Problem 22 - Chemistry: An Atoms-Focused Approach

Question

Which isotope in each of the following pairs has more protons and which has more neutrons? (a) \(^{92}\) Mo or \(^{92} \mathrm{Zr}\) (b) \(^{28} \mathrm{Si}\) or \(^{28} \mathrm{Ar} ;\) (c) \(^{111}\) In or \(^{114} \mathrm{In}\).

Step-by-Step Solution

Answer

Question: For each pair of isotopes, determine which isotope has more protons and which has more neutrons: (a) \(^{92} \mathrm{Mo}\) and \(^{92} \mathrm{Zr}\), (b) \(^{28} \mathrm{Si}\) and \(^{28} \mathrm{Ar}\), (c) \(^{111} \mathrm{In}\) and \(^{114} \mathrm{In}\). Answer: (a) \(^{92} \mathrm{Mo}\) has more protons, and \(^{92} \mathrm{Zr}\) has more neutrons. (b) \(^{28} \mathrm{Ar}\) has more protons, and \(^{28} \mathrm{Si}\) has more neutrons. (c) Both isotopes have the same number of protons, but \(^{114} \mathrm{In}\) has more neutrons.

Step 1: Find the atomic numbers of the elements.

To find the atomic numbers (number of protons), search for the elements in the periodic table: Mo (Molybdenum), Zr (Zirconium), Si (Silicon), Ar (Argon), In (Indium). Write down the atomic numbers for each element.

Step 2: Calculate the number of neutrons for each isotope.

To calculate the number of neutrons for each isotope, subtract the atomic number (number of protons) from the mass number (given as the superscript).

Step 3: Compare the number of protons and neutrons for each pair.

After calculating the number of protons and neutrons for each isotope, compare them within each pair to determine which has more protons and which has more neutrons. Let's apply these steps to each pair of isotopes: (a) \(^{92} \mathrm{Mo}\) and \(^{92} \mathrm{Zr}\):

Step 1:

Mo's atomic number is 42, and Zr's atomic number is 40.

Step 2:

For \(^{92} \mathrm{Mo}\): 92 (mass number) - 42 (atomic number) = 50 neutrons. For \(^{92} \mathrm{Zr}\): 92 - 40 = 52 neutrons.

Step 3:

\(^{92} \mathrm{Mo}\) has more protons (42) than \(^{92} \mathrm{Zr}\) (40). \(^{92} \mathrm{Zr}\) has more neutrons (52) than \(^{92} \mathrm{Mo}\) (50). (b) \(^{28} \mathrm{Si}\) and \(^{28} \mathrm{Ar}\):

Step 1:

Si's atomic number is 14, and Ar's atomic number is 18.

Step 2:

For \(^{28} \mathrm{Si}\): 28 - 14 = 14 neutrons. For \(^{28} \mathrm{Ar}\): 28 - 18 = 10 neutrons.

Step 3:

\(^{28} \mathrm{Ar}\) has more protons (18) than \(^{28} \mathrm{Si}\) (14). \(^{28} \mathrm{Si}\) has more neutrons (14) than \(^{28} \mathrm{Ar}\) (10). (c) \(^{111} \mathrm{In}\) and \(^{114} \mathrm{In}\):

Step 1:

In's atomic number is 49.

Step 2:

For \(^{111} \mathrm{In}\): 111 - 49 = 62 neutrons. For \(^{114} \mathrm{In}\): 114 - 49 = 65 neutrons.

Step 3:

Both \(^{111} \mathrm{In}\) and \(^{114} \mathrm{In}\) have the same number of protons (49) since they are isotopes of the same element. However, \(^{114} \mathrm{In}\) has more neutrons (65) than \(^{111} \mathrm{In}\) (62). The final answer is: (a) \(^{92} \mathrm{Mo}\) has more protons, and \(^{92} \mathrm{Zr}\) has more neutrons. (b) \(^{28} \mathrm{Ar}\) has more protons, and \(^{28} \mathrm{Si}\) has more neutrons. (c) Both isotopes have the same number of protons, but \(^{114} \mathrm{In}\) has more neutrons.

Key Concepts

Protons

Protons are positively charged particles found in the nucleus of an atom. They play a crucial role in defining the identity of an element. The number of protons in an atom is called the atomic number. This atomic number is unique for each element and determines its position on the periodic table.

• Molybdenum (Mo) has an atomic number of 42, meaning it has 42 protons.
• Zirconium (Zr) has 40 protons.
• Silicon (Si) contains 14 protons.
• Argon (Ar) has 18 protons.
• Indium (In), regardless of the isotope, always has 49 protons.

The presence of protons not only defines the element but also contributes to the mass of the atom along with neutrons.

Neutrons

Neutrons are subatomic particles found in the nucleus alongside protons. Unlike protons, neutrons carry no charge; they are neutral. The number of neutrons can vary in the atoms of a single element, leading to the formation of isotopes. To determine the number of neutrons in an isotope, subtract the atomic number from the mass number:

• For an isotope like \( ^{92} \text{Mo} \), the calculation would be 92 (mass number) - 42 (atomic number) = 50 neutrons.
• For \( ^{92} \text{Zr} \), it is 92 - 40 = 52 neutrons.

Having different numbers of neutrons affects the mass and stability of the isotope but does not alter the chemical identity of the element.

Atomic Number

The atomic number is a fundamental characteristic of an element, representing the total number of protons in the nucleus of its atoms. This number is critical because it unambiguously identifies the chemical element. The periodic table is arranged by increasing atomic numbers.
Atomic numbers help in understanding the properties and behavior of atoms:

• Molybdenum's atomic number is 42, which places it in the transition metals category.
• Argon, with an atomic number of 18, is a noble gas, indicating it is inert.
• Silicon, with its atomic number of 14, is a well-known semiconductor.

Knowing the atomic number allows chemists to predict how atoms will interact in chemical reactions.

Mass Number

Mass number is the total count of protons and neutrons in an atom's nucleus. It is not found on the periodic table, as it can vary for isotopes of a given element. The mass number is often provided as a superscript to the left of an element's symbol.
When comparing isotopes, the difference in their mass numbers typically arises from varying numbers of neutrons, since the number of protons remains constant for isotopes of the same element.

• For example, \( ^{111} \text{In} \) and \( ^{114} \text{In} \) are isotopes of Indium, with different mass numbers due to a difference in the number of neutrons.
• The higher mass number generally indicates more neutrons.

Understanding mass number helps in calculating an isotope's atomic mass, which is crucial for dealing with atomic weights in chemical equations.