The first four successive ionization energies for an element are 6 , 113 , 11.871, 50.908,67.01 (in eV) respectively . The number of velence shell electrons is ____ .

Answer

To determine the number of valence shell electrons from the given ionization energies, we can follow these steps:

### Step 1: Analyze the Ionization Energies
The first four successive ionization energies provided are:
- \( IE_1 = 6 \, \text{eV} \)
- \( IE_2 = 11.3 \, \text{eV} \)
- \( IE_3 = 11.871 \, \text{eV} \)
- \( IE_4 = 50.908 \, \text{eV} \)
- \( IE_5 = 67.01 \, \text{eV} \)

### Step 2: Identify the Trend
Ionization energies generally increase as electrons are removed because the effective nuclear charge experienced by the remaining electrons increases. This means that the energy required to remove each successive electron should be higher.

### Step 3: Look for Large Gaps
When there is a significant jump in the ionization energy values, it indicates that the electron being removed is from a new, more stable electron shell (core electrons).

### Step 4: Compare the Values
From the values given:
- The increase from \( IE_1 \) to \( IE_2 \) is \( 11.3 - 6 = 5.3 \, \text{eV} \)
- The increase from \( IE_2 \) to \( IE_3 \) is \( 11.871 - 11.3 = 0.571 \, \text{eV} \)
- The increase from \( IE_3 \) to \( IE_4 \) is \( 50.908 - 11.871 = 39.037 \, \text{eV} \)

### Step 5: Determine the Number of Valence Electrons
The large jump in ionization energy between \( IE_3 \) and \( IE_4 \) indicates that after removing three electrons, the next electron removed is from a much more stable inner shell. Therefore, the first three ionization energies correspond to the removal of valence electrons.

### Conclusion
Thus, the number of valence shell electrons for the element is **3**.

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