The successive ionization energies for element X is given below
`IE_(1)` : 250 kJ `"mo"^(-1)`
`IE_(2)` : 820 kJ `"mo"^(-1)`
`IE_(3)` : 1100 kJ `"mo"^(-1)`
`IE_(4)` : 1400 kJ `"mo"^(-1)`
Find out the number of valence electrons for the elements X.

Options

A. 3
B. 4
C. 2
D. 1

Answer

To determine the number of valence electrons for element X based on the given successive ionization energies, we can follow these steps:

### Step 1: Analyze the Ionization Energies
We have the following successive ionization energies for element X:
- \( IE_1 = 250 \, \text{kJ mol}^{-1} \)
- \( IE_2 = 820 \, \text{kJ mol}^{-1} \)
- \( IE_3 = 1100 \, \text{kJ mol}^{-1} \)
- \( IE_4 = 1400 \, \text{kJ mol}^{-1} \)

### Step 2: Calculate the Differences Between Successive Ionization Energies
Next, we calculate the differences between successive ionization energies to identify where a significant jump occurs:
- Difference between \( IE_1 \) and \( IE_2 \):
\[ IE_2 - IE_1 = 820 - 250 = 570 \, \text{kJ mol}^{-1} \]

- Difference between \( IE_2 \) and \( IE_3 \):
\[ IE_3 - IE_2 = 1100 - 820 = 280 \, \text{kJ mol}^{-1} \]

- Difference between \( IE_3 \) and \( IE_4 \):
\[ IE_4 - IE_3 = 1400 - 1100 = 300 \, \text{kJ mol}^{-1} \]

### Step 3: Identify the Significant Jump
From the differences calculated:
- The largest jump in ionization energy occurs between \( IE_1 \) and \( IE_2 \) (570 kJ/mol), while the differences between the subsequent ionization energies are much smaller (280 kJ/mol and 300 kJ/mol).

### Step 4: Conclusion on Valence Electrons
The significant increase in ionization energy indicates that after removing the first electron, the remaining electrons are held much more tightly. This suggests that element X has 1 valence electron. Therefore, the number of valence electrons in element X is:

\[ \text{Number of valence electrons} = 1 \]

### Summary
Element X has **1 valence electron**.

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