Question

Write the atomic symbol \(\left(\frac{A}{Z} X\right)\) for each of the isotopes described below. 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. \(\frac{17}{8} O\) b. \(\frac{37}{17} Cl\) c. \(\frac{60}{27} Co\) d. \(\frac{57}{26} Fe\) e. \(\frac{131}{53} I\) f. \(\frac{7}{3} Li\)

Step-by-step solution

Determine the mass number (A) and the element symbol (X) for each question if not provided

For each question, we first need to find the mass number (A) and the element symbol (X) if not given. a. The mass number (A) is the sum of protons (Z) and neutrons. So, A = Z + number of neutrons = 8 + 9 = 17. Oxygen (O) has an atomic number of 8, so X = O. b. The isotope of chlorine is given and A is provided (37). Chlorine (Cl) has an atomic number of 17, so Z = 17. c. Both A and Z are given (60 and 27). Find the element symbol (X) using the periodic table: Z = 27 corresponds to Cobalt (Co). d. The number of protons (26) and neutrons (31) are given. The atomic number (Z) is the number of protons, so Z = 26. Find the mass number (A) by adding the protons and neutrons: A = 26 + 31 = 57. Find the element symbol (X): Z = 26 corresponds to Iron (Fe). e. The isotope presented is of Iodine (I). Iodine has an atomic number (Z) of 53, and the mass number (A) is given, 131. f. The atomic number (Z) is given (3). Find the element symbol (X): Z = 3 corresponds to Lithium (Li). To find the mass number (A), add Z and the number of neutrons: A = 3 + 4 = 7.

Write the atomic symbol for each isotope

Now we will use the atomic symbol format \(\frac{A}{Z} X\) and the information from Step 1 to write the isotopes: a. Oxygen with 8 protons and 9 neutrons: \(\frac{17}{8} O\) b. Chlorine with A = 37: \(\frac{37}{17} Cl\) c. Cobalt with 27 protons and 60 atomic mass: \(\frac{60}{27} Co\) d. Iron with 26 protons and 31 neutrons: \(\frac{57}{26} Fe\) e. Iodine with a mass number of 131: \(\frac{131}{53} I\) f. Lithium with 3 protons and 4 neutrons: \(\frac{7}{3} Li\)

Key concepts

Atomic Number

The atomic number, symbolized as Z, is fundamental in understanding elements and isotopes. It is the number of protons present in the nucleus of an atom, which is unique to each element. For example, hydrogen has an atomic number of 1, meaning it has only one proton. The periodic table is organized by ascending atomic numbers. When solving exercises like the ones provided, knowing the atomic number allows you to identify the element and determine its chemical properties.

Knowing that oxygen has an atomic number of 8, as in exercise part a, immediately tells us that we are working with oxygen because no other element has 8 protons in its nucleus. Students should remember that the atomic number defines the element, as this concept is essential for correctly identifying and symbolizing isotopes.

Mass Number

The mass number, represented by A, is the total number of protons and neutrons in an atom's nucleus. The significance of the mass number becomes apparent in contexts such as determining the isotope of an element. Unlike the atomic number, the mass number is not fixed for a given element since an element can have several isotopes with different numbers of neutrons.

For instance, in exercise part d, once the number of protons (26) is known to be iron (Fe), the number of neutrons (31) can be added to it to find that the mass number (A) for this specific isotope of iron is 57. This is pivotal for students to learn as it helps them to not only represent isotopes using atomic symbols but also to understand the concept of atomic mass and its relation to isotopes.

Isotopes

Isotopes are atoms of the same element that have different mass numbers, which means they have the same number of protons but different numbers of neutrons. This is an enriching concept as it expands our understanding of the atomic structure beyond the periodic table. Isotopes of an element have nearly identical chemical properties because they have the same electronic configuration, but they can have vastly different physical properties due to the changes in mass.

In the textbook exercises, part e specifically asks to represent the isotope of Iodine with a mass number of 131. Iodine's atomic number is 53; however, it can have multiple isotopes with varying mass numbers, 131 being one of them. Students should realize isotopes explain why atomic weights of elements are not whole numbers on the periodic table and why such variations exist.

Periodic Table Elements

The periodic table is a systematic arrangement of the elements organized by increasing atomic number and grouped by similar chemical properties into columns known as 'groups' and rows called 'periods'. Each element's box in the periodic table provides vital information such as the atomic number, element symbol, and average atomic mass, which accounts for the natural isotope distribution.

When tackling problems like exercise part c, the periodic table lets you identify Cobalt (Co) when given the atomic number 27. It serves not only as a reference for elemental data but also as a roadmap for predicting the behavior of atoms in chemical reactions. Students utilizing the periodic table can enhance their comprehension of elemental characteristics and isotopic identities and should be encouraged to familiarize themselves with its layout and information.