Which of the following involves maximum amount of energy ?

Options

A. `Ca(g) rarr Ca^(+) (g)`
B. `Ca^(+) (g) rarr Ca^(2+)(g)`
C. `Mg^(+)(g)rarrMg^(2+)(g)`
D. `Mg^(2+)(g) rarr Mg^(3+)(g)`

Answer

To determine which of the given options involves the maximum amount of energy, we need to analyze the changes in electronic configurations and the stability of the ions involved.

### Step-by-Step Solution:

1. **Identify the Elements and Their Atomic Numbers:**
- Calcium (Ca) has an atomic number of 20.
- Magnesium (Mg) has an atomic number of 12.

2. **Write the Electronic Configurations:**
- For Calcium (Ca):
- Ground state: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\)
- Ca⁺: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\)
- Ca²⁺: \(1s^2 2s^2 2p^6 3s^2 3p^6\) (stable noble gas configuration of Argon)
- For Magnesium (Mg):
- Ground state: \(1s^2 2s^2 2p^6 3s^2\)
- Mg⁺: \(1s^2 2s^2 2p^6 3s^1\)
- Mg²⁺: \(1s^2 2s^2 2p^6\) (stable noble gas configuration of Neon)
- Mg³⁺: \(1s^2 2s^2 2p^5\)

3. **Analyze the Energy Changes for Each Ionization:**
- **Ca to Ca⁺:** Energy is required to remove one electron from a stable configuration.
- **Ca⁺ to Ca²⁺:** Energy is required to remove another electron, but this is from a less stable configuration.
- **Mg to Mg⁺:** Energy is required to remove one electron from a stable configuration.
- **Mg⁺ to Mg²⁺:** Energy is required to remove another electron, leading to a stable configuration.
- **Mg²⁺ to Mg³⁺:** Energy is required to remove an electron from a stable configuration (Mg²⁺).

4. **Determine Which Transition Requires the Most Energy:**
- The transition from Mg²⁺ to Mg³⁺ involves removing an electron from a stable noble gas configuration (Neon) to a less stable configuration. This process requires the most energy because it disturbs the stable state.
- The other transitions (Ca to Ca⁺, Ca⁺ to Ca²⁺, Mg to Mg⁺, and Mg⁺ to Mg²⁺) involve removing electrons from configurations that are less stable compared to Mg²⁺.

5. **Conclusion:**
- The transition that involves the maximum amount of energy is **Mg²⁺ to Mg³⁺**.

### Final Answer:
The option that involves the maximum amount of energy is **Mg²⁺ to Mg³⁺**.