Problem 9 - Chemistry The Central Science In Si Units

Question

Indicate the number of protons and neutrons in the following nuclei: \((\mathbf{a}){ }_{94}^{239} \mathrm{Pu},(\mathbf{b}){ }^{142} \mathrm{Ba},(\mathbf{c})\) potassium- 41 .

Step-by-Step Solution

Answer

Pu-239: 94 protons, 145 neutrons; Ba-142: 56 protons, 86 neutrons; K-41: 19 protons, 22 neutrons.

Step 1: Understanding Atomic Number and Mass Number

To determine the number of protons and neutrons in an atomic nucleus, you need to understand two key concepts: the atomic number and the mass number. The atomic number (denoted as the subscript, e.g., \(_{94}\)) represents the number of protons. The mass number (denoted as the superscript, e.g., \(^{239}\)) represents the total number of protons and neutrons in the nucleus.

Step 2: Identify Components of Each Nucleus

For each nucleus given in the exercise, first extract the atomic number and the mass number, which will help us determine the number of protons and neutrons.

Step 1: Counting Protons in Pu-239

For \(_{94}^{239} \mathrm{Pu}\), the atomic number is 94, indicating there are 94 protons. This is common to all isotopes of plutonium.

Step 2: Counting Neutrons in Pu-239

The mass number for \(_{94}^{239} \mathrm{Pu}\) is 239. The number of neutrons is therefore calculated by subtracting the number of protons: \[ 239 - 94 = 145 \]Thus, there are 145 neutrons in this isotope of plutonium.

Step 3: Counting Protons in Ba-142

For \(^142\mathrm{Ba}\), the atomic number is not given, but barium (Ba) can be found on the periodic table with an atomic number of 56. Therefore, it has 56 protons.

Step 4: Counting Neutrons in Ba-142

The mass number for \(^142\mathrm{Ba}\) is 142. The number of neutrons is calculated by subtracting the number of protons: \[ 142 - 56 = 86 \] Hence, there are 86 neutrons in this isotope of barium.

Step 5: Counting Protons in Potassium-41

Potassium (K) has an atomic number of 19, which indicates it has 19 protons in all isotopes including potassium-41.

Step 6: Counting Neutrons in Potassium-41

For potassium-41, the mass number is 41. The number of neutrons is calculated as follows: \[ 41 - 19 = 22 \] So, there are 22 neutrons in this isotope of potassium.

Key Concepts

Atomic Number

The atomic number is a fundamental concept in chemistry and physics, giving each element its unique identity. This number tells us how many protons are in the nucleus of an atom. Protons carry a positive charge and are located in the atom’s nucleus.
Because protons define the element, the atomic number is unique for each element. For example, Potassium has an atomic number of 19, which means every atom of Potassium has 19 protons. No other element has this atomic number.

• If you know the atomic number, you can immediately know what element you are dealing with, as the periodic table is organized by increasing atomic number.
• A change in the number of protons transforms the atom into a different element altogether.

The atomic number is often represented as a subscript in atomic notation, for instance, does not appear in front and deserves a distinct position. Understanding it is crucial for identifying elements and their chemical behavior.

Mass Number

Mass number is another essential concept, revealing the total count of protons and neutrons in an atom's nucleus. Unlike the atomic number, the mass number is not fixed for an element but rather varies among isotopes.
Isotopes are versions of the same element that have different numbers of neutrons, hence different mass numbers. For example, has several isotopes, such as Potassium-39, Potassium-40, and Potassium-41.

• The mass number is a whole number and is typically displayed as a superscript when writing atomic symbols.
• To find the mass number, just add up the numbers of protons and neutrons.

This number is crucial when you're trying to determine the isotope of a given element. It helps in identifying the exact isotope and understanding its nuclear composition.

Neutrons

Neutrons are neutral particles found in the nucleus of an atom, and they play a significant role in stabilizing the nucleus.
Unlike protons, neutrons do not carry a charge, meaning they do not affect the electrical charge of the atom but greatly influence the atom's mass. Neutrons, together with protons, account for almost the entirety of an atom’s mass.

• To find the number of neutrons in an isotope, you subtract the atomic number from the mass number.
• Neutrons allow for the existence of isotopes; atoms with the same number of protons but different numbers of neutrons.
• They also contribute to the different physical properties of an element's isotopes.

Understanding the concept of neutrons is vital for studying isotopes, nuclear reactions, and the stability of different atoms.