Question

The successive ionization energy values for an element \(\mathrm{X}\) are given below: (a) lst ionization energy \(=410 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) 2 nd ionization energy \(=820 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) 3 rd ionization energy \(=1100 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) 4 th ionization energy \(=1500 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (e) 5 th ionization energy \(=3200 \mathrm{~kJ} \mathrm{~mol}^{-1}\) Find out the number of valence electron for the atom, \(X\). (a) 4 (b) 3 (c) 5 (d) 2

Short answer

The element X has 4 valence electrons.

Step-by-step solution

Understanding Ionization Energy

Ionization energy is the energy required to remove an electron from an isolated gaseous atom or ion. The successive ionization energies provide a clue about the electron configuration and the number of valence electrons. A distinct increase in ionization energy indicates the removal of an electron from a more stable, inner electronic shell.

Analyze the Provided Ionization Energies

The energies given are 410, 820, 1100, 1500, and 3200 kJ/mol. Notice the first significant jump in energy between the 4th and 5th ionization energies (from 1500 to 3200 kJ/mol), which suggests that the 5th electron is being removed from a closer, more stable shell.

Determine Number of Valence Electrons

The large increase after the 4th ionization implies that the outermost electrons (valence electrons) are exhausted after the removal of the 4th electron, thus there are 4 valence electrons. Electrons within a filled shell require significantly more energy to remove.

Key concepts

Valence Electrons

Valence electrons are the electrons in the outermost shell of an atom. They play a critical role in determining an element's chemical properties and reactivity. When it comes to ionization, only the valence electrons are generally involved. From the successive ionization energies given, we deduce the number of valence electrons by observing the point at which the energy required to remove an electron significantly rises. This jump indicates that all outer electrons have been removed, and removing further electrons requires accessing a new, more stable shell.
For example, in the case of element X, the significant increase in ionization energy occurs after the removal of the fourth electron. Thus, we conclude that element X has 4 valence electrons.

Ionization Energy

Ionization energy is the energy required to remove an electron from an isolated gaseous atom or ion. It provides key insights into the stability and configuration of atoms. The energy tends to increase as each successive electron is removed. This increase can be attributed to the decrease in electron shielding and an increase in effective nuclear charge on the remaining electrons.

• The first ionization energy is relatively low because the valence electron is further from the nucleus, experiencing less nuclear pull.
• Subsequent ionization energies are higher as you begin removing more tightly held electrons.

The massive jump in energy between successive ionizations signals removal from a more stable shell.

Electron Configuration

Electron configuration describes the distribution of electrons among the various atomic orbitals. It follows specific rules that are based on principles such as the Aufbau principle, Hund's rule, and Pauli exclusion principle. The configuration directly influences the energy levels and effective nuclear charge experienced by electrons.
In our case, analyzing the ionization energies provides clues to the electron configuration of element X. Before the fifth ionization energy, all outer electrons are removed at significantly lower energies, indicating these electrons belong to the same outer shell or energy level.

Periodic Table Trends

Trends in the periodic table help us understand and predict the properties of elements. Two key trends regarding ionization energy include:

• Across a Period: Ionization energy increases from left to right as the effective nuclear charge increases and atomic radius decreases, causing electrons to be more tightly held.
• Down a Group: Ionization energy decreases as you move down a group due to an increase in atomic radius and electron shielding, which results in valence electrons being less tightly held by the nucleus.
  Understanding these trends aids in predicting and explaining the behavior of elements, such as why there is a substantial energy change when moving from one energy shell to another.