Question

Write the atomic symbol \(\left(\frac{A}{Z} X\right)\) for each of the following isotopes. a. \(Z=8\), number of neutrons \(=9\) b. the isotope of chlorine in which \(A=37\) c. \(Z=27, A=60\) d. number of protons \(=26\), number of neutrons \(=31\) e. the isotope of \(I\) with a mass number of 131 f. \(Z=3\), number of neutrons \(=4\)

Short answer

a. \(\frac{17}{8} \text{O}\) b. \(\frac{37}{17} \text{Cl}\) c. \(\frac{60}{27} \text{Co}\) d. \(\frac{57}{26} \text{Fe}\) e. \(\frac{131}{53} \text{I}\) f. \(\frac{7}{3} \text{Li}\)

Step-by-step solution

Problem a

Given: - \(Z=8\) (number of protons), - Number of neutrons \(=9\). The element with atomic number 8 is oxygen (O). To find the mass number (A), we can add the number of protons and neutrons: \[A = Z + N = 8 + 9 = 17\] Now we can write the atomic symbol: \[\frac{17}{8} \text{O}\]

Problem b

Given: - The isotope of chlorine, - \(A=37\). The element is chlorine (Cl), and its atomic number (Z) is 17. The mass number (A) is given as 37. Now, we can write the atomic symbol: \[\frac{37}{17} \text{Cl}\]

Problem c

Given: - \(Z=27\), - \(A=60\). The element with atomic number 27 is cobalt (Co). The mass number (A) is given as 60. Now, we can write the atomic symbol: \[\frac{60}{27} \text{Co}\]

Problem d

Given: - Number of protons \(=26\), - Number of neutrons \(=31\). The element with the atomic number 26 is iron (Fe). To find the mass number (A), we can add the number of protons and neutrons: \[A = Z + N = 26 + 31 = 57\] Now, we can write the atomic symbol: \[\frac{57}{26} \text{Fe}\]

Problem e

Given: - The isotope of I (iodine), - Mass number \(= 131\). The element is iodine (I), and its atomic number (Z) is 53. The given mass number (A) is 131. Now, we can write the atomic symbol: \[\frac{131}{53} \text{I}\]

Problem f

Given: - \(Z=3\) (number of protons), - Number of neutrons \(=4\). The element with atomic number 3 is lithium (Li). To find the mass number (A), we can add the number of protons and neutrons: \[A = Z + N = 3 + 4 = 7\] Now, we can write the atomic symbol: \[\frac{7}{3} \text{Li}\]

Key concepts

Isotopes Notation

Isotopes are variants of chemical elements that have the same number of protons but differ in the number of neutrons within their nuclei. This means that while they occupy the same position in the periodic table, they have different mass numbers.

When writing isotopes, scientists use a special notation that includes the element's symbol, its atomic number (Z), and its mass number (A). The atomic symbol is written as \(\frac{A}{Z} X\), where \(X\) is the chemical symbol of the element, \(A\) is the mass number, and \(Z\) represents the atomic number. The mass number, \(A\), is found by adding together the number of protons and neutrons in the isotope.

For instance, if we look at carbon-14, a famous isotope due to its use in radiocarbon dating, it would be notated as \(\frac{14}{6} C\) as it has 6 protons and 8 neutrons, adding up to a mass number of 14. The atomic number, 6, identifies the element as carbon. The use of isotopes notation is essential in fields such as chemistry, physics, and various applications in science and industry.

Atomic Mass Number

The atomic mass number (A) of an isotope is the total number of protons and neutrons in the nucleus of an atom. Since protons and neutrons are the heavier components and almost equally massive, the atomic mass number gives us a good estimation of the atom's overall mass.

Understanding the atomic mass number is crucial for identifying different isotopes of an element. To calculate the mass number, simply add the number of protons (atomic number) to the number of neutrons. This is a straightforward operation important for resolving exercises involving isotopic symbols, as seen in the textbook problems.

Atomic Number

The atomic number (Z) is a fundamental property of an element; it defines the identity of the element. It refers to the number of protons in the nucleus of an atom and, by extension, also determines the number of electrons in a neutral atom.

Each element on the periodic table has a unique atomic number, which makes it an essential tool for element identification. For example, hydrogen has an atomic number of 1, meaning it has one proton in its nucleus. It's essential to understand that while the mass number can vary among isotopes of the same element (due to different numbers of neutrons), the atomic number is constant for a given element.

Element Identification

Identifying an element from its atomic number or its isotopic notation is a fundamental skill in chemistry. The atomic number, as mentioned earlier, is unique for each element and is used to determine the element's position in the periodic table and, by extension, its chemical properties.

Element identification becomes straightforward once you know the atomic number, as every element is listed by increasing atomic number in the periodic table. For instance, if you have an isotope notation of \(\frac{238}{92} U\), you can identify the element as uranium simply by its atomic number 92. Even without memorizing the entire table, you can often deduce the identity of an element by knowing the properties of the elements surrounding it or by consulting a periodic table.