Problem 40 - Introductory Chemistry Atoms First

Question

Consider the symbol \({ }_{7}^{14} \mathrm{C}\). (a) What is wrong with this symbol? (b) Adjust the atomic number so that the symbol is correct. (c) Adjust the symbol letter so that the symbol is correct.

Step-by-Step Solution

Answer

(a) The problem with the given symbol \({}_{7}^{14}\mathrm{C}\) is that it has an incorrect atomic number (7 instead of 6 for carbon). (b) To correct the symbol, change the atomic number to 6: \({}_{6}^{14}\mathrm{C}\). (c) The symbol letter is already correct (C for carbon), so no further adjustment is needed. The final correct symbol is \({}_{6}^{14}\mathrm{C}\).

Step 1: 1. Evaluate the given symbol

We are given the symbol \({}_{7}^{14}\mathrm{C}\). Here: - 7 is the atomic number (Z) which represents the number of protons in the nucleus of the atom. - 14 is the mass number (A) which represents the total number of protons and neutrons in the nucleus of the atom. - C is the chemical symbol which represents the element carbon. It has an atomic number (Z) of 6.

Step 2: 2. Identify the problem

The problem with the given symbol \({}_{7}^{14}\mathrm{C}\) is that, instead of 6 (the atomic number of carbon), there is a 7 in the atomic number position.

Step 3: 3. Adjust the atomic number

To correct the symbol, we need to change the atomic number from 7 to 6, as carbon has an atomic number of 6. The symbol should be \({}_{6}^{14}\mathrm{C}\).

Step 4: 4. Adjust the symbol letter

The symbol letter is already correct. Carbon is represented by the letter C, so no further adjustment is needed. Finally, the correct symbol is \({}_{6}^{14}\mathrm{C}\).

Key Concepts

Atomic Number

The atomic number is a very important concept in chemistry. It tells us the number of protons in the nucleus of an atom. Every element on the periodic table has a unique atomic number that distinguishes it from other elements.
It is denoted by the symbol \( Z \) and is typically found as the lower left number in a chemical symbol.
For example, in the symbol \({}_{6}^{14}\mathrm{C}\), the number 6 is the atomic number. This indicates that there are 6 protons in the nucleus of a carbon atom. Understanding the atomic number is essential:

• It helps in identifying the type of element by matching it with the periodic table.
• It tells us about the charge of the nucleus which affects the chemical behavior of the atom.

The atomic number remains constant for a given element. This means if you change the atomic number of an atom, you change what element it is. In the context of our exercise, the incorrect atomic number 7 made the element incorrect as carbon actually has an atomic number of 6.

Mass Number

Mass number is the total count of protons and neutrons in an atomic nucleus. It is symbolized by \( A \) and is usually displayed as the upper left number in a chemical symbol.
For instance, in the symbol \({}_{6}^{14}\mathrm{C}\), the number 14 is the mass number, meaning carbon has 6 protons and 8 neutrons since \( 14 - 6 = 8 \).The mass number is crucial for understanding isotopes:

• Isotopes are atoms of the same element (same atomic number) with different mass numbers due to varying numbers of neutrons.
• The physical properties of an isotope can vary between isotopes, even though the chemical properties remain the same.

Adjustments to the mass number, while keeping the atomic number constant, do not change which element it is. They just provide insights into the isotope variant of the element.

Chemical Symbol

The chemical symbol is a one or two-letter abbreviation used to represent an element on the periodic table.
Each symbol is unique to an element and is usually derived from its English name or Latin name. For instance, the chemical symbol for carbon is \( \mathrm{C} \).
In our chemical notation like \({}_{6}^{14}\mathrm{C}\), \( \mathrm{C} \) stands for carbon.Chemical symbols help in:

• Easily identifying elements without ambiguity.
• Writing chemical equations and formulas succinctly.

In the original exercise example, carbon was represented by the symbol \( \mathrm{C} \). This was correct as per standard nomenclature rules, so no adjustment was needed.