Question

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

Short answer

Protons: Sm-62, Lu-71, Bi-83, Mo-42, Pb-82, Cs-55; Neutrons: Sm-91, Lu-106, Bi-130, Mo-57, Pb-130, Cs-76.

Step-by-step solution

Understanding Isotopes

Isotopes are variants of a particular chemical element which differ in neutron number, while their proton number remains the same. Each isotope is identified by the element name and a number (e.g., samarium-153), where the number indicates the total number of protons and neutrons, known as the mass number.

Finding Proton Numbers

The number of protons for an element is equal to its atomic number, which can be found on the periodic table. For each isotope: (a) Samarium: Atomic number = 62. (b) Lutetium: Atomic number = 71. (c) Bismuth: Atomic number = 83. (d) Molybdenum: Atomic number = 42. (e) Lead: Atomic number = 82. (f) Caesium: Atomic number = 55.

Calculating Neutron Numbers for Each Isotope

To find the number of neutrons, use the formula: Neutrons = Mass Number - Atomic Number. Compute the number of neutrons for each isotope: (a) Samarium-153: Neutrons = 153 - 62 = 91. (b) Lutetium-177: Neutrons = 177 - 71 = 106. (c) Bismuth-213: Neutrons = 213 - 83 = 130. (d) Molybdenum-99: Neutrons = 99 - 42 = 57. (e) Lead-212: Neutrons = 212 - 82 = 130. (f) Caesium-131: Neutrons = 131 - 55 = 76.

Finalize the Results

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

Key concepts

Protons

Protons are positively charged particles found in the nucleus of an atom. They are incredibly important because they define what element an atom is. The number of protons determines the atomic number of an element, which is unique for each type of atom. For instance:

• Hydrogen has 1 proton.
• Carbon has 6 protons.
• Oxygen has 8 protons.

This means that whenever you look at a periodic table, the number next to an element's symbol is its atomic number, or the number of protons in its nucleus. Without changing the number of protons, you are talking about the same element, even if other aspects like the neutron count might vary, such as in isotopes.
Protons are fundamental to understanding an element's chemical behavior because they influence the atom's electron configuration and, consequently, its chemical properties.

Neutrons

Neutrons are neutral particles, meaning they don't have any charge, and reside in the nucleus along with protons. While neutrons do not affect an atom's chemical properties directly the way protons do, they contribute significantly to the mass of an atom.
Neutrons play a crucial role in stabilizing the nucleus. Without enough neutrons, the electrostatic repulsion between protons could cause the nucleus to become unstable and break apart.
In the context of isotopes:

• Isotopes are atoms of the same element that have different numbers of neutrons.
• This difference in neutron number can affect the stability of the isotope and can lead to different radioactive properties.
  

For instance, while carbon typically has 6 neutrons (resulting in Carbon-12), Carbon-14, with 8 neutrons, is a well-known radioactive isotope. Thus, understanding neutrons and their interaction within the nucleus is key to exploring nuclear reactions and isotopic applications.

Mass Number

The mass number of an isotope is the sum of protons and neutrons in its nucleus. This number is vital because it gives us insight into the isotope's identity and properties. To clarify, mass number can be understood through the following equation:\[\text{Mass Number} = \text{Number of Protons} + \text{Number of Neutrons}\]Each isotope can be represented by its element name followed by the mass number (such as Carbon-14 or Uranium-238). The mass number provides a straightforward way to identify different isotopes of the same element.
For example:

• Carbon-12 and Carbon-14 are both isotopes of carbon because they have 6 protons, but differ in their neutron counts (6 and 8, respectively).
• Uranium-235 and Uranium-238 are isotopes of uranium because they both contain 92 protons, with different numbers of neutrons (143 versus 146 respectively).

The mass number helps scientists distinguish between isotopes and allows them to determine the total mass of an atom in atomic mass units.

Atomic Number

The atomic number is a fundamental property of an element and is equivalent to the number of protons in its nucleus. Every element on the periodic table is ordered by its atomic number, starting with hydrogen, which has an atomic number of 1.
This number is crucial because:

• It uniquely defines each element, with no two elements sharing the same atomic number.
• It determines the identity of the element and its position in the periodic table.
• It influences the element's chemical behavior by dictating its electron configuration.

For instance, nitrogen has an atomic number of 7, meaning every nitrogen atom has 7 protons. This is true for all isotopes of nitrogen; even though they may have differing neutron numbers, the atomic number remains constant. Understanding the atomic number helps in identifying elements and predicting how they might react chemically in various situations.