Problem 23 - Chemistry: The Central Science

Question

Which of the following pairs of atoms are isotopes of one another? \((\) a \(){ }^{11} \mathrm{~B},{ }^{11} \mathrm{C}\); (b) \({ }^{55} \mathrm{Mn},{ }^{54} \mathrm{Mn} ;(\mathbf{c}){ }_{50}^{118} \mathrm{Sn},{ }_{50}^{120} \mathrm{Sn}\)

Step-by-Step Solution

Answer

The pairs (b) \({ }^{55}\mathrm{Mn},{ }^{54}\mathrm{Mn}\) and (c) \({}_{50}^{118} \mathrm{Sn},{ }_{50}^{120}\mathrm{Sn}\) are isotopes of each other, while pair (a) \({}^{11} \mathrm{B},{ }^{11} \mathrm{C}\) is not.

Step 1: Identify atomic numbers and mass numbers in given pairs

For each pair of atoms, identify the atomic number (Z) and mass number (A) of each atom. The atomic number is the number of protons, while the mass number is the sum of protons and neutrons. (a) \({}^{11} \mathrm{B},{ }^{11} \mathrm{C}\) Boron (B) has an atomic number of 5, and Carbon (C) has an atomic number of 6. The mass number (A) for both is 11. (b) \({ }^{55}\mathrm{Mn},{ }^{54}\mathrm{Mn}\) Manganese (Mn) has an atomic number of 25. The mass number (A) for the first atom is 55 and for the second atom is 54. (c) \({}_{50}^{118} \mathrm{Sn},{ }_{50}^{120}\mathrm{Sn}\) Tin (Sn) has an atomic number of 50. The mass number (A) for the first atom is 118 and for the second atom is 120.

Step 2: Determine if the pairs are isotopes

To determine if the pairs are isotopes, check whether they have the same atomic number (Z) but different mass numbers (A). (a) \({}^{11} \mathrm{B},{ }^{11} \mathrm{C}\) The atomic numbers are different (Boron: Z = 5 and Carbon: Z = 6) These atoms are not isotopes. (b) \({ }^{55}\mathrm{Mn},{ }^{54}\mathrm{Mn}\) The atomic numbers are the same (Manganese: Z = 25) and the mass numbers are different (A = 55 and A = 54) These atoms are isotopes. (c) \({}_{50}^{118} \mathrm{Sn},{ }_{50}^{120}\mathrm{Sn}\) The atomic numbers are the same (Tin: Z = 50) and the mass numbers are different (A = 118 and A = 120) These atoms are isotopes.

Step 3: Conclusion

Out of the three given pairs of atoms, the pairs (b) and (c) are isotopes of each other, while pair (a) is not.

Key Concepts

Atomic Number

The atomic number, designated as Z, is one of the most fundamental properties of an element. It defines the identity of the element by denoting the number of protons present in the nucleus of an atom. Why is this important? Because the number of protons determines the chemical behavior of an atom. For example, all carbon atoms have 6 protons, while all boron atoms contain 5 protons.

When solving textbook problems, or simply trying to grasp atomic concepts, knowing the atomic number is crucial. It’s the atomic number that tells us whether two atoms are of the same element or different ones. That being said, the atomic number holds the key to understanding isotopes as well. Isotopes are atoms of the same element that contain the same number of protons but a different number of neutrons, leading to various mass numbers. Thus, when we say that atoms with different atomic numbers can never be isotopes, we’re recognizing the vital role the atomic number plays in the periodic table and in chemistry as a whole.

Mass Number

Moving beyond the atomic number, we have the mass number, symbolized as A. This is the sum of the protons and neutrons in an atom’s nucleus. Unlike the unchanging atomic number, the mass number can vary even within atoms of the same element due to the presence of different numbers of neutrons, thereby creating isotopes.

Why is the mass number significant? For one, it helps us calculate the number of neutrons by subtracting the atomic number from the mass number (=). This distinction between isotopes is pivotal in both natural processes, such as radioactivity, and practical applications like medical imaging and radiocarbon dating. Always remember that isotopes of an element will have the same Z but different A values. It’s this difference in the mass number that allows us to identify isotopes and understand their unique properties. In teaching, we emphasize clear identification of mass numbers in exercises because they can get mixed up with the atomic number, leading to confusion in determining isotopes.

Element Symbols

Finally, we have the element symbols, which are shorthand notations representing chemical elements. These symbols consist of one or two letters, with the first letter always capitalized and the second, if present, in lower case. The significance of element symbols cannot be overstated; they are like an international language for scientists, allowing for clear and concise communication of chemical compounds and reactions.

When examining isotopes, element symbols come with specific numbers denoting the atomic number and mass number, such as for an isotope of carbon with six protons and seven neutrons. Understanding element symbols is key to interpreting and solving chemical problems. It’s these symbols, together with their accompanying numbers, that help students accurately determine what element an atom is and whether two atoms could be isotopes of each other. Improving comprehension of these symbols is a goal of education, as they are the building blocks for reading and writing in chemistry.