Question

Identify the element represented by each of the following symbols and give the number of protons and neutrons in each: \((\mathbf{a})_{33}^{74} X,(\mathbf{b}) \frac{1}{33} X$$(\mathbf{c})_{63}^{152} \mathrm{X},(\mathbf{d}) \frac{209}{83} \mathrm{X}\).

Short answer

(a) \(_{33}^{74} X\) represents Arsenic (As) with 33 protons and 41 neutrons. (b) \(^1_{33} X\) is not possible since the number of neutrons cannot be negative. (c) \(_{63}^{152} \mathrm{X}\) represents Europium (Eu) with 63 protons and 89 neutrons. (d) \(^{209}_{83} \mathrm{X}\) represents Bismuth (Bi) with 83 protons and 126 neutrons.

Step-by-step solution

Identify the element represented by each symbol

For each of the given symbols, we can use the atomic number (the subscript) to identify the element by referring to the periodic table. Since the number of protons in an atom determines its identity, the atomic number represents the number of protons in the element.

Determine the number of protons and neutrons for each symbol

We already know that the atomic number represents the number of protons. To find the number of neutrons, we can subtract the atomic number from the atomic mass (the superscript). The atomic mass is the sum of the protons and neutrons in an atom.

Solve for each symbol

(a) \(_{33}^{74} X\) Element: The atomic number is 33, which corresponds to the element Arsenic (As). Number of Protons: Atomic number = Number of protons = 33 Number of Neutrons: Atomic mass - Atomic number = Number of neutrons 74 - 33 = 41 Answer: Arsenic (As) with 33 protons and 41 neutrons. (b) \(^1_{33} X\) Element: The atomic number is 33, which corresponds to the element Arsenic (As). Number of Protons: Atomic number = Number of protons = 33 Number of Neutrons: Atomic mass - Atomic number = Number of neutrons 1 - 33 = -32 Answer: This symbol is not possible since the number of neutrons cannot be negative. (c) \(_{63}^{152} \mathrm{X}\) Element: The atomic number is 63, which corresponds to the element Europium (Eu). Number of Protons: Atomic number = Number of protons = 63 Number of Neutrons: Atomic mass - Atomic number = Number of neutrons 152 - 63 = 89 Answer: Europium (Eu) with 63 protons and 89 neutrons. (d) \(^{209}_{83} \mathrm{X}\) Element: The atomic number is 83, which corresponds to the element Bismuth (Bi). Number of Protons: Atomic number = Number of protons = 83 Number of Neutrons: Atomic mass - Atomic number = Number of neutrons 209 - 83 = 126 Answer: Bismuth (Bi) with 83 protons and 126 neutrons.

Key concepts

Atomic Number

Every element on the periodic table has a unique atomic number, which is one of its most fundamental identifiers. The atomic number, denoted as a subscript in isotope notation, represents the number of protons in the nucleus of an atom.

For example, if an element has an atomic number of 33, it means there are 33 protons in its nucleus. This is how we identify the element as Arsenic (As), regardless of how many neutrons it might have. The atomic number is critical because it determines the chemical properties of the element and defines each element's unique place on the periodic table.

• The periodic table orders elements by increasing atomic number.
• Elements with the same atomic number share identical chemical behavior.

Understanding the atomic number is crucial for any chemistry student, as it offers insights into an element's identity and its interactions with other elements.

Protons and Neutrons

Inside an atom, the nucleus is densely packed with protons and neutrons. Protons positively charge the nucleus, while neutrons are neutral, having no charge. Together, they contribute to most of an atom's mass.

The number of protons is fixed for any given element, as previously mentioned, but the neutrons can vary. This variability leads to different isotopes of the same element. To determine the number of neutrons in an isotope, you simply subtract the atomic number from the atomic mass. For example, if you have an isotope notation of \(_{33}^{74} X\), the number of neutrons can be found by subtracting 33 (the protons) from 74 (the atomic mass), leaving you with 41 neutrons.

• Protons define the element; neutrons modify the isotope.
• Species with different numbers of neutrons but the same number of protons are isotopes of each other.

This relationship between protons and neutrons is foundational to nuclear chemistry.

Periodic Table

The periodic table is a powerful tool for chemists, organizing elements by increasing atomic number and grouping them by shared properties. It's arranged in rows called periods and columns called groups.

Each element's position on the table not only indicates its atomic number but can also give you insights into its electron configuration and chemical behavior. Elements in the same group typically share similar properties—think of the noble gases or the reactive alkali metals.

• Elements in the same group react in similar ways.
• Elemental properties can be predicted based on their location on the table.

By understanding an element's position on the periodic table, you can predict its reactivity and how it will interact with other elements.

Isotope Notation

Isotope notation is a shorthand way of expressing important information about a specific isotope of an element. This notation is crucial when discussing nuclear chemistry and atomic structure.

It highlights the atomic number (protons) and the mass number (protons plus neutrons) of an element. Typically, isotope notation is written with the element's symbol, the atomic number in the subscript, and the mass number in the superscript. \(^A_{Z} \text{X}\), where \(A\) is the mass number and \(Z\) is the atomic number.

• Isotopes of an element differ only in their number of neutrons.
• Isotope notation helps identify the isotope and its nuclear composition.

This notation is fundamental for recognizing isotopes quickly and understanding their particular nuclear properties.