Atoms and Molecules: Isotopes, Isobars & Isotones

Isobars are defined as nuclides that have the same mass number, which is the total number of protons and neutrons in the nucleus, but differ in their atomic numbers, meaning they have different numbers of protons. This results in isobars being different elements. For example, carbon-14 and nitrogen-14 are isobars; both have a mass number of 14 but different atomic numbers (6 for carbon and 7 for nitrogen).

To calculate the average atomic mass of magnesium, we use the formula that takes into account the mass and abundance of each isotope. This involves multiplying the mass of each isotope by its relative abundance (expressed as a fraction) and summing these products. For magnesium, the contributions are: (23.985 amu * 0.7899) + (24.986 amu * 0.10) + (25.983 amu * 0.1101). The total yields an average atomic mass of approximately 24.305 amu, which reflects the weighted average of its isotopes based on their natural abundances.

Isobars are atoms of different elements that have the same mass number but different atomic numbers. This means they contain the same total number of nucleons (protons and neutrons) but differ in the number of protons, which defines the element. Therefore, isobars cannot have the same number of protons, as that would imply they are the same element.

Isotopes are variants of the same chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. In this case, ¹²C (carbon-12) and ¹⁴C (carbon-14) are both isotopes of carbon, as they share the same atomic number (6 protons) but differ in their neutron count (6 and 8 neutrons, respectively). The other pairs listed do not share the same element, which is why they are not considered isotopes.

To determine the number of neutrons in a radioisotope, subtract the number of protons from the mass number. Here, the mass number is 81 and the element has 36 protons, indicating it is Krypton (Kr). Therefore, the number of neutrons is 81 - 36 = 45. This confirms that the isotope in question is Krypton with 45 neutrons.

To calculate the average atomic mass of silver, we use the abundances and masses of its isotopes. The average atomic mass is determined by multiplying the mass of each isotope by its relative abundance (expressed as a fraction), then summing these products. For silver, this is calculated as follows: (106.905 amu × 0.51839) + (108.905 amu × 0.48161) = 107.868 amu. This value reflects the weighted average based on the isotopic distribution in nature.

³²S and ³²P are isobars because they both have the same mass number of 32, indicating that they contain the same total number of protons and neutrons. However, they differ in the number of protons; sulfur (S) has 16 protons, while phosphorus (P) has 15. This distinction in proton number classifies them as different elements, but their equal mass number qualifies them as isobars, which are nucleides that share the same mass number but differ in atomic number.

Isotones are nuclides that have the same number of neutrons but different numbers of protons. Since the number of protons determines the element, this means that isotones must belong to different elements. For example, carbon-14 and nitrogen-15 are isotones; both have 8 neutrons but differ in their proton count, confirming they are distinct elements. Thus, the statement is true.

To determine the number of neutrons in the isotope ¹³¹I, we subtract the atomic number of iodine, which is 53, from its mass number, 131. The mass number represents the total number of protons and neutrons in the nucleus. Therefore, the calculation is 131 (mass number) - 53 (atomic number) = 78 neutrons. This indicates that ¹³¹I has 78 neutrons, which is essential for understanding its stability and behavior in medical applications like thyroid cancer treatment.

To find the average atomic mass of element X, we multiply the mass of each isotope by its relative abundance (expressed as a fraction) and then sum these values. For isotope 1, we calculate \(27.977 \times 0.9223\); for isotope 2, \(28.976 \times 0.0467\); and for isotope 3, \(29.974 \times 0.0310\). Adding these products gives us the weighted average, which results in approximately 28.086 amu. This value reflects the average mass of the element considering the distribution of its isotopes.

To calculate the average atomic mass of an element with two isotopes, you multiply the mass of each isotope by its relative abundance (expressed as a decimal) and then sum these values. For Isotope A: 10.013 amu * 0.199 = 1.988587 amu. For Isotope B: 11.009 amu * 0.801 = 8.825209 amu. Adding these values together gives 1.988587 amu + 8.825209 amu = 10.813796 amu, which rounds to 10.811 amu. This value reflects the weighted average based on the isotopes' abundances.

Technetium-99m (⁹⁹ᵐTc) has a mass number of 99, which represents the total number of protons and neutrons in its nucleus. The "m" indicates that it is a metastable state of Technetium-99, meaning it is in an excited state and can emit gamma radiation. In isotopes, the mass number is crucial for identifying the specific isotope and its properties, making 99 the defining characteristic of Technetium-99m.

To calculate the average atomic mass of copper, we use the formula that accounts for both the mass and abundance of each isotope. Multiply the mass of each isotope by its relative abundance (expressed as a decimal), then sum these values. For Cu-63: 62.930 amu × 0.6917 = 43.525 amu, and for Cu-65: 64.928 amu × 0.3083 = 20.045 amu. Adding these results gives 63.570 amu, which rounds to 63.546 amu, reflecting the weighted average based on the isotopes' natural abundances.

To determine the number of neutrons in the isotope ²³⁵U, we subtract the atomic number of uranium (92) from its mass number (235). The atomic number represents the number of protons, and for uranium, it is 92. Therefore, the calculation is 235 (mass number) - 92 (atomic number) = 143 neutrons. This value indicates the stability and properties of the isotope, which is significant in nuclear applications.

Isotones are nuclei that have the same number of neutrons but different numbers of protons. In the case of ¹⁴C (Carbon-14) and ¹⁵N (Nitrogen-15), both isotopes have 8 neutrons, despite having different atomic numbers (6 for Carbon and 7 for Nitrogen). This characteristic distinguishes them as isotones. The other options either have the same number of protons or differ in neutron count, thus not fitting the definition of isotones.

Isotones are defined as nuclides that have the same number of neutrons but differ in the number of protons. This characteristic results in different chemical properties, as the number of protons determines the element's identity. However, the shared neutron count influences the stability and nuclear properties of the isotones. Understanding isotones is essential in nuclear physics and chemistry, as it helps in studying nuclear reactions and the behavior of elements in various isotopic forms.

Isobars are nuclides that have the same mass number but different atomic numbers, meaning they contain the same total number of nucleons (protons and neutrons) but differ in their elemental identity. In the given options, both ⁴⁰Ca (calcium) and ⁴⁰Ar (argon) share a mass number of 40, as do ¹⁴C (carbon) and ¹⁴N (nitrogen), making both pairs isobars. The other options, ¹H (hydrogen) and ²H (deuterium), are isotopes rather than isobars, as they differ in mass number. Thus, both A and B qualify as isobaric pairs.

The mass number of an isotope is calculated by adding the number of protons and neutrons together. In this case, the isotope has 15 protons and 16 neutrons. Therefore, the mass number is 15 (protons) + 16 (neutrons) = 31. This value represents the total number of nucleons in the nucleus of the isotope, which is why the mass number is 31.

In the isotope ⁵⁶Fe³⁺, the atomic number of iron (Fe) is 26, indicating it has 26 protons. The mass number is 56, which is the sum of protons and neutrons, leading to 30 neutrons (56 - 26 = 30). The ³⁺ charge indicates it has lost three electrons, resulting in 23 electrons (26 - 3 = 23). Thus, the isotope has 26 protons, 30 neutrons, and 23 electrons.

To find the percent abundance of Cl-35, we use the formula for average atomic mass, which is a weighted average of the isotopes. Let x be the fraction of Cl-35 and (1-x) be the fraction of Cl-37. The equation is:

\[ 34.969x + 36.966(1-x) = 35.453 \]

Solving this gives x ≈ 0.7577, or 75.77%. This indicates that approximately 75.77% of naturally occurring chlorine is Cl-35, while the remainder is Cl-37.