Problem 27 - Chemistry The Central Science

Question

How many protons, neutrons, and electrons are in the following atoms? (a) \(^{40} \mathrm{Ar},(\mathbf{b})^{65} \mathrm{Zn},(\mathbf{c})^{70} \mathrm{Ga},(\mathbf{d})^{80} \mathrm{Br},(\mathbf{e})^{184} \mathrm{W}\) \((\mathbf{f})^{243} \mathrm{Am} .\)

Step-by-Step Solution

Answer

(a) \(^{40}Ar\): 18 protons, 22 neutrons, 18 electrons; (b) \(^{65}Zn\): 30 protons, 35 neutrons, 30 electrons; (c) \(^{70}Ga\): 31 protons, 39 neutrons, 31 electrons; (d) \(^{80}Br\): 35 protons, 45 neutrons, 35 electrons; (e) \(^{184}W\): 74 protons, 110 neutrons, 74 electrons; (f) \(^{243}Am\): 95 protons, 148 neutrons, 95 electrons.

Step 1: Identifying Atomic Numbers and Mass Numbers

The given isotopes are expressed by the element symbols and mass numbers. \(^{A}X\), where A is the mass number and X is the element symbol. We can find the atomic number, Z, by looking at the periodic table.

Step 2: (a) \(^{40}Ar\)

For Argon (Ar), the atomic number is Z = 18. We are given the mass number A = 40. Use the following relationships to determine the number of protons, neutrons, and electrons. Protons: Z = 18 Neutrons: A - Z = 40 - 18 = 22 Electrons: Z = 18 (neutral atom)

Step 3: (b) \(^{65}Zn\)

For Zinc (Zn), the atomic number is Z = 30. We are given the mass number A = 65. Apply the same relationships as in (a) to determine the number of protons, neutrons, and electrons. Protons: Z = 30 Neutrons: A - Z = 65 - 30 = 35 Electrons: Z = 30 (neutral atom)

Step 4: (c) \(^{70}Ga\)

For Gallium (Ga), the atomic number is Z = 31. We are given the mass number A = 70. Apply the same relationships as in (a) and (b) to find the number of protons, neutrons, and electrons. Protons: Z = 31 Neutrons: A - Z = 70 - 31 = 39 Electrons: Z = 31 (neutral atom)

Step 5: (d) \(^{80}Br\)

For Bromine (Br), the atomic number is Z = 35. We are given the mass number A = 80. Apply the relationships again to find the number of protons, neutrons, and electrons. Protons: Z = 35 Neutrons: A - Z = 80 - 35 = 45 Electrons: Z = 35 (neutral atom)

Step 6: (e) \(^{184}W\)

For Tungsten (W), the atomic number is Z = 74. We are given the mass number A = 184. Apply the relationships again to find the number of protons, neutrons, and electrons. Protons: Z = 74 Neutrons: A - Z = 184 - 74 = 110 Electrons: Z = 74 (neutral atom)

Step 7: (f) \(^{243}Am\)

For Americium (Am), the atomic number is Z = 95. We are given the mass number A = 243. Apply the relationships again to find the number of protons, neutrons, and electrons. Protons: Z = 95 Neutrons: A - Z = 243 - 95 = 148 Electrons: Z = 95 (neutral atom)

Key Concepts

Isotopes

Isotopes are different forms of the same element that have the same number of protons but different numbers of neutrons in their nuclei. This difference in neutron count means isotopes have different mass numbers. For instance, while all atoms of argon have 18 protons, the isotope \( ^{40}\mathrm{Ar} \) has 22 neutrons, while another isotope may have a different count of neutrons.

• Protons define the element's identity; thus, all isotopes of a single element still retain the same chemical behavior.
• Mass number is the total count of protons and neutrons in an atom's nucleus.
• Most naturally occurring elements have more than one stable isotope.

This concept is critical in fields like chemistry and physics because it helps explain the variations seen in atomic mass and the stability of elements.

Neutron Calculation

Calculating the number of neutrons in an atom involves subtracting the atomic number from the mass number. This is because the mass number is the sum of protons and neutrons in an atom:

• The atomic number (Z) represents the number of protons and is unique to each element.
• The mass number (A) is the total number of protons and neutrons in an atom.
• To find the number of neutrons: \( \text{Neutrons} = A - Z \).

For example, in the isotope \( ^{65}\mathrm{Zn} \), where \( A = 65 \) and \( Z = 30 \), the number of neutrons would be \( 65 - 30 = 35 \). This formula is handy for determining the neutron count whenever given an isotope's notation.

Electron Configuration

Electron configuration refers to the distribution of electrons in an atom's orbitals. Electrons are subatomic particles carrying a negative charge, and they occupy specific energy levels around the nucleus:

• The atomic number also indicates the number of electrons in a neutral atom.
• Electrons fill orbitals in order of increasing energy, starting from the lowest energy level.
• Common electron configuration notations involve writing out the occupied energy levels and orbitals.

In a neutral atom, the number of electrons equals the number of protons. For example, \(^{80}\mathrm{Br} \) has 35 electrons, reflecting its atomic number of 35. Understanding electron configurations is crucial for predicting element behavior and bonding in chemical reactions.