Question

Let IP stand for ionization potential. Then element for which the value of \(\mathrm{IP}_{1}, \mathrm{IP}_{2}, \mathrm{IP}_{3}, \mathrm{IP}_{4}\) are \(50,100,250\) and \(2051 \mathrm{eV}\) respectively, is (a) \(\mathrm{Al}\) (b) \(\mathrm{Na}\) (c) \(\mathrm{Mg}\) (d) Si

Short answer

The element is Magnesium (Mg).

Step-by-step solution

Understanding Ionization Potentials

Ionization potential (IP) is the energy required to remove an electron from an atom or ion. The sequence \( \mathrm{IP}_1, \mathrm{IP}_2, \mathrm{IP}_3, \mathrm{IP}_4 \) represents the energy needed to remove the first, second, third, and fourth electrons, respectively.

Analyze the Given Ionization Potentials

We have the ionization potentials \( \mathrm{IP}_1 = 50 \, \mathrm{eV} \), \( \mathrm{IP}_2 = 100 \, \mathrm{eV} \), \( \mathrm{IP}_3 = 250 \, \mathrm{eV} \), and \( \mathrm{IP}_4 = 2051 \, \mathrm{eV} \). Notice the drastic increase in \( \mathrm{IP}_4 \). This large increase indicates the removal of an electron from a more stable, typically fully filled, or half-filled shell.

Identify the Element by Reviewing Ionization Patterns

Reviewing typical ionization energy values and the significant jump in energy at \( \mathrm{IP}_4 \), we hypothesize that this increase corresponds to the removal of an electron from a noble gas configuration. Mg, after losing 2 electrons, achieves the noble gas configuration of Ne; removing a third electron would require a significantly higher energy.

Cross-Verify with the Options

Check the elements based on their electron configurations:- \( \mathrm{Al} \) (Aluminum) has \( IP_3 \) extensive but not a large jump by \( IP_4 \).- \( \mathrm{Na} \) (Sodium) shows a massive jump from \( IP_1 \) to \( IP_2 \), not shown here.- \( \mathrm{Mg} \) (Magnesium) loses the third electron after achieving a stable configuration, matching the observed \( IP_4 \).- \( \mathrm{Si} \) (Silicon), \( IP_4 \) does not fit as well.These observations indicate that \( \mathrm{Mg} \) is the element in question.

Conclusion with the Correct Answer

Based on the analysis, the element having these ionization potentials is Magnesium \( \mathrm{Mg} \).

Key concepts

Electron Configuration

Electron configuration refers to how electrons are arranged in an atom's orbitals. This arrangement follows principles like the Aufbau principle, where electrons fill orbitals in order of increasing energy levels. Each element has a unique electron configuration that determines many of its chemical properties.
Magnesium (Mg), for example, has an electron configuration of \( 1s^2 \,2s^2 \,2p^6 \,3s^2 \). This indicates it has two electrons in its outermost shell, making it likely to lose these electrons during chemical reactions to achieve a stable noble gas configuration, like that of Neon (Ne).
Understanding electron configurations helps us predict how elements will interact with one another. Electron configuration is crucial in explaining the ionization energies exhibited by Magnesium in the exercise - once two 3s electrons are removed, it achieves the stable configuration of a noble gas, causing the ionization energy to dramatically increase.

Ionization Energy Trends

Ionization energy is the amount of energy needed to remove an electron from an atom or ion. This energy generally increases across a period and decreases down a group on the periodic table. Elements achieve varying stability as electrons are removed, reflected in their ionization energies.
For Magnesium (Mg), the given ionization energies \( \mathrm{IP}_1 = 50 \, \mathrm{eV} \), \( \mathrm{IP}_2 = 100 \, \mathrm{eV} \), and a significant \( \mathrm{IP}_4 = 2051 \, \mathrm{eV} \) illustrate this trend. After the first and second electrons are removed, Mg attains a stable configuration, similar to Neon.

• The slight increase from \( \mathrm{IP}_1 \) to \( \mathrm{IP}_2 \) reflects the difficulty of removing a second electron as the positive charge of the ion attracts electrons more strongly.
• The massive jump at \( \mathrm{IP}_4 \) indicates the removal of an electron from a stable, filled orbit, requiring substantially more energy.

This pattern is crucial for understanding why Magnesium, after losing its first two electrons, shows such a substantial increase in ionization energy.

Periodic Table Elements

The periodic table organizes all known chemical elements based on atomic number and electron configuration. It provides a visual framework for understanding elemental properties, including ionization energy, electronegativity, and atomic radius.
Magnesium (Mg), a group 2 element in the periodic table, has properties typical of alkaline earth metals. It is known for being light and strong, used widely in materials requiring such properties. In its elemental state, it typically forms a 2+ ion due to the loss of its two outermost electrons.

• Alkali metals, located just before Mg in the periodic table, exhibit a steep climb in ionization energy after losing a single electron due to achieving the stable outer electron configurations.
• Alkaline earth metals like Mg have a similar but slightly less pronounced pattern owing to their additional electron.

Understanding Magnesium's place in the periodic table helps identify why such drastic ionization potential changes occur, illustrating the broader trends in behavior across different elements.