Problem 43 - Chemistry An Atoms First Approach

Question

How many protons and neutrons are in the nucleus of each of the following atoms? In a neutral atom of each element, how many electrons are present? a. \(^{79} \mathrm{Br}\) d. \(^{133} \mathrm{Cs}\) b. \(^{81} \mathrm{Br}\) e. \(^{3} \mathrm{H}\) c. \(^{239} \mathrm{Pu}\) f. \(^{56} \mathrm{Fe}\)

Step-by-Step Solution

Answer

a. \(^{79} Br\): 35 protons, 44 neutrons, 35 electrons d. \(^{133} Cs\): 55 protons, 78 neutrons, 55 electrons b. \(^{81} Br\): 35 protons, 46 neutrons, 35 electrons e. \(^{3} H\): 1 proton, 2 neutrons, 1 electron c. \(^{239} Pu\): 94 protons, 145 neutrons, 94 electrons f. \(^{56} Fe\): 26 protons, 30 neutrons, 26 electrons

Step 1: Finding the number of Protons

Since Bromine (Br) has an atomic number of 35, it has 35 protons.

Step 2: Finding the number of Neutrons

To find the number of neutrons, subtract the number of protons from the mass number (79): \( 79 - 35 = 44 \) neutrons.

Step 3: Finding the number of Electrons

In a neutral atom of Bromine-79, the number of electrons is equal to the number of protons, which is 35 electrons. d. \( ^{133} Cs \)

Step 4: Finding the number of Protons

Since Cesium (Cs) has an atomic number of 55, it has 55 protons.

Step 5: Finding the number of Neutrons

To find the number of neutrons, subtract the number of protons from the mass number (133): \( 133 - 55 = 78 \) neutrons.

Step 6: Finding the number of Electrons

In a neutral atom of Cesium-133, the number of electrons is equal to the number of protons, which is 55 electrons. b. \( ^{81} Br \)

Step 7: Finding the number of Protons

Since Bromine (Br) has an atomic number of 35, it has 35 protons.

Step 8: Finding the number of Neutrons

To find the number of neutrons, subtract the number of protons from the mass number (81): \( 81 - 35 = 46 \) neutrons.

Step 9: Finding the number of Electrons

In a neutral atom of Bromine-81, the number of electrons is equal to the number of protons, which is 35 electrons. e. \( ^{3} H \)

Step 10: Finding the number of Protons

Since Hydrogen (H) has an atomic number of 1, it has 1 proton.

Step 11: Finding the number of Neutrons

To find the number of neutrons, subtract the number of protons from the mass number (3): \( 3 - 1 = 2 \) neutrons.

Step 12: Finding the number of Electrons

In a neutral atom of Hydrogen-3 (Tritium), the number of electrons is equal to the number of protons, which is 1 electron. c. \( ^{239} Pu \)

Step 13: Finding the number of Protons

Since Plutonium (Pu) has an atomic number of 94, it has 94 protons.

Step 14: Finding the number of Neutrons

To find the number of neutrons, subtract the number of protons from the mass number (239): \( 239 - 94 = 145 \) neutrons.

Step 15: Finding the number of Electrons

In a neutral atom of Plutonium-239, the number of electrons is equal to the number of protons, which is 94 electrons. f. \( ^{56} Fe \)

Step 16: Finding the number of Protons

Since Iron (Fe) has an atomic number of 26, it has 26 protons.

Step 17: Finding the number of Neutrons

To find the number of neutrons, subtract the number of protons from the mass number (56): \( 56 - 26 = 30 \) neutrons.

Step 18: Finding the number of Electrons

In a neutral atom of Iron-56, the number of electrons is equal to the number of protons, which is 26 electrons.

Key Concepts

Protons

Protons are fundamental particles found in the nucleus of an atom. They have a positive electric charge, symbolized as \(+1\). The number of protons in an atomic nucleus directly determines the element to which the atom belongs. This number is invariant for each element and is known as the atomic number.

• Example: All hydrogen atoms have 1 proton; thus, its atomic number is 1.
• Similarly, oxygen atoms always have 8 protons.

The atomic number serves as a unique identifier for elements in the periodic table. Protons, being positively charged, affect the atom's interactions with electrons and other atoms, playing a crucial role in chemical bonding.

Neutrons

Neutrons are neutral particles, meaning they have no electric charge, and they reside within the nucleus alongside protons. Although they don’t alter the charge of an atom, they have a significant effect on the atom's mass and stability. Neutrons shield protons from each other's repulsive forces due to their like-positive charges. One key concept involving neutrons is isotopes. Atoms of the same element (same number of protons) can have different numbers of neutrons, resulting in different isotopes.

• Example: Carbon-12 and Carbon-14 are isotopes of Carbon, having 6 and 8 neutrons respectively.

The number of neutrons can be calculated by subtracting the atomic number from the mass number.

Electrons

Electrons are subatomic particles with a negative charge \(-1\). They orbit the nucleus in electron clouds, often visualized as shells in basic models. In a neutral atom, the number of electrons equals the number of protons, balancing the charges.Electron distribution determines many properties of an atom, including its reactivity and ability to bond with other atoms. Electrons can exist in various energy levels, defined by quantum mechanics. These levels explain the chemical characteristics and the arrangement of the periodic table.

• Low energy levels are filled before higher ones.
• Electron configurations determine element properties like reactivity and state at room temperature.

Mass Number

The mass number of an atom is the sum of the number of protons and neutrons in its nucleus. It is represented as the superscript to the left of an element's symbol, for example, in \(^{79} \mathrm{Br}\) where 79 is the mass number.

• Mass number = Protons + Neutrons

While it gives insight into an atom's mass, it isn't a measure of actual mass but rather a count of nucleons (protons and neutrons). Different isotopes of an element are denoted by varying mass numbers, reflecting differences in neutron count, even when they have the same proton count.

Atomic Number

Atomic number is essentially the fingerprint of elements. It signifies the number of protons in an atom's nucleus and thereby determines the element's identity.

• A hydrogen atom, for example, with its atomic number of 1, signals that it has one proton.
• For oxygen with an atomic number of 8, it contains 8 protons.

This number remains constant for a given element across isotopes and is usually listed above the element symbol in the periodic table. The atomic number is a crucial point of reference for chemical reactions and when balancing nuclear equations.