Problem 18 - Chemistry: The Central Science

Question

Indicate the number of protons and neutrons in the following nuclei: (a) \({ }_{24}^{56} \mathrm{Cr}\), (b) \({ }^{193} \mathrm{Tl}\), (c) argon-38.

Step-by-Step Solution

Answer

\( (a) 24 \text{ protons,} \: 32 \text{ neutrons}, (b) 81 \text{ protons,} \: 112 \text{ neutrons}, (c) 18 \text{ protons,} \: 20 \text{ neutrons}\)

Step 1: Identify atomic number and mass number

In the given nucleus, chromium is represented by \({}_{24}^{56} \mathrm{Cr}\), where 24 is the atomic number (Z) and 56 is the mass number (A).

Step 2: Calculate the number of protons and neutrons

We know: Number of protons (Z) = 24 To find the number of neutrons, use the formula: Number of neutrons = Mass number (A) - Atomic number (Z) Number of neutrons = 56 - 24 Thus, the number of neutrons in chromium is 32. Chromium has 24 protons and 32 neutrons. #b) Thallium (Tl)#

Step 1: Identify atomic number and mass number

In the given nucleus, thallium is represented by \({ }^{193} \mathrm{Tl}\). The mass number (A) is 193. We do not have an atomic number given, so we need to find it.

Step 2: Find the atomic number for Thallium

To determine the atomic number for thallium, we can refer to the periodic table, which shows us that the atomic number for thallium (Tl) is 81.

Step 3: Calculate the number of protons and neutrons

Since we have the atomic number (Z) and mass number (A), we can calculate the number of neutrons: Number of protons (Z) = 81 Number of neutrons = Mass number (A) - Atomic number (Z) Number of neutrons = 193 - 81 Thus, the number of neutrons in thallium is 112. Thallium has 81 protons and 112 neutrons. #c) Argon-38#

Step 1: Identify atomic number and mass number

The nucleus provided is for argon-38, with 38 representing the mass number (A). We need to find the atomic number for argon.

Step 2: Find the atomic number for Argon

To determine the atomic number for argon, we can refer to the periodic table, which shows us that the atomic number for argon (Ar) is 18.

Step 3: Calculate the number of protons and neutrons

Once we have the atomic number (Z) and mass number (A), we can determine the number of neutrons: Number of protons (Z) = 18 Number of neutrons = Mass number (A) - Atomic number (Z) Number of neutrons = 38 - 18 Thus, the number of neutrons in argon-38 is 20. Argon-38 has 18 protons and 20 neutrons.

Key Concepts

Atomic Number

The atomic number, often symbolized as "Z," is a fundamental property of an element, defining the number of protons found in the nucleus of an atom. This number is crucial because it determines the identity of the element. For example, all atoms of chromium (Cr) have an atomic number of 24, meaning every chromium atom contains 24 protons. Similarly, thallium (Tl) has an atomic number of 81, while argon (Ar) holds an atomic number of 18.
Atomic number gives elements their unique place on the periodic table, lining them up in order of increasing number of protons. This definition helps us distinguish between different elements and understand their chemical behavior.

• Defines the element.
• Determines position in the periodic table.
• Is always equal to the number of protons in a neutral atom.

Mass Number

Mass number, abbreviated as "A," is another important concept in nuclear chemistry. It is the total count of protons and neutrons present in an atom's nucleus. Unlike the atomic number, the mass number is not found on the periodic table; rather, it varies between different isotopes of an element. For example, the mass number of chromium in this particular problem is 56, indicating a total of 56 protons and neutrons combined.
Calculating the mass number is straightforward:

• Mass number (A) = Number of protons (Z) + Number of neutrons.

Knowing the mass number helps identify isotopes of elements, which are atoms with the same number of protons but varying numbers of neutrons, giving them different mass numbers.

Neutrons

Neutrons are one of the key subatomic particles found in an atom's nucleus, often symbolized by "n". They, along with protons, contribute to the mass of the atom. Neutrons have no electric charge, which influences the stability of the nucleus. Understanding the number of neutrons in an atom can be important in identifying different isotopes of the same element.
Calculating the number of neutrons is simple if you know the atomic and mass numbers:

• Number of neutrons = Mass number (A) - Atomic number (Z).

For example, chromium has 32 neutrons, calculated as 56 (mass number) minus 24 (atomic number). This calculation helps to determine any isotope's unique characteristics and contributes to our understanding of nuclear composition.
Neutrons play a critical role in maintaining stability within the atom; too many or too few can result in unstable nuclei, leading to radioactive decay.