Problem 15 - Chemistry and Chemical Reactivity

Question

Cobalt has three radioactive isotopes used in medical studies. Atoms of these isotopes have 30 \(31,\) and 33 neutrons, respectively. Give the complete symbol for each of these isotopes.

Step-by-Step Solution

Answer

The isotopes are \\({}^{57}_{27}Co\\), \\({}^{58}_{27}Co\\), and \\({}^{60}_{27}Co\\).

Step 1: Identify the Symbol for Cobalt

The chemical symbol for cobalt is 'Co'. This is the starting point for writing the complete symbol for cobalt's isotopes.

Step 2: Determine the Atomic Number of Cobalt

Cobalt has an atomic number of 27, which means it has 27 protons. This number remains constant for all cobalt isotopes.

Step 3: Calculate the Mass Numbers

The mass number of an isotope is the sum of the number of protons and neutrons. For each isotope, calculate the mass number by adding 27 (protons) to the given number of neutrons: - First isotope: 27 + 30 = 57 - Second isotope: 27 + 31 = 58 - Third isotope: 27 + 33 = 60.

Step 4: Write the Complete Symbols

The complete symbol for an isotope includes the mass number as a superscript and the atomic number as a subscript on the left side of the chemical symbol. Write the complete symbol for each isotope:- First isotope: \({}^{57}_{27}Co\)- Second isotope: \({}^{58}_{27}Co\)- Third isotope: \({}^{60}_{27}Co\)

Key Concepts

Radioactive Isotopes

Radioactive isotopes are atoms that have unstable nuclei, causing them to release energy in the form of radiation in a process known as radioactive decay. This property makes these isotopes useful in various fields, particularly in medicine, where they help in diagnostic imaging and treatment.

• Cobalt isotopes like Co-57, Co-58, and Co-60 are some examples of radioactive isotopes used in medical studies.
• Each of these isotopes has a different number of neutrons but the same number of protons, which is why they are considered isotopes of the same element, cobalt.
• These isotopes are chosen for medical applications because their radioactive properties allow them to trace processes in the body or target diseased cells.

For instance, Cobalt-60 is widely used in the treatment of cancer due to its ability to produce gamma rays. Understanding the nature of radioactive isotopes is crucial for reacting appropriately to their capabilities and risks.

Mass Number Calculation

Calculating the mass number of an isotope is straightforward but critical for identifying isotopes. The mass number is the total count of protons and neutrons in an atom's nucleus. Since protons are positively charged particles that essentially define the identity of an element, this number never changes for a given element.

• To find an isotope's mass number, simply add the atomic number (total protons) to the neutron number.
• For example, cobalt, which has 27 protons (as its atomic number), will have isotopes with mass numbers calculated by adding 27 to the neutron counts of 30, 31, and 33 respectively.
• This results in mass numbers of 57, 58, and 60 for the three cobalt isotopes.

Understanding how to calculate the mass number ensures precision in writing the nuclear symbol and distinguishing between different isotopes of the same element.

Atomic Structure

The atomic structure of an element is an organized arrangement of protons, neutrons, and electrons within an atom. This structure helps define not only the chemical properties of an element but also its physical behavior. Cobalt, like all elements, is characterized by specific atomic structures that include its isotopes.

• In its nucleus, cobalt has 27 protons, which determine its atomic number and place on the periodic table.
• Protons are accompanied by varying numbers of neutrons depending on the isotope. These variations create different isotopes, each with unique nuclear properties.
• Electrons orbit around the nucleus, providing charge balance to the positively charged protons.

Atomic structures develop distinct identities by the quantity of these subatomic particles, which influences how atoms interact with each other. Proper knowledge of atomic structure aids in identifying isotopes and understanding their applications in science and industry.