Question

Write the atomic symbol \(\left({ }_{z}^{A} X\right)\) for each of the isotopes described below. a. number of protons \(=27\), number of neutrons \(=31\) b. the isotope of boron with mass number 10 c. \(Z=12, A=23\) d. atomic number 53, number of neutrons \(=79\) e. \(Z=9\), number of neutrons \(=10\) f. number of protons \(=29\), mass number 65

Short answer

a. \(\left({ }_{27}^{58} Co\right)\) b. \(\left({ }_{5}^{10} B\right)\) c. \(\left({ }_{12}^{23} Mg\right)\) d. \(\left({ }_{53}^{132} I\right)\) e. \(\left({ }_{9}^{19} F\right)\) f. \(\left({ }_{29}^{65} Cu\right)\)

Step-by-step solution

Find \(Z\), \(A\), and \(X\) for isotope in part a

We are given the number of protons and neutrons for this isotope: - Number of protons = \(27\) - Number of neutrons = \(31\) Mass number, \(A = \) number of protons + number of neutrons = \(27+31=58\) We can look up the chemical symbol for the element with 27 protons which is cobalt (Co). Now, we have all the required values to represent the atomic symbol: \(\left({ }_{27}^{58} Co\right)\) #b.

Find \(Z\), \(A\), and \(X\) for isotope in part b

We are given the isotope of boron with mass number 10. The chemical symbol for boron is B and its atomic number (protons) is 5. So, we can write the atomic symbol for this isotope using the given information: \(\left({ }_{5}^{10} B\right)\) #c.

Find \(Z\), \(A\), and \(X\) for isotope in part c

In this part, we are given the values of \(Z\) and \(A\): - \(Z=12\) - \(A=23\) The element with the atomic number 12 is magnesium (Mg). Now, we can write the atomic symbol for this isotope: \(\left({ }_{12}^{23} Mg\right)\) #d.

Find \(Z\), \(A\), and \(X\) for isotope in part d

We are given the atomic number and the number of neutrons for this isotope: - Atomic number = \(53\) - Number of neutrons = \(79\) We can look up the element's chemical symbol with an atomic number of 53, which is iodine (I). To find the mass number, we can sum the number of protons and neutrons: \(A = 53 + 79 = 132\) Now, we can represent the atomic symbol for this isotope: \(\left({ }_{53}^{132} I\right)\) #e.

Find \(Z\), \(A\), and \(X\) for isotope in part e

We are given the values of \(Z\) and the number of neutrons for this isotope: - \(Z=9\) - Number of neutrons = \(10\) The element with atomic number 9 is fluorine (F). To find the mass number, we can add the number of protons and neutrons: \(A = 9 + 10 = 19\) Now, we can represent the atomic symbol for this isotope: \(\left({ }_{9}^{19} F\right)\) #f.

Find \(Z\), \(A\), and \(X\) for isotope in part f

We are given the number of protons and mass number for this isotope: - Number of protons = \(29\) - Mass number = \(65\) We can look up the element's chemical symbol for an element with 29 protons, which is copper (Cu). Now, we can represent the atomic symbol for this isotope: \(\left({ }_{29}^{65} Cu\right)\)

Key concepts

Atomic Number

The atomic number, often represented by the symbol Z, is one of the most fundamental properties of an element. It tells us the number of protons that are present in the nucleus of an atom.
Protons carry a positive charge, and because they are unique to each element, the atomic number also defines the identity of the element. For instance, carbon will always have an atomic number of 6 because it always has 6 protons in its nucleus. When solving problems related to atomic symbols, you first need to identify the atomic number to determine which element you're dealing with.

Mass Number

The mass number, denoted by A, is the sum of protons and neutrons found in an atom's nucleus. Neutrons, like protons, contribute to the mass of an atom but do not affect the chemical properties in the same way. This is because they are neutral particles.
When representing isotopes, it's imperative to calculate the mass number if it's not already given. For example, if an isotope has 6 protons (which is the atomic number for carbon) and 7 neutrons, the mass number will be A = 6+7 = 13. The mass number is crucial for distinguishing between different isotopes of the same element. In problems like the textbook exercise above, knowing how to calculate the mass number allows you to write the complete atomic symbol.

Chemical Symbols

Chemical symbols are shorthand notations to represent elements on the periodic table. Each symbol consists of one or two letters, where the first letter is always capitalized and, if present, the second letter is lower case. For example, the chemical symbol for Hydrogen is H, while that for calcium is Ca.
Understanding chemical symbols is vital when writing isotopic notation. These symbols are an essential part of the atomic symbol that represents an isotope, as seen in the solution steps for various isotopes. By using the atomic number, we can find the corresponding chemical symbol to correctly identify the element in question.

Atomic Structure

Atomic structure refers to the composition of an atom, which typically consists of a nucleus containing protons and neutrons, surrounded by electrons in different energy levels. The number of protons determines the atomic number and the element's identity, while the combination of protons and neutrons defines the mass number. Electrons are arranged around the nucleus in various shells and subshells based on their energy levels.
An important aspect of atomic structure related to our textbook exercise is the concept of isotopes. Isotopes are variations of the same element that have the same number of protons but different numbers of neutrons. This unique arrangement leads to different mass numbers, although the chemical properties remain largely unchanged since they are determined by the electron configuration.