Identify each element below, and give the symbols of the other elements in its group: (a) \([\mathrm{Ar}] 4 s^{2} 3 d^{10} 4 p^{4}\) (b) \([\mathrm{Xe}] 6 s^{2} 4 f^{14} 5 d^{2}\) (c) \([\mathrm{Ar}] 4 s^{2} 3 d^{5}\)

Understanding electron configuration helps us determine the distribution of electrons in an atom. It's like a map that shows where each electron 'lives' in the atom. The electron configuration is written using the notation that lists the energy levels and sublevels in order, along with the number of electrons in each sublevel.
For example, in \(\text{Ar}] 4s^2 3d^{10} 4p^4\), 'Ar' represents Argon, a noble gas with 18 electrons, serving as a shorthand for its complete configuration. Understanding this notation helps in finding out the number of electrons in an element. Just add the electrons from the noble gas core and the additional electrons in the specified sublevels.
Here’s a breakdown:

• \text{'Ar' contributes 18 electrons}
• \text{'4s^2' contributes 2 electrons}
• \text{'3d^{10}' contributes 10 electrons}
• \text{'4p^4' contributes 4 electrons}

By adding these up, we get a total of 34 electrons, making our element Selenium (Se).
In another example, \([\text{Xe}] 6s^2 4f^{14} 5d^2\), Xe means Xenon which has 54 electrons.
Adding the rest, we get 72 electrons total, identifying the element as Hafnium (Hf).
Electron configurations help us understand where electrons are located around the nucleus and aid in predicting an element’s chemical behavior.

Identifying the group to which an element belongs is crucial for understanding its properties and reactivity. Elements in the same group share similar chemical properties because they have the same number of electrons in their outermost shell. For instance, Selenium (Se) with configuration \([\text{Ar}] 4s^2 3d^{10} 4p^4\) has six electrons in its outer shell and belongs to Group 16, also known as the Chalcogens. This group includes elements like Oxygen (O) and Sulfur (S) which share similar properties. Likewise, Hafnium (Hf) with configuration \([\text{Xe}] 6s^2 4f^{14} 5d^2\) is part of Group 4. Elements in this group, including Titanium (Ti) and Zirconium (Zr), have four outer electrons, exhibiting similar metallic properties. Group 7, also known as the Manganese group, includes Manganese (Mn) which is identified with an electron configuration of \([\text{Ar}] 4s^2 3d^5\). The similarity in electron arrangements within the outer shell of the groups leads to periodic trends in properties like ionization energy, electronegativity, and atomic radius.

The atomic number of an element is the number of protons in its nucleus and is denoted by 'Z'. It uniquely identifies an element and also equals the number of electrons in an electrically neutral atom. By determining the total number of electrons from the electron configuration, one can easily find the atomic number. For example:

• Selenium (Se), identified from the configuration \([\text{Ar}] 4s^2 3d^{10} 4p^4\), has 34 electrons, hence the atomic number is 34.
• Hafnium (Hf), with \([\text{Xe}] 6s^2 4f^{14} 5d^2\), has 72 electrons, so its atomic number is 72.
• Manganese (Mn), with configuration \([\text{Ar}] 4s^2 3d^5\), has 25 electrons and therefore an atomic number of 25.

Atomic numbers are fundamental as they not only identify the element but also help in locating it in the Periodic Table and predicting its properties. Elements are arranged in ascending order of their atomic numbers in the Periodic Table, forming groups and periods that reflect repeating patterns in element properties.