, in our exercise, the element X ion, despite normally having 88 electrons (which is the atomic number for Radium), had only 86 electrons. This loss of two negatively charged electrons resulted in a positively charged ion, specifically a 2+ ion. The understanding of the correlation between protons and electrons in determining the charge of an ion is crucial for students to clearly grasp how to determine the identity and characteristics of ions.

Mass Number and Neutrons

The mass number, unlike the atomic number, is the total of protons and neutrons in an atom's nucleus. Neutrons have no charge and thus do not influence the electrical attributes of an atom, but they contribute to the atom's mass and stability.

By using the mass number and knowing the atomic number, one can deduce the number of neutrons. In the given exercise, the mass number of element X's ion is 230. With an atomic number of 88 (which represents protons), we calculated the neutron count by subtracting the atomic number from the mass number, yielding 142 neutrons for the element. The ability to calculate the number of neutrons is key in comprehending the full picture of an atom's structure and is pivotal for various calculations and understandings in chemistry.