Problem 25 - Chemistry: An Atoms-Focused Approach

Question

How many protons, neutrons, and electrons are in the following atoms? (a) \(^{14} \mathrm{C} ;\) (b) \(^{59} \mathrm{Fe} ;\) (c) \(^{90} \mathrm{Sr} ;\) (d) \(^{210} \mathrm{Pb}\)

Step-by-Step Solution

Answer

Question: Determine the number of protons, neutrons, and electrons in the following atoms: (a) \(^{14}\mathrm{C}\), (b) \(^{59}\mathrm{Fe}\), (c) \(^{90}\mathrm{Sr}\), and (d) \(^{210}\mathrm{Pb}\). Answer: (a) \(^{14}\mathrm{C}\): 6 protons, 8 neutrons, and 6 electrons. (b) \(^{59}\mathrm{Fe}\): 26 protons, 33 neutrons, and 26 electrons. (c) \(^{90}\mathrm{Sr}\): 38 protons, 52 neutrons, and 38 electrons. (d) \(^{210}\mathrm{Pb}\): 82 protons, 128 neutrons, and 82 electrons.

Step 1: Identify known values

For each atom, we are given its isotopic notation, which contains the mass number (A) and the element's symbol. The atomic number (Z) can be found using a periodic table.

Step 2: Find the number of protons for each atom

Using a periodic table, we can look up the atomic number (Z) for each element. This value corresponds to the number of protons in the nucleus of the atom. (a) For \(^{14}\mathrm{C}\), the atomic number of carbon (C) is 6. Therefore, there are 6 protons in the nucleus. (b) For \(^{59}\mathrm{Fe}\), the atomic number of iron (Fe) is 26. Therefore, there are 26 protons in the nucleus. (c) For \(^{90}\mathrm{Sr}\), the atomic number of strontium (Sr) is 38. Therefore, there are 38 protons in the nucleus. (d) For \(^{210}\mathrm{Pb}\), the atomic number of lead (Pb) is 82. Therefore, there are 82 protons in the nucleus.

Step 3: Find the number of neutrons for each atom

Using the mass number (A) and the atomic number (Z), we can calculate the number of neutrons (N) by subtracting the number of protons (Z) from the mass number (A): N = A - Z (a) For \(^{14}\mathrm{C}\), there are 14 - 6 = 8 neutrons in the nucleus. (b) For \(^{59}\mathrm{Fe}\), there are 59 - 26 = 33 neutrons in the nucleus. (c) For \(^{90}\mathrm{Sr}\), there are 90 - 38 = 52 neutrons in the nucleus. (d) For \(^{210}\mathrm{Pb}\), there are 210 - 82 = 128 neutrons in the nucleus.

Step 4: Find the number of electrons for each atom

Since the atom is neutral, the number of electrons is equal to the number of protons. (a) For \(^{14}\mathrm{C}\), there are 6 electrons. (b) For \(^{59}\mathrm{Fe}\), there are 26 electrons. (c) For \(^{90}\mathrm{Sr}\), there are 38 electrons. (d) For \(^{210}\mathrm{Pb}\), there are 82 electrons.

Step 5: Final Answers

For each given atom: (a) \(^{14}\mathrm{C}\): 6 protons, 8 neutrons, and 6 electrons. (b) \(^{59}\mathrm{Fe}\): 26 protons, 33 neutrons, and 26 electrons. (c) \(^{90}\mathrm{Sr}\): 38 protons, 52 neutrons, and 38 electrons. (d) \(^{210}\mathrm{Pb}\): 82 protons, 128 neutrons, and 82 electrons.

Key Concepts

Protons

Protons are subatomic particles found in the nucleus of an atom. They carry a positive electric charge denoted by "+1". The number of protons, also called the atomic number (Z), uniquely identifies a chemical element. For example, carbon (C) always has 6 protons, iron (Fe) has 26, strontium (Sr) has 38, and lead (Pb) has 82. This consistency is crucial, as changing the number of protons transforms the element into a different one.

To find the number of protons in an atom, use the atomic number from the periodic table. This step is straightforward, as each element has its atomic number listed directly under its symbol on the periodic table. Understanding the role of protons helps in recognizing the identity and properties of different elements.

Neutrons

Neutrons are neutral particles located in the nucleus of an atom. They carry no electric charge, which means they do not affect the charge of the atom. Neutrons play a significant role in adding mass to an atom and stabilizing the nucleus by offsetting the repulsive forces between protons. To find the number of neutrons in an atom, use the formula:

• \[ \text{Number of Neutrons} = \text{Mass Number (A)} - \text{Atomic Number (Z)} \]

For example, in a carbon atom represented as \( ^{14}\mathrm{C} \), the mass number is 14 and the atomic number is 6. Therefore, the carbon atom has 14 - 6 = 8 neutrons.

Understanding the number of neutrons is pivotal in studies about isotopes, which are atoms of the same element that have different numbers of neutrons.

Electrons

Electrons are negatively charged particles that orbit the nucleus of an atom. They are \(-1\) charged. In a neutral atom, the number of electrons equals the number of protons, balancing the positive and negative charges to maintain overall neutrality.

• For example, a neutral iron atom with 26 protons also has 26 electrons.

Electrons are involved in chemical bonding and reactions, making them vital to understanding how different substances interact. They occupy regions called electron shells or energy levels, and their arrangement is key to determining an element's chemical properties and reactivity.

By gaining or losing electrons, atoms become ions and take on positive or negative charges, leading to the formation of ionic compounds.

Isotopic Notation

Isotopic notation provides a convenient way to express the number of protons and neutrons in an atom. It is given in the form \(^{A}_{Z}\mathrm{X}\), where \(A\) is the mass number (total protons and neutrons), \(Z\) is the atomic number (number of protons), and \(X\) is the chemical symbol of the element.

• For \(^{14}\mathrm{C}\), \(A = 14\), \(Z = 6\), and the element is carbon.
• For \(^{59}\mathrm{Fe}\), \(A = 59\), \(Z = 26\), and the element is iron.

Isotopic notation is essential for identifying isotopes, which are variants of the same element with differing numbers of neutrons. Knowing how to read isotopic notation helps identify the number of protons and neutrons in an atom quickly and efficiently, allowing for deeper insights into nuclear properties and reactions.