Question

Naturally occurring potassium consists of three isotopes: potassium- 39, potassium- 40 , and potassium- 41 . a. Write the atomic symbol for each isotope. b. In what ways are the isotopes similar and in what ways do they differ?

Short answer

1. \(^\{39\}_{19}\text{K}\), \(^\{40\}_{19}\text{K}\), and \(^\{41\}_{19}\text{K}\). 2. They have the same number of protons but different numbers of neutrons.

Step-by-step solution

Identify the Atomic Symbols for Each Isotope

The atomic symbol includes the element symbol, atomic number, and mass number. Potassium’s symbol is K, and its atomic number is 19. For each isotope, the atomic symbol will be written as: 1. Potassium-39: \(^\{39\}_{19}\text{K}\)2. Potassium-40: \(^\{40\}_{19}\text{K}\)3. Potassium-41: \(^\{41\}_{19}\text{K}\)

Compare the Similarities of the Isotopes

Isotopes of potassium have the same number of protons. Therefore, all isotopes of potassium share the same atomic number (19), and thus, they have the same chemical properties and belong to the same element: potassium (K).

Compare the Differences of the Isotopes

While the isotopes have the same number of protons (19) and same chemical properties, they differ in the number of neutrons in the nucleus. 1. Potassium-39 has 20 neutrons (mass number 39 - atomic number 19).2. Potassium-40 has 21 neutrons (mass number 40 - atomic number 19).3. Potassium-41 has 22 neutrons (mass number 41 - atomic number 19).

Key concepts

Atomic Symbols

Atomic symbols are shorthand notations used to represent atoms. They include information about the element, the atomic number, and the mass number. For example, the symbol for potassium is K.
The atomic number, which is the number of protons, is written as a subscript to the left of the element’s symbol. The mass number, which is the sum of protons and neutrons, is written as a superscript to the left.
In the given exercise, the atomic symbols for potassium isotopes are written as follows:
- Potassium-39: \(^\{39\} _{19} \text{K}\)
- Potassium-40: \(^\{40\} _{19} \text{K}\)
- Potassium-41: \(^\{41\} _{19} \text{K}\)
This notation helps to quickly convey the essential details about the isotopes.

Protons Neutrons

Protons and neutrons are subatomic particles found in the nucleus of an atom. Protons have a positive charge, whereas neutrons have no charge.
The number of protons in an atom’s nucleus is its atomic number, and it determines the element's identity. For example, all potassium atoms have 19 protons.
The number of neutrons, however, can vary. This variance creates different isotopes of the same element.
In the case of the potassium isotopes:
- Potassium-39 has 20 neutrons \(19 + 20 = 39\)
- Potassium-40 has 21 neutrons \(19 + 21 = 40\)
- Potassium-41 has 22 neutrons \(19 + 22 = 41\)
Although these isotopes have different neutron numbers, the number of protons remains constant, making them the same element.

Chemical Properties

Chemical properties describe how an element reacts with other substances. These properties are largely determined by the number of protons and electrons in an atom, which remain constant across isotopes of a given element.
Potassium’s chemical properties include a strong reactivity with water, forming potassium hydroxide and hydrogen gas.
Because isotopes have the same atomic number and electron configuration, they have identical chemical properties.
In the exercise, while potassium-39, potassium-40, and potassium-41 have different neutron counts, their chemical behavior remains the same.

Mass Number

The mass number of an atom is the total count of protons and neutrons within its nucleus. It is represented by a superscript number to the upper left of the atomic symbol.
For isotopes, while the atomic number remains the same, the mass number varies due to different neutron counts.
In the given potassium isotopes:
\(^{39}_{19} \text{K}\) has a mass number of 39.
\(^{40}_{19} \text{K}\) has a mass number of 40.
\(^{41}_{19} \text{K}\) has a mass number of 41.
This numerical difference helps identify specific isotopes of an element and is key for calculations involving atomic mass and nuclear reactions.