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 \(=19\) Atomic Mass \(=39 \quad\) Atomic Mass \(=40 \quad\) Atomic Mass \(=41\)

Short answer

Protons = 19; Neutrons: K-39: 20, K-40: 21, K-41: 22.

Step-by-step solution

Determine the Number of Protons

The atomic number gives the number of protons in an atom. For all potassium isotopes, \( Z = 19 \). Thus, each isotope of potassium has 19 protons.

Calculate Neutrons for Potassium-39

To find the number of neutrons, subtract the atomic number from the atomic mass: \( 39 - 19 = 20 \) neutrons. Potassium-39 has 19 protons and 20 neutrons.

Calculate Neutrons for Potassium-40

For Potassium-40, subtract the atomic number from the atomic mass: \( 40 - 19 = 21 \) neutrons. Potassium-40 has 19 protons and 21 neutrons.

Calculate Neutrons for Potassium-41

For Potassium-41, subtract the atomic number from the atomic mass: \( 41 - 19 = 22 \) neutrons. Potassium-41 has 19 protons and 22 neutrons.

Key concepts

Atomic Number

The atomic number is a fundamental property of an element that distinguishes it from other elements. For each element on the periodic table, the atomic number is unique. It represents the number of protons found in the nucleus of an atom. These protons carry a positive charge, and for electrically neutral atoms, the number of protons equals the number of electrons. In the case of potassium, the atomic number is 19. This means that every atom of potassium has 19 protons. The atomic number provides essential information for identifying an element, which is why it is often used as a key identifier in chemical representations.

• An atomic number of 19 signifies potassium.
• The atomic number is always equal to the number of protons.
• It defines the chemical identity of the element.

Understanding atomic number is crucial for distinguishing among elements and for comprehending their unique properties.

Atomic Mass

Atomic mass, sometimes referred to as atomic weight, is an average mass of atoms of an element, calculated using the abundance and relative mass of each isotope of the element. The atomic mass provides insight into the nucleus's composition, indicating the total number of protons and neutrons. Unlike the atomic number, which remains constant for all isotopes of an element, the atomic mass can vary depending on the number of neutrons. For isotopes of potassium, we have three different atomic masses:

• Potassium-39 with an atomic mass of 39.
• Potassium-40 with an atomic mass of 40.
• Potassium-41 with an atomic mass of 41.

These different atomic masses are due to the different numbers of neutrons in each isotope, while the number of protons (19) remains constant. It's important to note that atomic mass is not the same as mass number, which is the sum of protons and neutrons in a specific isotope. Understanding atomic mass helps in distinguishing isotopes and in calculations involving molecular weight and stoichiometry.

Neutrons Calculation

Calculating the number of neutrons in an atom is a simple yet essential process in understanding the isotopic nature of elements. Neutrons, along with protons, make up the nucleus of an atom, and their number can vary even among atoms of the same element, leading to different isotopes. The number of neutrons in an atom can be determined by using the formula:\[ \text{Number of Neutrons} = \text{Atomic Mass} - \text{Atomic Number} \]This calculation is straightforward as it involves subtracting the atomic number (which gives you the number of protons) from the atomic mass (which is the sum of protons and neutrons).Applying this to potassium:

• For Potassium-39: Atomic mass is 39, Atomic number is 19, hence neutrons = 39 - 19 = 20.
• For Potassium-40: Atomic mass is 40, Atomic number is 19, hence neutrons = 40 - 19 = 21.
• For Potassium-41: Atomic mass is 41, Atomic number is 19, hence neutrons = 41 - 19 = 22.

The differences in neutron numbers cause the variations in the atomic mass of different isotopes. Understanding this calculation reinforces the concept of natural isotopic diversity in elements like potassium.