Using the periodic table to locate each element, write the electron configuration of (a) \(\mathrm{Zn} ;\) (b) \(\mathrm{Mn} ;\) (c) Re.

The periodic table is a chart that organizes all known elements by increasing atomic number, which is the number of protons in an atom's nucleus. Each element is positioned in a unique spot that provides important information, including:
- **Group**: Columns on the table indicate groups or families of elements with similar properties.
- **Period**: Rows indicate periods, showing elements with the same number of electron shells.
- **Block**: The table is divided into s, p, d, and f blocks, which denote the electron orbital types that are being filled as you move through the elements.
Think of the periodic table as a map for understanding how elements interact. For example, elements in the same group often react similarly. The table helps predict the properties and behaviors of each element, including their electron configurations.

The atomic number is fundamental to identifying an element. It tells us the number of protons in an atom's nucleus. For a neutral atom, it also equals the number of electrons.
Why is this important? Because the atomic number determines the element's location on the periodic table and its chemical properties.
For instance, in the exercise:

• *Zinc (Zn)* has an atomic number of 30, meaning it has 30 protons and 30 electrons.
• *Manganese (Mn)* has an atomic number of 25, so it has 25 protons and 25 electrons.
• *Rhenium (Re)* has an atomic number of 75, giving it 75 protons and 75 electrons.

With the atomic number, you can easily locate an element on the periodic table and begin to understand its electron configuration.

Energy levels (or electron shells) are layers around the nucleus where electrons are found. The energy levels increase as you move away from the nucleus and are numbered as n=1, n=2, n=3, etc.
Each energy level can hold a maximum number of electrons:

• The 1st energy level (n=1) can hold up to 2 electrons.
• The 2nd energy level (n=2) can hold up to 8 electrons.
• The 3rd energy level (n=3) can hold up to 18 electrons.

The distribution of electrons in these levels follows specific rules, often described using the electron configuration notation.
In our examples:

• *Zinc (Zn)*: The electron configuration is written as \(1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \), showing electrons filling up to the 4th energy level.
• *Manganese (Mn)*: The configuration \(1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^5 \), indicates electrons up to the 4th energy level.
• *Rhenium (Re)*: The configuration is longer \(1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6 \, 5s^2 \, 4d^{10} \, 5p^6 \, 6s^2 \, 4f^{14} \, 5d^5 \), showing a filling up to the 6th energy level.

By learning how electrons are arranged in these energy levels, you can better understand the structure and reactivity of elements.