Problem 10 - Chemistry: The Central Science in SI Units, Global Edition

Question

Indicate the number of protons and neutrons in the following nuclei: \((\mathbf{a}){ }^{214} \mathrm{Bi},(\mathbf{b}){ }^{210} \mathrm{~Pb},(\mathbf{c})\) uranium- \(235 .\).

Step-by-Step Solution

Answer

The number of protons and neutrons for the given nuclei are: - \(^{214}\mathrm{Bi}\): 83 protons and 131 neutrons - \(^{210}\mathrm{Pb}\): 82 protons and 128 neutrons - uranium-235: 92 protons and 143 neutrons

Step 1: Find the atomic numbers for Bi, Pb, and U.

To determine the atomic numbers for Bismuth (Bi), Lead (Pb), and Uranium (U), we can look up these elements in the periodic table. Doing so, we find the following atomic numbers: - Bismuth (Bi): Z = 83 - Lead (Pb): Z = 82 - Uranium (U): Z = 92

Step 2: Calculate the number of protons for each nucleus.

Using the atomic numbers found in Step 1, the number of protons will be equal to the atomic number for each nucleus: - \(^{214}\mathrm{Bi}\): 83 protons - \(^{210}\mathrm{Pb}\): 82 protons - uranium-235: 92 protons

Step 3: Calculate the number of neutrons for each nucleus.

To find the number of neutrons, subtract the atomic number (number of protons) from the mass number for each nucleus. We have the following: - \(^{214}\mathrm{Bi}\): Neutrons = A - Z = 214 - 83 = 131 neutrons - \(^{210}\mathrm{Pb}\): Neutrons = A - Z = 210 - 82 = 128 neutrons - uranium-235: Neutrons = A - Z = 235 - 92 = 143 neutrons In summary, the number of protons and neutrons for the given nuclei are: - \(^{214}\mathrm{Bi}\): 83 protons and 131 neutrons - \(^{210}\mathrm{Pb}\): 82 protons and 128 neutrons - uranium-235: 92 protons and 143 neutrons

Key Concepts

Atomic Number

The atomic number is a fundamental property of an element. It is represented by the symbol \( Z \) and indicates the number of protons in the nucleus of an atom. Each element on the periodic table has its own unique atomic number. This number determines the specific identity of an element, as it reflects the number of protons an atom of that element has.
For example, in the exercise provided, the atomic numbers for Bismuth (Bi), Lead (Pb), and Uranium (U) are 83, 82, and 92, respectively. These values not only represent the number of protons in each atom but also dictate the element's chemical properties.
- Atomic Number \( Z \): Equivalent to the number of protons in an atom.
- Determines the identity of the element.
- Unique for each element on the periodic table.

Mass Number

The mass number, denoted by \( A \), is crucial for understanding the overall composition of an atomic nucleus. It is the sum of protons and neutrons within the nucleus. Unlike the atomic number, the mass number is not unique to one element because different isotopes of the same element have different numbers of neutrons, thus different mass numbers.
For instance, the mass numbers given in the problem for Bismuth, Lead, and Uranium are 214, 210, and 235, respectively. These figures include both the protons and neutrons in their nuclei.
- Mass Number \( A \): Total count of protons and neutrons.
- Varies among isotopes of the same element.
- Does not appear on the periodic table, unlike the atomic number.

Protons and Neutrons

Protons and neutrons are subatomic particles found in the nucleus of an atom. They play a vital role in defining the characteristics of an atom.
**Protons** have a positive charge and their quantity in an atom is defined by the atomic number. They are pivotal in determining the identity and the chemical behavior of an element. For example, the atomic number indicates that Bismuth has 83 protons, Lead has 82, and Uranium has 92.
**Neutrons** are electrically neutral, meaning they carry no charge, but they contribute to the mass of the nucleus. The number of neutrons can vary in isotopes of an element, yet it does not change the chemical properties of the element. For instance, the problem indicates that Bi has 131 neutrons, Pb has 128 neutrons, and U has 143 neutrons.
- **Protons**: Determine the element's identity through the atomic number.
- **Neutrons**: Contribute to nuclear stability and create isotopes when their numbers vary.
- Together with protons, they form the core of an atom's mass.