Problem 170 - Introductory Chemistry Atoms First

Question

What is the valence shell in \(\mathrm{Mg}\), Ge, \(\mathrm{W}\), \(C \mathrm{~s} ?\)

Step-by-Step Solution

Answer

The valence shells for the four elements are: Magnesium (Mg) - 3rd shell, Germanium (Ge) - 4th shell, Tungsten (W) - 6th shell, and Cesium (Cs) - 6th shell.

Step 1: 1. Valence shell of Magnesium (Mg)

Magnesium (Mg) has an atomic number of 12. Based on its location in the periodic table, the electronic configuration can be written as: \(1s^2 2s^2 2p^6 3s^2\). The valence shell is the outermost shell with electrons, which is the 3rd shell in the case of Mg.

Step 2: 2. Valence shell of Germanium (Ge)

Germanium (Ge) has an atomic number of 32. Based on its location in the periodic table, its electronic configuration can be written as: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^2\). The valence shell is the outermost shell with electrons, which is the 4th shell in the case of Ge.

Step 3: 3. Valence shell of Tungsten (W)

Tungsten (W) has an atomic number of 74. Its electronic configuration can be written as: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2 5p^6 4f^{14} 5d^4 6s^2\). The valence shell is the outermost shell with electrons, which is the 6th shell in the case of W.

Step 4: 4. Valence shell of Cesium (Cs)

Cesium (Cs) has an atomic number of 55. Based on its location in the periodic table, its electronic configuration can be written as: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2 5p^6 4f^{14} 5d^{10} 6s^1\). The valence shell is the outermost shell with electrons, which is the 6th shell in the case of Cs.

Key Concepts

Understanding Electronic Configuration

Electronic configuration is like the address for electrons in an atom. It tells us where electrons live in an atom and which shells and subshells they occupy. Electrons fill specific energy levels or shells, and they do so in a particular order. Each shell has a specific capacity, and the order they fill is based on the increasing energy of orbitals. For instance, after filling the first shell, electrons move to the second shell, and so on. This arrangement is guided by the Aufbau principle, which dictates that electrons fill orbitals starting with the lowest energy levels first. By knowing the electronic configuration, we can determine how many electrons are in each shell, which ultimately helps to identify the valence shell—crucial in chemical bonding.

The Role of the Periodic Table

The periodic table is an invaluable tool in understanding elements. It's like a map that shows each element's properties, atomic structure, and relationships with other elements. Elements are arranged in order of increasing atomic number, which also generally reflects their electronic configurations. The table’s layout allows us to identify patterns and predict properties of different elements. Each column, or group, contains elements with similar properties and the same number of valence electrons, which they owe to similar electronic configurations. This organization helps in predicting how an element might react chemically, just by looking at its position on the table.

Significance of Atomic Number

The atomic number of an element is a fundamental concept in chemistry. It tells us how many protons are in an atom’s nucleus, and in a neutral atom, it also indicates the number of electrons. Knowing the atomic number helps us determine where an element sits on the periodic table. Since the electronic configuration is based on the number of electrons, the atomic number directly informs us how electrons are distributed across shells. For example, Magnesium (Mg) with an atomic number of 12 means it has 12 protons and 12 electrons. Its electronic configuration is derived from arranging these electrons in a manner dictated by energy levels.

Exploring Electron Shells

Electron shells are like layers or rings around the nucleus where electrons reside. Each shell can hold a set maximum number of electrons, determined by the formula \( 2n^2 \) where \( n \) is the shell number.These shells are designated by numbers or letters, e.g., 1 is K, 2 is L, 3 is M, and so on. Electrons in the outermost shell (the valence shell) play a crucial role in chemical reactions and bonding, as these are the electrons involved in forming bonds with other atoms.Understanding how electrons are distributed among these shells can explain an element's reactivity and ability to bond with other elements, making electron shells a key concept in chemistry.