Problem 28 - Chemistry: The Central Science in SI Units, Global Edition

Question

Each of the following isotopes is used in medicine. Indicate the number of protons and neutrons in each isotope: (a) samarium-153, (b) lutetium-177, (c) bismuth-213, (d) molybdenum-99, (e) lead-212, (f) caesium-131.

Step-by-Step Solution

Answer

The number of protons and neutrons for each isotope are: (a) Samarium-153: 62 protons and 91 neutrons (b) Lutetium-177: 71 protons and 106 neutrons (c) Bismuth-213: 83 protons and 130 neutrons (d) Molybdenum-99: 42 protons and 57 neutrons (e) Lead-212: 82 protons and 130 neutrons (f) Caesium-131: 55 protons and 76 neutrons

Step 1: Find the atomic number of each element

To find the atomic number (number of protons) of each element, refer to the periodic table. Atomic numbers are as follows: - Samarium (Sm): 62 - Lutetium (Lu): 71 - Bismuth (Bi): 83 - Molybdenum (Mo): 42 - Lead (Pb): 82 - Caesium (Cs): 55

Step 2: Calculate the number of neutrons for each isotope

To find the number of neutrons in each isotope, subtract the atomic number (number of protons) from the mass number of each isotope. (a) Samarium-153 Neutrons = mass number - atomic number Neutrons = 153 - 62 Neutrons = 91 (b) Lutetium-177 Neutrons = mass number - atomic number Neutrons = 177 - 71 Neutrons = 106 (c) Bismuth-213 Neutrons = mass number - atomic number Neutrons = 213 - 83 Neutrons = 130 (d) Molybdenum-99 Neutrons = mass number - atomic number Neutrons = 99 - 42 Neutrons = 57 (e) Lead-212 Neutrons = mass number - atomic number Neutrons = 212 - 82 Neutrons = 130 (f) Caesium-131 Neutrons = mass number - atomic number Neutrons = 131 - 55 Neutrons = 76 So, the number of protons and neutrons for each isotope are: (a) Samarium-153: 62 protons and 91 neutrons (b) Lutetium-177: 71 protons and 106 neutrons (c) Bismuth-213: 83 protons and 130 neutrons (d) Molybdenum-99: 42 protons and 57 neutrons (e) Lead-212: 82 protons and 130 neutrons (f) Caesium-131: 55 protons and 76 neutrons

Key Concepts

Atomic Number

The atomic number is a fundamental characteristic of an element. You can think of it as the element's fingerprint. It's the number of protons found in the nucleus of an atom of that element. Each element on the periodic table is unique because of its atomic number. For example, hydrogen, with an atomic number of 1, has one proton. The importance of the atomic number cannot be overstated. It determines the element's identity and that of its isotopes. When we talk about isotopes, we refer to atoms that have the same number of protons (and hence the same atomic number) but different numbers of neutrons. Therefore, knowing the atomic number helps in distinguishing one element from another and identifying isotopes of the same element.

Mass Number

The mass number of an atom is a simple but crucial concept. It is defined as the sum of protons and neutrons in an atom's nucleus. This value is not the same as the atomic mass, which is a weighted average of all isotopes' masses. When we refer to isotopes by their mass number—like carbon-14 or hydrogen-1—we use this number to distinguish between different isotopes of the same element. The mass number is what you subtract from the atomic number to find the number of neutrons in an isotope. Let's take bismuth-213 as an example. The number 213 indicates the mass number, which means the total of protons and neutrons is 213. With an atomic number of 83 (from the periodic table), we can easily calculate the number of neutrons.

Neutrons Calculation

Calculating the number of neutrons in an isotope is straightforward once you know both the atomic number and the mass number. The formula to use is:\[\text{Neutrons} = \text{Mass Number} - \text{Atomic Number}\]By applying this formula, you can determine the neutron count for any isotope. Consider samarium-153: It has a mass number of 153 and an atomic number of 62. Thus, the number of neutrons is calculated as:\[153 - 62 = 91 \]This calculation helps in understanding isotopes better since isotopes of a given element will have varying numbers of neutrons, affecting their nuclear properties and applications, particularly in medicine.

Periodic Table Elements

The periodic table is a map for understanding chemical elements and their properties. It organizes all known elements by increasing atomic number—arranging elements that show similar properties into columns known as groups. Each element's square on the table provides a wealth of information, from its chemical symbol to the atomic number. This arrangement helps chemists and scientists predict behaviors of elements and compounds. The periodic table is a useful tool for finding the atomic number of any element. For instance, if you need to know the atomic number for molybdenum, a quick look at the table tells you it's 42. Understanding how to use the periodic table is crucial in solving problems related to isotopes, as it assists you in knowing the atomic numbers imperative for neutron calculations and identifying isotopes employed in various fields, such as medicine.