Problem 26 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) Which two of the following are isotopes of the same element: \({ }_{46}^{106} \mathrm{X},{ }_{46}^{107} \mathrm{X},{ }_{47}^{107} \mathrm{X} ?(\mathbf{b})\) What is the identity of the element whose isotopes you have selected?

Step-by-Step Solution

Answer

The two isotopes of the same element are \( _{46}^{106}\mathrm{X}\) and \( _{46}^{107}\mathrm{X}\). The identity of the element whose isotopes were selected is Palladium (Pd).

Step 1: In the given exercise, we are given three different atoms: \( _{46}^{106}\mathrm{X}\), \( _{46}^{107}\mathrm{X}\), and \( _{47}^{107}\mathrm{X}\). We need to identify which two of these atoms have the same atomic number. The atomic number is represented by the subscript (number at the bottom left). Remember that isotopes have the same atomic number. Here, we can see that the first two atoms, \( _{46}^{106}\mathrm{X}\) and \( _{46}^{107}\mathrm{X}\), have an atomic number of 46, while the third atom has an atomic number of 47. Thus, the two isotopes of the same element are \( _{46}^{106}\mathrm{X}\) and \( _{46}^{107}\mathrm{X}\). #Step 2: Determine the identity of the element with the given atomic number#

Now that we have identified the isotopes with the same atomic number, we can use a periodic table to determine the identity of the element. Look for the element with the atomic number 46 in the periodic table, which corresponds to the element Palladium (Pd). Therefore, the element whose isotopes we have selected is Palladium. #Final answer#

Step 2: Isotopes of the same element

The two isotopes of the same element are \( _{46}^{106}\mathrm{X}\) and \( _{46}^{107}\mathrm{X}\).

Step 3: Identity of the element

The identity of the element whose isotopes were selected is Palladium (Pd).

Key Concepts

Atomic Number

The atomic number is a fundamental concept in chemistry that defines the identity of an element. It is represented by the number of protons in the nucleus of an atom.

In any atom, this number is unique and determines the element's characteristics. For example:

• An atom with 1 proton is always hydrogen.
• An atom with 6 protons is carbon.
• The exercise involves identifying isotopes. Isotopes have the same atomic number, meaning they are forms of the same element but with different numbers of neutrons.

This exercise focuses on identifying which atoms share the same atomic number to determine their isotopic relationship.

Periodic Table

The periodic table is an organized chart of all known elements. It arranges elements by increasing atomic number, so you can easily locate an element by counting the protons.

Each element has a distinctive position on this table, reflecting its properties:

• The rows are called periods. Elements in the same period have the same number of atomic orbitals.
• The columns are called groups, and elements in the same group often share similar chemical properties.

In this exercise, the periodic table helps us identify Palladium (Pd) at atomic number 46, thereby allowing us to find which isotopes belong to this element.

Element Identity

The identity of an element is intricately linked to its atomic number. Knowing the atomic number allows you to locate the element on the periodic table instantly.

Here’s why it's crucial:

• It uniquely identifies an element, regardless of its isotopic form.
• Isotopes (atoms with the same atomic number but different masses) will have the same chemical properties.

By finding which isotopes share the atomic number of 46, we confirmed that they are forms of Palladium, a key element used in various industrial processes.

Palladium

Palladium, symbolized as Pd, is a silvery-white metal with diverse applications, notably in electronics and catalytic converters in cars. It holds a special place on the periodic table with an atomic number of 46.

This element's importance extends beyond its practical uses:

• It often occurs in nature as a mixture of isotopes.
• Besides its use in technology, it is also valued in jewelry and dentistry.

Within the exercise, understanding Palladium’s atomic number helped us identify which isotopes belong to this element and enhanced our comprehension of isotopic relationships.