Question

How many protons and how many neutrons are there in a nucleus of the most common isotope of (a) silicon, \(^{28}_{14}Si\); (b) rubidium, \(^{85}_{37}Rb\); (c) thallium, \(^{205}_{81}Tl\)?

Short answer

(a) 14 protons, 14 neutrons; (b) 37 protons, 48 neutrons; (c) 81 protons, 124 neutrons.

Step-by-step solution

Understanding Nuclear Symbols

Each nuclear symbol is written in the form \( ^{A}_{Z}X \), where \( A \) is the mass number, \( Z \) is the atomic number, and \( X \) is the chemical symbol of the element. The atomic number \( Z \) represents the number of protons and thus identifies the element.

Finding Protons in Silicon

For silicon \( ^{28}_{14}Si \), the atomic number \( Z \) is 14. Therefore, the number of protons in silicon is 14.

Calculating Neutrons in Silicon

The mass number \( A \) for silicon is 28. To find the number of neutrons, use the formula: Neutrons = Mass number - Atomic number. For silicon, Neutrons = 28 - 14 = 14.

Finding Protons in Rubidium

For rubidium \( ^{85}_{37}Rb \), the atomic number \( Z \) is 37. Therefore, the number of protons in rubidium is 37.

Calculating Neutrons in Rubidium

The mass number \( A \) for rubidium is 85. To find the number of neutrons, use the formula: Neutrons = Mass number - Atomic number. For rubidium, Neutrons = 85 - 37 = 48.

Finding Protons in Thallium

For thallium \( ^{205}_{81}Tl \), the atomic number \( Z \) is 81. Therefore, the number of protons in thallium is 81.

Calculating Neutrons in Thallium

The mass number \( A \) for thallium is 205. To find the number of neutrons, use the formula: Neutrons = Mass number - Atomic number. For thallium, Neutrons = 205 - 81 = 124.

Key concepts

Nuclear Symbols

Nuclear symbols play a crucial role in understanding the fundamentals of nuclear physics. They provide a shorthand way to denote the specific characteristics of an element's nucleus. The format for nuclear symbols is typically expressed as \( ^{A}_{Z}X \), where each part has its own distinct meaning:

• \( A \) is the mass number, representing the total number of protons and neutrons within the nucleus.
• \( Z \) is the atomic number, which indicates the number of protons in the nucleus, determining the element's identity.
• \( X \) is the chemical symbol of the element, such as Si for silicon, Rb for rubidium, or Tl for thallium.

When interpreting nuclear symbols, focus on these values to understand the composition of the nucleus. This notation aids in calculating the number of neutrons as well, using the mass and atomic numbers.

Protons and Neutrons

Protons and neutrons together form the nucleus of an atom, and their arrangement significantly influences the atom's properties. Protons are positively charged particles, and their number, given by the atomic number, defines the element. Neutrons, on the other hand, are neutral particles that essentially serve as a "glue," helping to bind protons together within the nucleus despite their mutual repulsion due to like charges.

• Protons determine the charge and identity of the atom.
• Neutrons contribute to the mass of the atom and influence its stability.

The balance between protons and neutrons is crucial for the atom's stability. This balance can vary among isotopes, which are atoms of the same element with different numbers of neutrons. Understanding the roles of protons and neutrons helps in predicting the chemical behavior and stability of elements.

Atomic Number

The atomic number, denoted by \( Z \), is a fundamental concept in nuclear physics. It specifies the number of protons found in the nucleus of an atom. Since protons are positively charged, the atomic number also reflects the charge of the nucleus.- The atomic number is unique for each element and determines its position in the periodic table.- For example, silicon has an atomic number of 14, rubidium 37, and thallium 81.The atomic number is crucial because it dictates how atoms interact chemically with each other. Elements with the same atomic number but different mass numbers are known as isotopes, possessing varied numbers of neutrons.

Mass Number

Mass number, symbolized as \( A \), represents the total number of protons and neutrons in an atom's nucleus. Unlike the atomic number, the mass number can change in isotopes of the same element due to a different count of neutrons.

• For example, silicon's mass number is 28, rubidium's is 85, and thallium's is 205.
• It's calculated as: \( A = \ ext{Number of protons} + \ ext{Number of neutrons} \).

Knowing the mass number allows for the calculation of the number of neutrons by using the formula: \[\text{Neutrons} = A - Z \]Where \( A \) is the mass number and \( Z \) is the atomic number. The mass number's variability among isotopes influences the atomic mass seen in periodic tables.