Problem 50 - Chemistry Matter and Change

Question

Calculate the neutron-to-proton ratio for each atom. \(\begin{array}{ll}{\text { a. } \operatorname{tin}-134} & {\text { c. carbon-12 }} \\ {\text { b. silver-107 }} & {\text { d. carbon-1 } 4}\end{array}\)

Step-by-Step Solution

Answer

The neutron-to-proton ratios are: - Tin-134: 1.68 - Silver-107: 1.28 - Carbon-12: 1.00 - Carbon-14: 1.33

Step 1: Understanding Atomic Notation

In atomic notation, an element is described with its mass number, which is the sum of protons and neutrons, and its atomic number, which is the number of protons. For example, in tin-134, 134 is the mass number.

Step 2: Determine Proton Count

Use the periodic table to find the element's atomic number, which tells us the number of protons. - **Tin (Sn)**: Atomic number 50 - **Silver (Ag)**: Atomic number 47 - **Carbon (C)**: Atomic number 6 for both carbon-12 and carbon-14

Step 3: Calculate Neutron Count

Subtract the atomic number from the mass number to find the number of neutrons. - **Tin-134**: 134 - 50 = 84 neutrons - **Silver-107**: 107 - 47 = 60 neutrons - **Carbon-12**: 12 - 6 = 6 neutrons - **Carbon-14**: 14 - 6 = 8 neutrons

Step 4: Calculate Neutron-to-Proton Ratio

Divide the number of neutrons by the number of protons for each element to find the neutron-to-proton ratio. - **Tin-134**: \( \frac{84}{50} = 1.68 \)- **Silver-107**: \( \frac{60}{47} \approx 1.28 \)- **Carbon-12**: \( \frac{6}{6} = 1.00 \)- **Carbon-14**: \( \frac{8}{6} \approx 1.33 \)

Key Concepts

Atomic Notation

Atomic notation is a way of representing information about an element using its mass number and atomic number. This notation helps identify the fundamental particles inside an atom. In any given element, you will often see it written as {{ Element-Symbol}} followed by two numbers: one at the upper left and the other at the bottom left. These are the mass number and the atomic number, respectively.

• The **mass number** is a sum of both protons and neutrons present in the nucleus.
• The **atomic number** represents the number of protons in the element's nucleus.

For example, in the atomic notation of **tin-134**, the number "134" is the mass number and the symbol Sn represents tin. The atomic number for tin is 50, signaling that it has 50 protons in the nucleus. This notation gives us valuable insight into the atomic structure of each element.

Mass Number

The mass number is a crucial part of understanding the composition of an atom. It reflects the total number of protons and neutrons contained within the nucleus, and it's essential for distinguishing different isotopes of an element.

Although the mass number appears similar to the atomic weight, they are not the same. The mass number is a whole number, whereas atomic weight is the average weight of an atom that accounts for isotopes and their abundance.

To compute mass number:

• Add the number of protons (atomic number) to the number of neutrons.

For example, with **silver-107**, the mass number is 107, which includes all the protons and neutrons in its atom, giving us a full picture of its atomic structure.

Atomic Number

The atomic number is a fundamental property of an element, defining its identity on the periodic table. It indicates the amount of protons in an atom's nucleus, and it’s often denoted as a subscript next to the elemental symbol.

Using the atomic number, you can

• Identify an element immediately, as no two elements have the same atomic number.
• Determine the number of electrons in a neutral atom, which balances the positive charge of protons.

For example, tin (Sn) has an atomic number of 50, meaning every tin atom has 50 protons in its nucleus. Similarly, with **carbon**, its atomic number is 6, signifying it has 6 protons and, typically in a neutral atom, 6 electrons.

Neutron Count

Understanding the neutron count in an atom is vital for calculating several atomic characteristics, including the neutron-to-proton ratio. Neutrons are neutral particles, meaning they do not carry a charge, found within an atom's nucleus alongside protons.

To find the neutron count of an atom:

• Subtract the atomic number from the mass number. This equation symbolizes the balance between the protons and neutrons in the nucleus.

Taking **carbon-14** as an example, the process would look like this: Subtract carbon's atomic number (6) from the mass number (14), resulting in 8 neutrons. Recognizing the number of neutrons helps predict an atom's behavior in various chemical reactions and its stability.