What is the effective nuclear charge (Z_eff) experienced by a 3p electron in phosphorus (atomic number 15)?

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Q: What is the effective nuclear charge (Z_eff) experienced by a 3p electron in phosphorus (atomic number 15)?

Solution: Using Slater's rules, Z_eff = Z - S. For P, Z = 15 and S = 8, so Z_eff = 15 - 8 = 7.

Steps: 7

Step 1: Identify the atomic number (Z) of phosphorus. For phosphorus, Z = 15.
Step 2: Determine the electron configuration of phosphorus, which is 1s² 2s² 2p⁶ 3s² 3p³.
Step 3: Identify the electron of interest, which is the 3p electron in phosphorus.
Step 4: Use Slater's rules to calculate the shielding constant (S) for the 3p electron. Count the number of electrons that shield the 3p electron.
Step 5: According to Slater's rules, the 1s and 2s/2p electrons contribute more to shielding than the same shell electrons. For phosphorus, S = 8.
Step 6: Calculate the effective nuclear charge (Z_eff) using the formula Z_eff = Z - S.
Step 7: Substitute the values: Z_eff = 15 (Z) - 8 (S) = 7.