Question

The element zinc in nature consists of five isotopes with higher than \(0.5 \%\) 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 isotopes of zinc are: \(_{30}^{64}Zn\), \(_{30}^{66}Zn\), \(_{30}^{67}Zn\), \(_{30}^{68}Zn\), and \(_{30}^{70}Zn\). All isotopes of zinc contain 30 protons. The number of neutrons in each isotope are: Zinc-64 has 34 neutrons, Zinc-66 has 36 neutrons, Zinc-67 has 37 neutrons, Zinc-68 has 38 neutrons, and Zinc-70 has 40 neutrons.

Step-by-step solution

Find the atomic number of zinc

From the periodic table, we can find that the atomic number of zinc is 30, which means it has 30 protons in its nucleus.

Write the nuclear symbol for each isotope

To write the nuclear symbol, we use the general format as follows: \(_{Z}^{A}X\), where: - \(Z\) is the atomic number (number of protons) - \(A\) is the mass number (sum of protons and neutrons) - \(X\) is the element symbol Using this format, we can create the nuclear symbols for each isotope of zinc: - \(_{30}^{64}Zn\): Zinc-64 - \(_{30}^{66}Zn\): Zinc-66 - \(_{30}^{67}Zn\): Zinc-67 - \(_{30}^{68}Zn\): Zinc-68 - \(_{30}^{70}Zn\): Zinc-70

Determine the number of protons in each isotope

Since the atomic number of all zinc isotopes is 30, each isotope has 30 protons.

Determine the number of neutrons in each isotope

To find the number of neutrons, we can subtract the atomic number (protons) from the mass number (protons and neutrons) for each isotope: - Zinc-64: \(64 - 30 = 34\) neutrons - Zinc-66: \(66 - 30 = 36\) neutrons - Zinc-67: \(67 - 30 = 37\) neutrons - Zinc-68: \(68 - 30 = 38\) neutrons - Zinc-70: \(70 - 30 = 40\) neutrons

Key concepts

Nuclear Symbol

Understanding the nuclear symbol is crucial when discussing elements and their isotopes. The nuclear symbol is a shorthand notation that represents the atomic nucleus and displays key information about an element. It incorporates the element's symbol, atomic number, and mass number in a specific format. Let's take zinc isotopes as an example.

The general format for a nuclear symbol is \( _{Z}^{A}X \), where \(Z\) is the atomic number indicating the number of protons, \(A\) is the mass number representing the total number of protons and neutrons, and \(X\) is the chemical symbol of the element. So, for the isotope of zinc with a mass number of 64, the nuclear symbol would be \( _{30}^{64}Zn \). This compact symbol encapsulates vital information, showing that this isotope of zinc has 30 protons and a total of 64 nucleons (protons and neutrons combined).

Atomic Number

The atomic number is a fundamental characteristic of an element that defines its identity in the periodic table. It's represented by the symbol \(Z\) and signifies the number of protons in an atom's nucleus. This number is unique to each element and determines its place in the periodic table. For zinc, the atomic number is 30, which means every zinc atom contains exactly 30 protons, regardless of its isotope.

Since atoms are electrically neutral, the atomic number also equals the number of electrons in a neutral atom, giving it its chemical properties. The atomic number is an essential concept for understanding the structure of atoms and the chemical behavior of elements. It is also a critical factor in the calculation of the number of neutrons in isotopes, as it is the difference between the mass number and the atomic number.

Neutrons in Isotopes

Atoms of the same element with different numbers of neutrons are known as isotopes. These variations allow for the existence of multiple forms of an element, each with unique mass numbers but the same chemical properties. For zinc isotopes, the neutron number is the difference between the mass number \(A\) and the atomic number \(Z\).

For an isotope with mass number 64 and atomic number 30 (\( _{30}^{64}Zn \) as an example), the calculation would be \(64 - 30 = 34\) neutrons. This calculation helps us identify the specific isotope and its characteristics. Isotopes are vital in fields such as nuclear chemistry and medicine, as different isotopes of an element can have significantly different stability and radioactivity.