Potassium has the greatest difference between its first and second ionization energies among potassium, calcium and gallium, so the correct option is (a) Potassium. This large jump is directly linked to its noble-gas-like electron configuration after losing one electron.​

Introduction

Understanding the difference between the first and second ionization energies of elements like potassium, calcium and gallium is crucial for mastering periodic trends and cracking exams such as NEET, JEE and other competitive tests. These differences reveal how electronic configuration controls the energy needed to remove successive electrons from an atom.​

Concept of first and second ionization energy

The first ionization energy (IE₁) is the energy required to remove the first electron from a gaseous neutral atom, forming a +1 ion. The second ionization energy (IE₂) is the energy needed to remove a second electron from the resulting +1 ion, forming a +2 ion, and is always higher than IE₁ because the electron is being removed from a positively charged ion with stronger attraction to the nucleus.​

For comparing “difference between first and second ionization energies”, one evaluates IE₂ − IE₁ for each element and relates it to the stability of the configuration obtained after the first ionization.​

Data for K, Ca and Ga (numerical check)

From ionization-energy data:​

• Potassium (K):

  • IE₁ = 418.8 kJ/mol

  • IE₂ = 3052 kJ/mol

  • Difference = 3052 − 418.8 ≈ 2633 kJ/mol (very large jump)

• Calcium (Ca):

  • IE₁ = 589.8 kJ/mol

  • IE₂ = 1145.4 kJ/mol

  • Difference = 1145.4 − 589.8 ≈ 556 kJ/mol (moderate increase)

• Gallium (Ga):

  • IE₁ = 578.8 kJ/mol

  • IE₂ = 1979.3 kJ/mol

  • Difference = 1979.3 − 578.8 ≈ 1401 kJ/mol (large, but less than K)

Clearly, K has the greatest IE₂ − IE₁ difference among the three.​

Electron configurations and reasoning

• Potassium (K, Z = 19):

  • Ground state: [Ar]4s1[Ar]4s1.​

  • After first ionization (K → K⁺): configuration becomes $[Ar]$, a noble gas core, which is extremely stable; removing a second electron now means disturbing this closed-shell configuration, so IE₂ becomes very high and the jump IE₂ − IE₁ is huge.​

• Calcium (Ca, Z = 20):

  • Ground state: [Ar]4s2[Ar]4s2.​

  • Ca → Ca⁺ (IE₁): removes one 4s electron, leaving [Ar]4s1[Ar]4s1, which is not a noble-gas configuration; Ca⁺ → Ca²⁺ (IE₂) removes the second 4s electron, giving $[Ar]$, so both IE₁ and IE₂ correspond to removing valence 4s electrons and the increase from IE₁ to IE₂ is relatively modest.​

• Gallium (Ga, Z = 31):

  • Ground state: [Ar]3d104s24p1[Ar]3d104s24p1.​

  • Ga → Ga⁺ (IE₁): usually removes the single 4p electron.

  • Ga⁺ → Ga²⁺ (IE₂): removes a 4s electron; after IE₂, configuration approaches [Ar]3d104s1[Ar]3d104s1, which is more stable than Ga but still not a noble gas; thus the jump IE₂ − IE₁ is significant but smaller than the “core-breaking” jump seen in K.​

The enormous jump in potassium occurs because after losing one electron it already has a noble-gas configuration, so the second electron must be taken from an inner (core) shell, requiring much more energy.​

Option-by-option explanation

Option (a) Potassium

Potassium shows the greatest difference IE₂ − IE₁ because IE₁ removes the lone 4s valence electron to give a very stable $[Ar]$ core, while IE₂ must remove a core electron from this closed-shell configuration. As a result, IE₂ is extremely high compared to IE₁, giving a difference of about 2633 kJ/mol.​

Therefore, option (a) Potassium is correct.

Option (b) Calcium

In calcium, both IE₁ and IE₂ involve removal of valence 4s electrons: first from [Ar]4s2[Ar]4s2 to [Ar]4s1[Ar]4s1, then from [Ar]4s1[Ar]4s1 to $[Ar]$. Since neither step removes a core electron and screening is similar, the increase from IE₁ to IE₂ is moderate (difference ≈ 556 kJ/mol), not the highest among the three.​

Thus, option (b) Calcium is incorrect.

Option (c) Gallium

Gallium’s IE₁ removes a 4p electron and IE₂ removes a 4s electron, so there is a sizeable increase in ionization energy and IE₂ − IE₁ is larger than in calcium. However, Ga⁺ after IE₁ does not yet have a noble-gas configuration, and IE₂ still removes a valence electron rather than a true core electron, so the jump is smaller than in potassium (≈ 1401 kJ/mol versus ≈ 2633 kJ/mol).​

Thus, option (c) Gallium is also incorrect.

Option (d) All have the same difference as they are in the same row

Even though K, Ca and Ga lie in the same period (period 4), the differences between successive ionization energies depend strongly on their individual electron configurations, not simply on their position in a row. Since the numerical differences IE₂ − IE₁ are clearly unequal (K >> Ga > Ca), the statement that “all have the same difference” is false.​

Therefore, option (d) is incorrect.

Quick summary table (for revision)

Hence, among potassium, calcium and gallium, potassium has the greatest difference between its first and second ionization energies, making option (a) the correct answer.​