Question

Indicate the number of protons and neutrons in the following nuclei: $(\mathbf{a}){}^{239}\mathrm{Pu},(\mathbf{b}){}^{142}\mathrm{Ba},(\mathbf{c})$ potassium- $41.$.

Short answer

a) ${}^{239}\mathrm{Pu}$: 94 protons and 145 neutrons. b) ${}^{142}\mathrm{Ba}$: 56 protons and 86 neutrons. c) Potassium-41: 19 protons and 22 neutrons.

Step-by-step solution

Identify the Atomic Number (Z) from the Periodic Table

First, let's find the atomic numbers of the given elements from the periodic table: a) Pu (Plutonium) has an atomic number (Z) of 94. b) Ba (Barium) has an atomic number (Z) of 56. c) K (Potassium) has an atomic number (Z) of 19.

Determine the Number of Protons and Neutrons using Atomic Mass Number (A) and Atomic Number (Z)

Now that we have the atomic numbers, the number of protons is equal to the atomic number (Z). Calculate the number of neutrons by subtracting the atomic number (Z) from the atomic mass number (A). a) For Pu: Number of protons = Atomic Number (Z) = 94 Number of neutrons = Atomic Mass Number (A) - Atomic Number (Z) = 239 - 94 = 145 b) For Ba: Number of protons = Atomic Number (Z) = 56 Number of neutrons = Atomic Mass Number (A) - Atomic Number (Z) = 142 - 56 = 86 c) For Potassium-41: Number of protons = Atomic Number (Z) = 19 Number of neutrons = Atomic Mass Number (A) - Atomic Number (Z) = 41 - 19 = 22 The number of protons and neutrons in each isotope is as follows: a) ${}^{239}\mathrm{Pu}$: 94 protons and 145 neutrons. b) ${}^{142}\mathrm{Ba}$: 56 protons and 86 neutrons. c) Potassium-41: 19 protons and 22 neutrons.

Key concepts

Atomic Number

The atomic number, denoted by $Z$, is a fundamental property of an element that defines its identity. It's the number of protons in the nucleus of an atom. This number determines the element itself because each element has a unique number of protons. For instance, Plutonium has an atomic number of 94, which means every atom of Plutonium has 94 protons. Similarly, Barium's atomic number is 56, and Potassium's is 19. The atomic number also tells us about the element's place in the periodic table.

Elements are arranged in order of their atomic numbers, from smallest to largest. This arrangement helps us predict predictable trends in element properties. It's important to remember that the atomic number also equals the number of electrons in a neutral atom, providing a balanced charge with the positively charged protons.

Atomic Mass Number

The atomic mass number $A$ is the total number of protons and neutrons in an atom's nucleus. It provides a way to quantify the bulk of an atom. Unlike the atomic number, the atomic mass number is not found directly on the periodic table because it can change with different isotopes of an element. For example, in Plutonium, the atomic mass number of 239 means there are 239 protons and neutrons combined in the nucleus. Barium has a mass number of 142, and Potassium-41 indicates the isotope of Potassium with an atomic mass number of 41.

The atomic mass number is crucial in nuclear chemistry because it helps us understand nuclear reactions and stability. To find it, add the number of protons to the number of neutrons. When dealing with isotopes, knowing the atomic mass number allows us to calculate how it varies from the average atomic mass listed on the periodic table.

Protons and Neutrons

Protons and neutrons form the core of an atom, known as the nucleus. Protons are positively charged particles, while neutrons carry no charge, making them neutral. Together, they provide most of the atomic mass. The number of protons in an atom is equal to its atomic number, and for a given isotope, the sum of protons and neutrons equals the atomic mass number.

Let's see an example:

• For Plutonium: 94 protons (atomic number) and 145 neutrons since 239 - 94 = 145.
• For Barium: 56 protons (atomic number) and 86 neutrons since 142 - 56 = 86.
• For Potassium-41: 19 protons and 22 neutrons since 41 - 19 = 22.

Understanding the balance between protons and neutrons is important in nuclear chemistry. It can affect the stability of a nucleus and has implications for nuclear reactions and decay.

Isotopes

Isotopes are variants of a particular element that have the same number of protons but different numbers of neutrons. Thus, isotopes have the same atomic number but different atomic mass numbers. This difference causes variations in their physical properties and, in some cases, their stability. Isotopes are commonly designated by the element name followed by their atomic mass number.

For example, Potassium-41 is an isotope of Potassium where the mass number is 41. This isotope form differs from other isotopes of Potassium. Isotopes like Barium-142 and Plutonium-239 serve important roles in various applications, from medicine to energy production. Knowledge of isotopes provides insights into nuclear decay processes and radioactivity, which are important in fields like radiology and nuclear energy.