Question

Write the correct symbol, with both superscript and subscript, for each of the following. Use the list of elements inside the front cover as needed: (a) the isotope of platinum that contains 118 neutrons, (b) the isotope of krypton with mass number \(84,(\mathbf{c})\) the isotope of arsenic with mass number \(75,(\mathbf{d})\) the isotope of magnesium that has an equal number of protons and neutrons.

Short answer

The isotopes for the given elements are: (a) \(_{78}^{196}\text{Pt}\), (b) \(_{36}^{84}\text{Kr}\), (c) \(_{33}^{75}\text{As}\), and (d) \(_{12}^{24}\text{Mg}\).

Step-by-step solution

Find the Atomic Number of Platinum

Using the periodic table, we can find that the atomic number of platinum (Pt) is 78. This means that platinum has 78 protons in its nucleus.

Calculate the mass number

Platinum has 118 neutrons as given in the exercise. To find the mass number, we add the number of protons to the number of neutrons: \(78 (protons) + 118 (neutrons) = 196\).

Write the isotope symbol

Now that we have the mass number (196) and atomic number (78), we write the isotope symbol for platinum: \(_{78}^{196}\text{Pt}\). #b) The isotope of krypton with mass number 84#

Find the Atomic Number of Krypton

Using the periodic table, we can find that the atomic number of krypton (Kr) is 36. This means that krypton has 36 protons in its nucleus.

Write the isotope symbol

The exercise tells us that the mass number of this particular isotope is 84. With the atomic number of 36, the isotope symbol is: \(_{36}^{84}\text{Kr}\). #c) The isotope of arsenic with mass number 75#

Find the Atomic Number of Arsenic

Using the periodic table, we can find that the atomic number of arsenic (As) is 33. This means that arsenic has 33 protons in its nucleus.

Write the isotope symbol

The exercise tells us that the mass number of this particular isotope is 75. With the atomic number of 33, the isotope symbol is: \(_{33}^{75}\text{As}\). #d) The isotope of magnesium that has an equal number of protons and neutrons#

Find the Atomic Number of Magnesium

Using the periodic table, we can find that the atomic number of magnesium (Mg) is 12. This means that magnesium has 12 protons in its nucleus.

Calculate the mass number

We're told that this isotope of magnesium has an equal number of protons and neutrons. Since it has 12 protons, then it also must have 12 neutrons: \(12 (protons) + 12 (neutrons) = 24\).

Write the isotope symbol

Now that we have the mass number (24) and atomic number (12), we write the isotope symbol for this magnesium isotope: \(_{12}^{24}\text{Mg}\).

Key concepts

Atomic Number

The atomic number is a fundamental concept in chemistry that helps identify the number of protons in the nucleus of an atom. Each element has a unique atomic number, which determines its place in the periodic table. For example, hydrogen has an atomic number of 1 because it has one proton, while carbon has an atomic number of 6 because it has six protons. These protons carry a positive charge, and in a neutral atom, the number of electrons (negatively charged particles) equals the number of protons.

In isotopic notation, the atomic number is crucial for writing the symbol of the isotope. It appears as a subscript to the left of the element's symbol. For example, the atomic number of platinum (Pt) is 78, which explains why it appears as \(_{78}\text{Pt}\) in the isotope notation.

Mass Number

The mass number of an element is the total count of protons and neutrons present in its nucleus. This number provides insight into the isotope's mass, which is why it's called the "mass number." To find the mass number, simply add the number of protons and neutrons together. Neutrons have no charge but contribute significantly to the atom's mass because they are about the same size as protons.

For instance, if platinum has 78 protons and 118 neutrons, the mass number would be calculated as follows:

• Protons: 78
• Neutrons: 118
• Mass Number: 78 + 118 = 196

Thus, the isotope of platinum would be denoted as \(_{78}^{196}\text{Pt}\). The mass number is always shown in the isotope notation as a superscript to the left of the element's symbol.

Periodic Table

The periodic table is an organized chart where all known chemical elements are listed. Each element on the periodic table is placed based on its atomic number, electron configuration, and recurring chemical properties. The layout of the table helps predict the properties of elements and their compounds. Understanding the periodic table is essential because it acts like a map displaying elements, much like cities on a roadmap.

Rows in the table are called periods, and each period indicates the number of electron shells an atom possesses. Columns are referred to as groups or families and share similar chemical properties. For instance, all noble gases are in Group 18 and are known for being inert.

By using the periodic table, we can quickly identify the atomic number or mass number of an element, which is crucial for understanding isotopic notation and the properties of isotopes like those in the exercise, whether it's determining the numbers for platinum, krypton, arsenic, or magnesium.