Question

How many neutrons are in an atom with each atomic number and mass number? (a) \(Z=28, A=59\) (b) \(Z=92, A=235\) (c) \(Z=21, A=46\) (d) \(Z=18, A=42\)

Short answer

(a) 31 neutrons, (b) 143 neutrons, (c) 25 neutrons, (d) 24 neutrons.

Step-by-step solution

Understanding the Problem

To find the number of neutrons in an atom, use the formula: Number of neutrons = Mass number (A) - Atomic number (Z). The atomic number (Z) represents the number of protons, and the mass number (A) is the sum of protons and neutrons in the nucleus.

Calculating Neutrons for (a) Z=28, A=59

Subtract the atomic number from the mass number: Number of neutrons = 59 - 28.

Calculating Neutrons for (b) Z=92, A=235

Subtract the atomic number from the mass number: Number of neutrons = 235 - 92.

Calculating Neutrons for (c) Z=21, A=46

Subtract the atomic number from the mass number: Number of neutrons = 46 - 21.

Calculating Neutrons for (d) Z=18, A=42

Subtract the atomic number from the mass number: Number of neutrons = 42 - 18.

Final Answer for All Parts

Compute the differences obtained in steps 2 to 5 to get the final neutron counts for each atom.

Key concepts

Atomic Number

The atomic number, often denoted by the letter Z, is an essential element in understanding the atomic structure of an element. It is a unique identifier for each chemical element, representing the number of protons found in the nucleus of an atom. Since protons carry a positive charge, the atomic number also reflects the charge identity of the nucleus.

In nuclear chemistry, the atomic number serves as the basis for distinguishing one element from another. For instance, carbon has an atomic number of 6, which means every atom of carbon has 6 protons. This value is crucial when calculating the number of neutrons, as illustrated in the textbook exercise, since the number of neutrons can change in isotopes without altering the atomic number.

Mass Number

The mass number, designated as A, provides the total count of protons and neutrons in an atom's nucleus. It is an integer value as protons and neutrons, which are collectively referred to as nucleons, have similar masses and are far heavier than electrons.

As opposed to the atomic number, the mass number isn't unique to each element. This is because elements can have different isotopes, varieties of the same element with different numbers of neutrons. Thus, it is the variation in the number of neutrons that results in different isotopes of an element having the same atomic number but different mass numbers, a concept reinforced by the exercise steps that calculate the neutron count by subtracting the atomic number from the mass number.

Nuclear Chemistry

Nuclear chemistry focuses on the processes and changes that occur within the nucleus of an atom. It explores phenomena such as radioactivity, nuclear transmutation, and nuclear properties of elements. Understanding the difference between the atomic number and the mass number is key in this field.

In nuclear reactions, unlike chemical reactions that involve the electron shell, it’s the changes in the nucleus—such as the conversion of one element into another, often with the emission or absorption of particles like neutrons—that are of interest. The textbook exercise on calculating neutrons directly relates to nuclear chemistry because it involves understanding isotopes, which are central to how nuclear reactions occur and how they are studied.

Atomic Structure

Atomic structure refers to the organized arrangement of protons, neutrons, and electrons that compose an atom. The protons and neutrons are tightly bound in the nucleus at the center of the atom, with electrons orbiting around it at various energy levels.

The structure of the atom is pivotal to chemical properties and behaviors. For example, the number of electrons in the outermost shell dictates an element's valency and its capability to bond with other elements. However, the exercises posed here focus on the nuclear component—the nucleus—highlighting the relationship between the number of protons (atomic number) and the mass number to deduce the number of neutrons, which has implications for both the stability of the atom and its nuclear characteristics.