Problem 164 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following sets of ions represents the collection of isoelectronic species? (a) \(\mathrm{K}+\mathrm{Ca}^{2+}, \mathrm{Sc}^{3+}, \mathrm{Cl}^{-}\) (b) \(\mathrm{Na}^{+}, \mathrm{Ca}^{2+}, \mathrm{S} \mathrm{c}^{3+}, \mathrm{F}^{-}\) (c) \(\mathrm{K}^{+}, \mathrm{Cl}^{-}, \mathrm{Mg}^{2+}, \mathrm{Sc}^{3+}\) (d) \(\mathrm{Na}^{+} \mathrm{Mg}^{2+}, \mathrm{Al}^{3+}, \mathrm{Cl}\)

Step-by-Step Solution

Answer

The isoelectronic set is (a) \(\mathrm{K}^{+}, \mathrm{Ca}^{2+}, \mathrm{Sc}^{3+}, \mathrm{Cl}^{-}\).

Step 1: Define Isoelectronic Species

Isoelectronic species are atoms, molecules, or ions that have the same number of electrons. This means their electronic configurations will be the same.

Step 2: Determine Total Electrons in Each Ion

To find the total number of electrons in an ion, adjust the number of protons (atomic number) by the charge of the ion. If the ion is positively charged, subtract the charge from the atomic number. If negatively charged, add the charge to the atomic number.

Step 3: Calculate Electrons for Set (a)

- For \(\mathrm{K}^{+}\) (potassium ion), the atomic number is 19. After losing one electron for the positive charge, there are 18 electrons.- For \(\mathrm{Ca}^{2+}\) (calcium ion), the atomic number is 20. It loses 2 electrons, resulting in 18 electrons.- For \(\mathrm{Sc}^{3+}\) (scandium ion), the atomic number is 21. It loses 3 electrons, leading to 18 electrons.- For \(\mathrm{Cl}^{-}\) (chloride ion), the atomic number is 17. It gains 1 electron, resulting in 18 electrons.

Step 4: Assess Electrons for Other Sets

- In set (b): - \(\mathrm{Na}^{+}\): 11 - 1 = 10 electrons - \(\mathrm{Ca}^{2+}\): 18 electrons (as before) - \(\mathrm{Sc}^{3+}\): 18 electrons (as before) - \(\mathrm{F}^{-}\): 9 + 1 = 10 electrons- In set (c): - \(\mathrm{K}^{+}\), \(\mathrm{Cl}^{-}\), \(\mathrm{Mg}^{2+}\), and \(\mathrm{Sc}^{3+}\) all have 18 electrons.- In set (d): - \(\mathrm{Na}^{+}\): 10 electrons - \(\mathrm{Mg}^{2+}\): 10 electrons - \(\mathrm{Al}^{3+}\): 10 electrons - \(\mathrm{Cl}\): 17 electrons

Step 5: Identify Isoelectronic Set

From the calculations, it is clear that sets (a) and (c) have ions with an equal number of electrons—18 electrons each.

Step 6: Conclusion

The correct choice representing isoelectronic species is set (a) \(\mathrm{K}^{+}, \mathrm{Ca}^{2+}, \mathrm{Sc}^{3+}, \mathrm{Cl}^{-}\) since all these ions have 18 electrons.

Key Concepts

Atomic Number

The atomic number is a fundamental property of an element. It is the number of protons found in the nucleus of an atom. Each element on the periodic table has a unique atomic number, starting with hydrogen, which has an atomic number of 1. This number not only helps identify an element but also determines its position on the periodic table.

The atomic number is crucial when calculating the number of electrons in an atom or ion. For neutral atoms, the atomic number equals the number of electrons. However, for ions, the charge must be taken into account to find the total number of electrons:

• A positive charge implies the loss of electrons.
• A negative charge means a gain of electrons.

Understanding atomic numbers helps in exploring how different ions become isoelectronic, or having the same number of electrons.

Electron Configuration

Electron configuration describes how electrons are distributed in an atom's or ion's atomic orbitals. The order of filling these orbitals is dictated by principles such as the Aufbau principle and Hund's rule.

In a neutral atom, electrons fill orbitals starting from the lowest energy level to higher ones, following a specific sequence. When considering ions, electron configurations must adjust due to electron gain or loss:

• A cation (positive ion) results from losing electrons, affecting its configuration by removing electrons from the outermost orbitals.
• An anion (negative ion) forms when adding electrons, which then occupy the available orbitals according to existing configuration rules.

Isoelectronic species share identical electron configurations but differ in their atomic structures, often spanning different elements that have adjusted electron counts to match each other as ions.

Ionic Charge

The ionic charge of an atom refers to the difference between the number of protons and electrons. Protons have a positive charge, while electrons have a negative charge. By subtracting the negative charge from the positive, you get the ionic charge.

Here's how ionic charges affect ions:

• If an atom loses one or more electrons, it becomes a cation, having a positive charge. For instance, the potassium ion ( K^+ ) has lost one electron, resulting in a +1 charge.
• If an atom gains electrons, it becomes an anion, exhibiting a negative charge. For example, the chloride ion ( Cl^- ) gains one electron, giving it a -1 charge.

In exercises involving isoelectronic species, identifying the correct ionic charges is essential. By understanding ionic charges alongside atomic numbers and electron configurations, you can determine the electron count and see how ions of different elements can end up with equivalent electron configurations.