If the energy needed to remove the 1st, 2nd and 3rd valence electron from an atom is V, 2V and 3V then the energy required to remove all three in one step will be xV. What is numerical value of x ?

Explanation

To solve the problem, we need to determine the total energy required to remove all three valence electrons from an atom in one step, given that the energies required to remove the first, second, and third electrons are V, 2V, and 3V, respectively.

### Step-by-Step Solution:

1. **Identify the Ionization Energies**:
- The energy required to remove the first electron (IE1) = V
- The energy required to remove the second electron (IE2) = 2V
- The energy required to remove the third electron (IE3) = 3V

2. **Understanding the Process**:
- When we remove the first electron, the atom becomes a cation (M → M⁺).
- Removing the second electron requires more energy because it is being removed from a positively charged ion (M⁺ → M²⁺).
- Removing the third electron requires even more energy as it is being removed from a doubly charged ion (M²⁺ → M³⁺).

3. **Calculate Total Energy for Removing All Three Electrons**:
- The total energy required to remove all three electrons in one step is the sum of the individual ionization energies:
\[ \text{Total Energy} = IE1 + IE2 + IE3 = V + 2V + 3V \]

4. **Perform the Addition**:
- Combine the energies:
\[ \text{Total Energy} = V + 2V + 3V = 6V \]

5. **Relate to xV**:
- The problem states that the total energy required to remove all three electrons in one step is xV. From our calculation, we found that:
\[ xV = 6V \]
- Therefore, we can equate and find x:
\[ x = 6 \]

### Final Answer:
The numerical value of x is **6**.