Calculate Zeff for a valence electron in an oxygen atom. Express your answer numerically.
The Correct Answer and Explanation is:
To calculate the effective nuclear charge (Z_eff) for a valence electron in an oxygen atom, we need to follow these steps:
Step 1: Write down the relevant information
- Atomic number of Oxygen (Z) = 8
- Number of valence electrons = 6 (since oxygen is in Group 16 of the periodic table)
- Core electrons = 2 (since oxygen has a total of 8 electrons and the 2 electrons in the 1s orbital are the core electrons)
Step 2: Understand the concept of shielding
The shielding effect refers to how the inner electrons (core electrons) reduce the attraction between the nucleus and the valence electrons. The more core electrons there are, the more they “shield” the valence electrons from the full attractive force of the nucleus.
Step 3: Calculate Z_eff using the formula
The effective nuclear charge (Z_eff) can be approximated using the formula:Zeff=Z−SZ_{\text{eff}} = Z – SZeff=Z−S
Where:
- ZZZ is the atomic number (the total positive charge of the nucleus).
- SSS is the shielding constant, which is the extent to which the core electrons shield the valence electrons.
Step 4: Calculate the shielding constant
In the case of oxygen, we have 2 core electrons that shield the 6 valence electrons. According to Slater’s rules, the shielding constant for core electrons is approximately 0.85 per electron in the same shell.
- S (shielding constant) = 2 × 0.85 = 1.7.
Step 5: Substitute into the formula
Now we substitute the values into the equation:Zeff=8−1.7=6.3Z_{\text{eff}} = 8 – 1.7 = 6.3Zeff=8−1.7=6.3
Final Answer:
The effective nuclear charge ZeffZ_{\text{eff}}Zeff for a valence electron in an oxygen atom is 6.3.
Explanation:
The effective nuclear charge is a measure of the net positive charge felt by a valence electron. The valence electrons in an oxygen atom experience the full nuclear charge (8) but are shielded by the inner electrons (2 core electrons), which reduces the effective charge to 6.3. This means that the valence electrons feel a reduced attraction to the nucleus due to the shielding effect from the core electrons.
