Question

Write the atomic symbol \(\left(\begin{array}{l}\mathrm{A} \\\ \mathrm{Z}\end{array} \mathrm{X}\right)\) for each of the isotopes described below. a. \(Z=6,\) number of neutrons \(=7\) b. the isotope of carbon with a mass number of 13 c. \(Z=6, A=13\) d. \(Z=19, A=44\) e. the isotope of calcium with a mass number of 41 f. the isotope with 19 protons and 16 neutrons

Short answer

a. \(\left(\begin{array}{l}13 \\ 6\end{array} \mathrm{C}\right)\) b. \(\left(\begin{array}{l}13 \\ 6\end{array} \mathrm{C}\right)\) c. \(\left(\begin{array}{l}13 \\ 6\end{array} \mathrm{C}\right)\) d. \(\left(\begin{array}{l}44 \\ 19\end{array} \mathrm{K}\right)\) e. \(\left(\begin{array}{l}41 \\ 20\end{array} \mathrm{Ca}\right)\) f. \(\left(\begin{array}{l}35 \\ 19\end{array} \mathrm{K}\right)\)

Step-by-step solution

Find A

Add the number of protons (Z) and neutrons to find A: \(A = Z + n = 6 + 7 = 13\)

Identify the element

The element with atomic number 6 is Carbon (C).

Write the atomic symbol

The atomic symbol for this isotope is: \(\left(\begin{array}{l}13 \\ 6\end{array} \mathrm{C}\right)\) b. In this case, the mass number A=13 and the element is Carbon (C):

Find Z

Carbon has an atomic number of 6, so Z=6.

Write the atomic symbol

The atomic symbol for this isotope is: \(\left(\begin{array}{l}13 \\ 6\end{array} \mathrm{C}\right)\) c. In this case, Z=6 and A=13:

Identify the element

The element with atomic number 6 is Carbon (C).

Write the atomic symbol

The atomic symbol for this isotope is: \(\left(\begin{array}{l}13 \\ 6\end{array} \mathrm{C}\right)\) d. In this case, Z=19 and A=44:

Identify the element

The element with atomic number 19 is Potassium (K).

Write the atomic symbol

The atomic symbol for this isotope is: \(\left(\begin{array}{l}44 \\ 19\end{array} \mathrm{K}\right)\) e. In this case, A=41 and the element is Calcium (Ca):

Find Z

Calcium has an atomic number of 20, so Z=20.

Write the atomic symbol

The atomic symbol for this isotope is: \(\left(\begin{array}{l}41 \\ 20\end{array} \mathrm{Ca}\right)\) f. In this case, the isotope has 19 protons and 16 neutrons:

Find Z and A

The number of protons is the atomic number Z, so Z=19. Add the number of protons and neutrons to find A: \(A = Z + n = 19 + 16 = 35\)

Identify the element

The element with atomic number 19 is Potassium (K).

Write the atomic symbol

The atomic symbol for this isotope is: \(\left(\begin{array}{l}35 \\ 19\end{array} \mathrm{K}\right)\)

Key concepts

Atomic Number

The atomic number, often symbolized by the letter 'Z', is a fundamental characteristic of a chemical element. It represents the number of protons found in the nucleus of an atom. Since protons are positively charged, the atomic number also determines the electrical charge of the nucleus.
Each element on the periodic table is defined by its atomic number. For example, hydrogen has an atomic number of 1 because it has one proton in its nucleus, while carbon’s atomic number is 6, meaning it has six protons.
The Importance of Atomic Number:

• Identity of an Element: It determines the identity of an element. No two elements have the same atomic number.
• Chemical Properties: It influences the chemical properties of the element as it determines the electron configuration of an atom.
• Stoichiometry: In chemical reactions, knowing the atomic number assists in balancing equations and understanding the stoichiometry of the reaction.

Understanding the atomic number is crucial for classifying elements and predicting how they will react with others.

Mass Number

The mass number, symbolized as 'A', is the total number of protons and neutrons (collectively known as nucleons) in an atom's nucleus. It reveals an isotope's mass relative to the carbon-12 standard isotope.
The mass number is particularly important when discussing isotopes, which are atoms of the same element that have different numbers of neutrons. For example, carbon-12 and carbon-14 are isotopes of carbon, with mass numbers of 12 and 14 respectively because carbon-12 has 6 neutrons and carbon-14 has 8 neutrons.
Significance of Mass Number:

• Isotopic Identity: Helps in identifying different isotopes of the same element.
• Atomic Mass: Contributes to the average atomic mass of an element which is used in calculations in chemistry and physics.
• Radioactivity: The difference in mass number among isotopes of an element can explain radioactivity and nuclear stability.

Knowing an element's mass number is essential for calculating molecular weights and understanding the nuances of atomic structure.

Chemical Elements

Chemical elements are the simplest forms of matter that cannot be broken down into simpler substances by chemical reactions. Each element is made up of atoms that share the same atomic number, meaning they have the same number of protons.
There are currently 118 recognized elements, which are organized on the periodic table by their atomic number. Some familiar examples of chemical elements include hydrogen, oxygen, and iron.
Role in Science and Everyday Life:

• Building Blocks: Chemical elements are the building blocks of all matter in the universe.
• Physical and Chemical Reactions: Each element has unique properties that determine how it interacts with other elements in physical and chemical reactions.
• Technological Applications: Elements are used in various industries and technology, from manufacturing to medicine.

Understanding chemical elements and their properties is fundamental to the study of chemistry, physics, and many other scientific disciplines.