The value of second ionisation energy is than first ionisation energy.

Options

A. more
B. less
C. same
D. None of these

Explanation

To determine the relationship between the first and second ionization energies, let's analyze the concept step by step.

### Step 1: Understand Ionization Energy
Ionization energy is defined as the energy required to remove an electron from an isolated gaseous atom. The first ionization energy (IE1) refers to the energy needed to remove the first electron, while the second ionization energy (IE2) refers to the energy needed to remove a second electron after the first has already been removed.

**Hint:** Remember that ionization energy increases as you remove more electrons due to increased effective nuclear charge.

### Step 2: Consider the Example of Magnesium
Let's take magnesium (Mg) as an example. Magnesium has an atomic number of 12, which means it has 12 protons and, in its neutral state, 12 electrons. The electron configuration of magnesium is:
\[ \text{Mg: } 1s^2 2s^2 2p^6 3s^2 \]

**Hint:** Write down the electron configuration to visualize the arrangement of electrons in different shells.

### Step 3: First Ionization Energy (IE1)
When we remove the first electron from magnesium, we remove one electron from the outermost shell (3s). The resulting ion is Mg⁺, which has 12 protons and 11 electrons:
\[ \text{Mg} \rightarrow \text{Mg}^+ + e^- \]

**Hint:** After removing the first electron, note how many electrons remain and how many protons are still present.

### Step 4: Second Ionization Energy (IE2)
Now, to remove the second electron, we take it from the Mg⁺ ion. The configuration of Mg⁺ is:
\[ \text{Mg}^+: 1s^2 2s^2 2p^6 3s^1 \]
When we remove the second electron, we are left with Mg²⁺, which has 12 protons and 10 electrons:
\[ \text{Mg}^+ \rightarrow \text{Mg}^{2+} + e^- \]

**Hint:** Compare the number of protons to the number of electrons after the first ionization.

### Step 5: Analyze the Effective Nuclear Charge
After the first ionization, the effective nuclear charge experienced by the remaining electrons increases because the number of protons (12) remains the same, but the number of electrons has decreased to 11. This increased attraction makes it harder to remove the second electron.

**Hint:** Consider how the attraction between protons and electrons changes after each ionization.

### Step 6: Conclusion
Since the second ionization energy (IE2) involves removing an electron from an ion with a higher effective nuclear charge (more protons than electrons), it requires more energy than the first ionization energy (IE1). Therefore, we conclude that:
\[ \text{IE2} > \text{IE1} \]

**Final Answer:** The value of the second ionization energy is greater than the first ionization energy.