Question

Determine the number of protons and neutrons in each isotope. (a) \({ }_{11}^{23} \mathrm{Na}\) (b) \({ }_{88}^{266} \mathrm{Ra}\) (c) \({ }_{32}^{208} \mathrm{~Pb}\) (d) \({ }_{7}^{14} \mathrm{~N}\)

Short answer

The number of protons/neutrons for each isotope: (a) 11/12, (b) 88/178, (c) 82/126 (after correcting atomic number), (d) 7/7.

Step-by-step solution

Understanding Isotope Notation

Isotopes are represented by the notation \( {}_{Z}^{A}X \), where \( Z \) is the atomic number (number of protons), \( A \) is the mass number (number of protons and neutrons), and \( X \) is the chemical symbol for the element. To find the number of protons and neutrons, use the atomic number and the mass number.

Solving for Sodium-23

For the isotope \( {}_{11}^{23}Na \), the atomic number \( Z = 11 \), indicating there are 11 protons. The mass number \( A = 23 \), so the number of neutrons is the mass number minus the atomic number: \( 23 - 11 = 12 \) neutrons.

Solving for Radium-266

For the isotope \( {}_{88}^{266}Ra \), the atomic number \( Z = 88 \), indicating there are 88 protons. The mass number \( A = 266 \), so the number of neutrons is: \( 266 - 88 = 178 \) neutrons.

Solving for Lead-208

For the isotope \( {}_{32}^{208}Pb \), the atomic number \( Z = 82 \), since \( Pb \) (Lead) has an atomic number of 82 and not 32 which is a typo. There are 82 protons. The mass number \( A = 208 \), so the number of neutrons is: \( 208 - 82 = 126 \) neutrons.

Solving for Nitrogen-14

For the isotope \( {}_{7}^{14}N \), the atomic number \( Z = 7 \), indicating there are 7 protons. The mass number \( A = 14 \), so the number of neutrons is: \( 14 - 7 = 7 \) neutrons.

Key concepts

Atomic Number

Understanding the atomic number is crucial for studying elements and their isotopes. The atomic number, symbolized by the letter 'Z', refers to the total number of protons found in the nucleus of an atom. Protons are positively charged particles, and because they are unique to each element, the atomic number defines the type of element you're dealing with. For example, all atoms with 6 protons in their nuclei are carbon atoms, regardless of how many neutrons they might have.

Every element on the periodic table is organized by its atomic number, starting from hydrogen with an atomic number of 1 and increasing sequentially. The atomic number is not just a label; it dictates the chemical behavior of the element, as the number of protons determines the electric charge of the nucleus which, in turn, affects how the element will interact with other atoms.

Mass Number

The mass number, designated by the symbol 'A', is equally significant when examining isotopes. It represents the total count of protons and neutrons present in an atom's nucleus. Since protons and neutrons have approximately the same mass, with electrons being significantly lighter, the mass number essentially reflects the atom's mass. It is important to realize that the mass number is always a whole number as it counts particles, unlike atomic mass which can be a decimal as it reflects average weights.

Isotopes of an element have the same atomic number but differ in their mass numbers because they contain different numbers of neutrons. Knowing the mass number allows us to calculate the number of neutrons by subtracting the atomic number from the mass number. This distinction is vital in many scientific areas, such as chemistry, nuclear physics, and radiology.

Protons and Neutrons

Delving deeper into the subatomic world, protons and neutrons form the core of an atom, residing in the nucleus. Protons are carriers of a positive charge, while neutrons are neutral—hence their name. These particles together are sometimes referred to as nucleons.

The number of protons in the nucleus, as we've mentioned, defines an element's identity. Neutrons, on the other hand, have a unique role in stabilizing the nucleus. They allow protons to coexist closely within the small confines of the nucleus without repelling each other away due to their like charges. The number of protons and neutrons can vary in different isotopes of the same element, causing variations in mass and stability but not altering the chemical nature of the element. Understanding the balance between protons and neutrons is essential for studying atomic structure and the properties of various isotopes.

Chemical Symbols

Chemical symbols are abbreviated notations representing chemical elements. Each symbol usually consists of one or two letters derived from the element's name in English or Latin. For instance, 'H' stands for hydrogen, 'O' for oxygen, 'Fe' is the symbol for iron (from Latin 'ferrum'), and 'Au' represents gold (from Latin 'aurum').

Chemical symbols are universally accepted and provide a concise way for scientists around the world to communicate complex chemical formulas without language barriers. These symbols are found on the periodic table, where each corresponds with an element's atomic number, its usual mass number, and its standardized name. Alongside these, chemical symbols are used in the isotope notation to quickly identify the element being referred to, without which the remaining notation could not be accurately interpreted.