Question

The element zinc in nature consists of five isotopes with higher than $0.5\mathrm{\%}$ natural abundances, with mass numbers 64,66,67,68 , and 70 . Write the nuclear symbol for each of these isotopes. How many protons does each contain? How many neutrons does each contain?

Short answer

The nuclear symbols for the five isotopes of zinc are: 1. Isotope 1: ${}_{30}^{64}\text{Zn}$, containing 30 protons and 34 neutrons. 2. Isotope 2: ${}_{30}^{66}\text{Zn}$, containing 30 protons and 36 neutrons. 3. Isotope 3: ${}_{30}^{67}\text{Zn}$, containing 30 protons and 37 neutrons. 4. Isotope 4: ${}_{30}^{68}\text{Zn}$, containing 30 protons and 38 neutrons. 5. Isotope 5: ${}_{30}^{70}\text{Zn}$, containing 30 protons and 40 neutrons.

Step-by-step solution

Isotope 1: Zinc-64 (Zn-64)

The mass number of Zn-64 is 64. 1. Nuclear symbol: ${}_{30}^{64}\text{Zn}$ 2. Number of protons: 30 (the atomic number of zinc) 3. Number of neutrons: 64 - 30 = 34

Isotope 2: Zinc-66 (Zn-66)

The mass number of Zn-66 is 66. 1. Nuclear symbol: ${}_{30}^{66}\text{Zn}$ 2. Number of protons: 30 (the atomic number of zinc) 3. Number of neutrons: 66 - 30 = 36

Isotope 3: Zinc-67 (Zn-67)

The mass number of Zn-67 is 67. 1. Nuclear symbol: ${}_{30}^{67}\text{Zn}$ 2. Number of protons: 30 (the atomic number of zinc) 3. Number of neutrons: 67 - 30 = 37

Isotope 4: Zinc-68 (Zn-68)

The mass number of Zn-68 is 68. 1. Nuclear symbol: ${}_{30}^{68}\text{Zn}$ 2. Number of protons: 30 (the atomic number of zinc) 3. Number of neutrons: 68 - 30 = 38

Isotope 5: Zinc-70 (Zn-70)

The mass number of Zn-70 is 70. 1. Nuclear symbol: ${}_{30}^{70}\text{Zn}$ 2. Number of protons: 30 (the atomic number of zinc) 3. Number of neutrons: 70 - 30 = 40 So, in summary: 1. Isotope 1: ${}_{30}^{64}\text{Zn}$, 30 protons, 34 neutrons 2. Isotope 2: ${}_{30}^{66}\text{Zn}$, 30 protons, 36 neutrons 3. Isotope 3: ${}_{30}^{67}\text{Zn}$, 30 protons, 37 neutrons 4. Isotope 4: ${}_{30}^{68}\text{Zn}$, 30 protons, 38 neutrons 5. Isotope 5: ${}_{30}^{70}\text{Zn}$, 30 protons, 40 neutrons

Key concepts

Nuclear Symbol

The nuclear symbol of an element is a shorthand representation that provides important information about the isotope of an element. It consists of the element's chemical symbol accompanied by two numbers. The format typically looks like this:

• The mass number is located at the upper left corner of the symbol and denotes the total number of protons and neutrons in an atom.
• The atomic number is located at the lower left corner and indicates the number of protons, which is also the element's unique identifier.

For example, in the nuclear symbol ${}_{30}^{64}\text{Zn}$, the "Zn" stands for zinc, "64" is the mass number (sum of protons and neutrons), and "30" is the atomic number (protons). This notation is crucial for distinguishing isotopes of the same element, like zinc, which has several isotopes with varying mass numbers.

Protons

Protons are subatomic particles with a positive electric charge found within the nucleus of an atom. They play a critical role in determining the identity of an element, as the number of protons (atomic number) defines which element an atom is. Each element on the periodic table has a unique atomic number, representing the number of protons in its atoms.

For zinc, the atomic number is 30, meaning every zinc atom, including its isotopes, contains 30 protons. This uniformity of proton count is what identifies an atom as zinc, despite there being multiple isotopes with different numbers of neutrons.

• Protons contribute significantly to the atomic mass.
• The proton number is constant for all isotopes of an element.

Neutrons

Neutrons are neutral particles found in the nucleus of an atom. They do not have an electric charge, yet they significantly contribute to the atom's mass. The number of neutrons can vary among isotopes of the same element, which results in different mass numbers for each isotope.

To determine the number of neutrons in an isotope, you subtract the atomic number (protons) from the mass number. For zinc's isotopes:

• Zinc-64 (${}_{30}^{64}\text{Zn}$) has 34 neutrons (64 - 30).
• Zinc-66 (${}_{30}^{66}\text{Zn}$) has 36 neutrons (66 - 30).
• Zinc-67 (${}_{30}^{67}\text{Zn}$) has 37 neutrons (67 - 30).
• Zinc-68 (${}_{30}^{68}\text{Zn}$) has 38 neutrons (68 - 30).
• Zinc-70 (${}_{30}^{70}\text{Zn}$) has 40 neutrons (70 - 30).

This variation in neutron count is what allows for isotopes to exist.

Mass Number

The mass number of an isotope is the total sum of protons and neutrons within the nucleus of an atom. It is a key value that differentiates isotopes of the same element by reflecting the number of neutrons present. Displayed in the nuclear symbol, the mass number is crucial for calculating the atomic mass and understanding the isotope composition.

For example, the mass numbers for zinc's naturally occurring isotopes are 64, 66, 67, 68, and 70. This information helps in identifying each isotope because while all zinc atoms have 30 protons, the number of neutrons varies, altering the mass number.

• Mass number = protons + neutrons
• Essential for distinguishing isotopes with different atomic weights

Atomic Number

The atomic number is one of the most fundamental properties of an element. It signifies the number of protons in an atom's nucleus and defines the element's identity. This is why it is also listed on the periodic table alongside the element's symbol.

For the element zinc, the atomic number is 30. This number is consistent across all of zinc's isotopes, making it a reliable identifier. Every isotope of zinc, whether it is Zn-64 or Zn-70, has 30 protons.

• Atomic number = the number of protons
• Uniquely identifies the element irrespective of its neutrons

The atomic number not only determines the element's identity but also influences its chemical behavior and placement in the periodic table.