Question

Statement-1 : For an element order of successive ionisation energy is \(\mathrm{IE}_{1}<\mathrm{IE}_{2}<\) \(\mathrm{IE}_{3}<\mathrm{IE}_{4} \ldots \ldots .\) Statement-2 : Removal of an electron from cation is difficult than neutral atom because effective nuclear charge increases. (1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (2) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1. (3) Statement-1 is True, Statement-2 is False. (4) Statement- 1 is False, Statement-2 is True.

Short answer

1

Step-by-step solution

Understanding Statement-1

Statement-1 asserts that for an element, the order of successive ionization energies is \(\text{IE}_1 < \text{IE}_2 < \text{IE}_3 < \text{IE}_4\ldots\ldots\). This indicates that each subsequent ionization energy is greater than the previous one.

Understanding Statement-2

Statement-2 states that removing an electron from a cation is more difficult than from a neutral atom because the effective nuclear charge increases. This suggests that as more electrons are removed, the remaining electrons are held more tightly by the nucleus.

Verifying the Truth of Statement-1

Successive ionization energies increase because each removal of an electron results in a cation with fewer electrons, leading to a stronger attraction between the nucleus and the remaining electrons. Thus, \(\text{IE}_n > \text{IE}_{n-1}\) is indeed true.

Verifying the Truth of Statement-2

As electrons are removed, the effective nuclear charge (the net positive charge experienced by an electron in a multi-electron atom) increases because the relative nuclear attraction per electron increases. Thus, it is true that removing an electron from a cation is more difficult than from a neutral atom.

Determining the Relationship Between Statements

Statement-2 explains the rationale behind the increasing trend of ionization energies described in Statement-1. The increase in effective nuclear charge makes it progressively harder to remove each successive electron.

Key concepts

Ionization Energy Order

Ionization energy refers to the amount of energy required to remove an electron from an atom or ion. As you move across a period in the periodic table, the ionization energies tend to increase. This trend occurs because the atomic number increases, meaning more protons are in the nucleus, creating a stronger attraction to electrons.

When discussing successive ionization energies (IE), such as \(\text{IE}_1, \text{IE}_2, \text{IE}_3, \text{IE}_4\)... we notice a specific order: \(\text{IE}_1 < \text{IE}_2 < \text{IE}_3 < \text{IE}_4\). This means that the energy needed to remove the first electron is less compared to the second, and so on.

This happens because after the first electron is removed, the resulting ion has a higher positive charge, which holds the remaining electrons more tightly. Therefore, more energy is needed to remove each subsequent electron. Remember, the sequence always follows \(\text{IE}_1 < \text{IE}_2 < \text{IE}_3 < \text{IE}_4\)..., making it progressively harder to detach more electrons from the atom.

Effective Nuclear Charge

Effective nuclear charge is an essential concept to understand why ionization energy increases. It refers to the net positive charge that an electron experiences in an atom's multiple-electron environment. The effective nuclear charge increases as electrons are removed because each remaining electron feels a stronger pull from the nucleus.

Here's why that's important:

• When an electron is removed, the positively charged nucleus stays the same, but the electron-electron repulsion decreases.
• As a result, the remaining electrons are pulled closer to the nucleus.
• This increased attraction is the effective nuclear charge—the pull felt by remaining electrons from the protons in the nucleus.

Knowing this helps in explaining why successive ionization energies are greater. Each removed electron enhances the nucleus's hold on the remaining electrons, requiring more energy to remove the next one.

Electron Removal Difficulty

Understanding electron removal difficulty is crucial for grasping ionization energy trends. As each electron is removed, the atom becomes more positively charged leading to greater difficulty in removing further electrons.

Let's break it down:

• Neutral Atom: Initially, removing an electron from a neutral atom is somewhat straightforward since the electron cloud and the nucleus have balanced charges.
• First Cation: After the initial electron is removed, the atom becomes a positively charged ion (cation). The remaining electrons are now more strongly attracted to the nucleus which increases removal difficulty.
• Subsequent Cations: Each additional electron removed further increases this difficulty because the effective nuclear charge grows with fewer electrons available to counterbalance the proton count.

Therefore, removing electrons from cations is progressively harder, aligning with the observed trend that \(\text{IE}_n > \text{IE}_{n-1}\). The effective nuclear charge amplifies this difficulty, ensuring that each successive ionization requires more energy than the previous one.