Which of the following has the largest ionisation energy.

Options

A. `._(11)Na`
B. `._(19)K`
C. `._(12)Mg`
D. `._(37)Rb`

Explanation

To determine which of the given elements has the largest ionization energy, we can follow these steps:

### Step 1: Identify the Elements and Their Groups
The options provided are:
1. Sodium (Na) - Group 1
2. Potassium (K) - Group 1
3. Rubidium (Rb) - Group 1
4. Magnesium (Mg) - Group 2

### Step 2: Determine the Periods of Each Element
- Sodium (Na) is in Period 3.
- Potassium (K) is in Period 4.
- Rubidium (Rb) is in Period 5.
- Magnesium (Mg) is in Period 3.

### Step 3: Understand the Trend of Ionization Energy
- **Down a Group**: As you move down a group in the periodic table, the size of the atom increases due to the addition of electron shells. This increase in size leads to a decrease in ionization energy because the outermost electrons are further from the nucleus and are less tightly held.
- **Across a Period**: As you move from left to right across a period, the size of the atom decreases due to the increasing positive charge of the nucleus, which pulls the electrons closer. This results in an increase in ionization energy.

### Step 4: Compare the Elements
- **Rubidium (Rb)**: Being in Group 1 and Period 5, it has the lowest ionization energy among the options because it is the largest atom.
- **Potassium (K)**: Also in Group 1 but in Period 4, it has a higher ionization energy than rubidium but still lower than sodium and magnesium.
- **Sodium (Na)**: In Group 1 and Period 3, it has a higher ionization energy than both potassium and rubidium.
- **Magnesium (Mg)**: In Group 2 and Period 3, it has a higher ionization energy than sodium because it is smaller in size compared to sodium.

### Step 5: Conclusion
Based on the trends observed:
- Rubidium has the lowest ionization energy.
- Potassium has a higher ionization energy than rubidium.
- Sodium has a higher ionization energy than potassium.
- Magnesium has the highest ionization energy among the four elements because it is in the same period as sodium but belongs to Group 2.

Thus, the element with the largest ionization energy is **Magnesium (Mg)**.

### Final Answer
**Option C: Magnesium (Mg)** has the largest ionization energy.

---