Question

The information below refers to three isotopes of the element potassium. Using this information, determine the appropriate number of protons and neutrons for each isotope. Label each isotope in the manner used in the chapter. Atomic Number \(=19\) Atomic Number \(=19\) Atomic Number \(=19\) Mass Number \(=39\) Mass Number \(=40\) Mass Number \(=41\)

Short answer

Potassium-39: 19 protons, 20 neutrons; Potassium-40: 19 protons, 21 neutrons; Potassium-41: 19 protons, 22 neutrons.

Step-by-step solution

Understanding Atomic Structure

An isotope of an element has the same number of protons but a different number of neutrons. The atomic number of an element gives the number of protons in its atoms. Since the atomic number for potassium is given as 19, each isotope of potassium will have 19 protons.

Calculating Neutrons for Potassium-39

The mass number of an isotope is the sum of its protons and neutrons. For the Potassium-39 isotope, the mass number is given as 39. Since there are 19 protons, the number of neutrons is calculated as follows: \[\text{Number of Neutrons} = \text{Mass Number} - \text{Atomic Number} = 39 - 19 = 20.\]

Calculating Neutrons for Potassium-40

For the Potassium-40 isotope, the mass number is 40. Using the same formula, calculate the number of neutrons:\[\text{Number of Neutrons} = 40 - 19 = 21.\]

Calculating Neutrons for Potassium-41

For the Potassium-41 isotope, the mass number is 41. Calculate the number of neutrons using the formula:\[\text{Number of Neutrons} = 41 - 19 = 22.\]

Labeling Each Isotope

Each isotope should be labeled as Potassium followed by its mass number. Thus, the isotopes are labeled as follows: - Potassium-39 has 19 protons and 20 neutrons, - Potassium-40 has 19 protons and 21 neutrons, - Potassium-41 has 19 protons and 22 neutrons.

Key concepts

Atomic Number

The atomic number of an element is a fundamental property of its atoms. It represents the number of protons found in the nucleus of the atom. Protons are positively charged particles, which contribute to an atom’s identity.
Atomic number is key because it defines the element and maintains the element's consistency across different isotopes. For potassium, the atomic number is 19, signifying that all potassium atoms have 19 protons regardless of the isotope.

• If you change the atomic number, you are changing the element itself.
• Atomic numbers are unique to each element on the periodic table.
• Knowing the atomic number helps determine an element's place in the periodic table.

The atomic number remains constant for isotopes but helps differentiate between elements.

Mass Number

The mass number of an element is very important when understanding isotopes. It is the total number of protons and neutrons in an atom’s nucleus.
While the atomic number stays the same for isotopes, the mass number varies due to the differing number of neutrons present. This is why different isotopes of an element have different mass numbers. For potassium, three isotopes exist: with mass numbers of 39, 40, and 41.

• Mass number is used to label isotopes; for example, Potassium-39.
• It adds an insight into the nucleus make-up of atoms beyond just protons.
• Mass number is obtained by rounding the average atomic mass values taken from nature.

The mass number provides a complete "nuclear count" for atoms of isotopes.

Neutrons

Neutrons are neutral particles located in an atom’s nucleus alongside protons. Unlike protons, neutrons do not have a charge, but they play a crucial role in stabilizing the nucleus.
Determining the number of neutrons in an atom is essential for identifying isotopes. The number of neutrons is derived from subtracting the atomic number from the mass number. For potassium isotopes, the relevance of neutrons becomes clear:

• Potassium-39 has 20 neutrons: calculated as 39 (mass number) - 19 (atomic number).
• Potassium-40 has 21 neutrons: calculated similarly.
• Potassium-41 has 22 neutrons.

Neutrons play a role in the physical and sometimes chemical properties of the isotope.

Protons

Protons are among the most significant particles in an atom. They carry a positive electric charge and are found within the nucleus.
The number of protons identifies the element; in the case of potassium, this is set at 19 protons. Understanding protons is critical since they define:

• The atomic number, which is crucial for identifying elements.
• The charge balance in neutral atoms; they are compensated by electrons (negatively charged) outside the nucleus.
• The element's behavior in chemical reactions, as protons interact with electrons when bonds are formed.

Protons define the foundation of what the element is, making them a pivotal part of atomic science.