Question

\(\mathrm{IP}_{2}\) for an clement is invariably higher than \(\mathrm{IP}_{\mathrm{L}}\) because (1) The size of cation is smaller than its atom. (2) It is difficult to remove electron from cation. (3) Effective nuclear charge is more for cation. (4) All

Short answer

All the points (1, 2, and 3) explain why \(\text{IP}_{2}\) is higher than \(\text{IP}_{1}\).

Step-by-step solution

Understand Ionization Energy

Ionization energy (IP) is the energy required to remove an electron from an atom or ion.

Difference Between \(\text{IP}_{1}\) and \(\text{IP}_{2}\)

\(\text{IP}_{1}\) is the energy required to remove the first electron, while \(\text{IP}_{2}\) is the energy required to remove the second electron.

Relation Between Cation and Ionization Energy

After the first electron is removed, the atom becomes a cation. A cation has a higher effective nuclear charge which attracts the remaining electrons more strongly.

Smaller Size of Cation

The cation has a smaller atomic radius because it has fewer electrons. This increases the effective nuclear charge felt by the remaining electrons.

Difficulty in Removing Electron from Cation

Removing an electron from a cation is more difficult than from a neutral atom due to the increased effective nuclear charge.

Effective Nuclear Charge

Effective nuclear charge is the net positive charge experienced by electrons in an atom. For a cation, this charge is stronger.

Conclusion

All the points (1, 2, and 3) are correct and contribute to why \(\text{IP}_{2}\) is invariably higher than \(\text{IP}_{1}\).

Key concepts

Effective Nuclear Charge

The effective nuclear charge (ENC) is the net positive charge experienced by an electron in a multi-electron atom. This concept helps understand the attraction force between the nucleus and the electrons. Electrons in an atom are not only attracted to the protons in the nucleus but are also repelled by other electrons. This shielding effect reduces the actual positive charge that an electron feels.
The formula to express effective nuclear charge is:\[ Z_{\text{eff}} = Z - S \]where:

• Z: Total number of protons (atomic number)
• S: Average number of electrons between the nucleus and the electron in question (shielding or screening constant)

When an electron is removed, the remaining electrons experience a stronger ENC because there are fewer electrons to shield the nucleus. This explains why a cation, an atom that has lost one or more electrons, has a higher effective nuclear charge than its neutral counterpart. This increased attraction force makes it harder to remove another electron.

Cation Size

When an atom loses an electron and becomes a cation, its atomic radius decreases. This size reduction happens because the loss of an electron reduces electron-electron repulsion in the outer shells. Therefore, the remaining electrons are pulled closer to the nucleus due to the increased effective nuclear charge.
With a smaller atomic radius, the electrons are more tightly bound to the nucleus. This concentration of charge creates a stronger electrostatic force holding the remaining electrons. Hence, the smaller size of a cation compared to the neutral atom is a crucial reason why it requires more energy to remove additional electrons.
This concept also explains the trend in ionization energy across a period in the periodic table. As you move from left to right, atoms tend to gain more protons, increasing the overall nuclear charge, thus drawing electrons closer and reducing atomic size even before becoming cations.

Electron Removal Difficulty

Removing an electron from a cation is significantly more difficult than removing one from a neutral atom. This difficulty stems from the enhanced effective nuclear charge that remains after the first electron is removed. When the first electron is taken away, the atom becomes positively charged (a cation).
The cation form of an element has a higher effective nuclear charge, as mentioned previously. This means that the remaining electrons are held more tightly by the nucleus due to a stronger attraction force.
The reduced size of the cation also plays a role. The reduced distance between the remaining electrons and the nucleus results in a stronger electrostatic attraction, which requires more energy to overcome. Thus, it's evident why the second ionization energy (\(\text{IP}_{2}\)) is always higher than the first ionization energy (\(\text{IP}_{1}\)). This tendency highlights why concepts like effective nuclear charge and relative atomic and ionic sizes are fundamental to understanding ionization energies.