Periodic Properties of the Elements Your Turn 7.1 Estimate the approximate effective nuclear charge of scandium. Would you expect scandium’s valence electrons to be held more or less tightly than those of potassium? Use electron configurations to justify your answer.
The Correct Answer and Explanation is:
Correct Answer:
The approximate effective nuclear charge (Z_eff) of scandium (Sc) is about +3.
Scandium’s valence electrons are held more tightly than those of potassium.
Explanation (Approx. 300 words):
To estimate the effective nuclear charge (Z_eff), we use the formula:
Z_eff = Z − S
Where:
- Z is the atomic number
- S is the shielding or screening constant (approximate number of core electrons)
Scandium (Sc) has an atomic number of 21. Its electron configuration is:
1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹
The electrons in the n = 1, 2, and 3 shells (that is, 1s through 3p) are considered core electrons. These add up to:
2 (1s²) + 2 (2s²) + 6 (2p⁶) + 2 (3s²) + 6 (3p⁶) = 18 core electrons
So, Z = 21 and S ≈ 18, giving:
Z_eff ≈ 21 − 18 = +3
This effective nuclear charge is experienced by scandium’s outermost electrons, primarily the 4s² and 3d¹ electrons. Since Z_eff is relatively high, these valence electrons are attracted more strongly by the nucleus.
Now, compare this with potassium (K), atomic number 19. Its configuration is:
1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹
Potassium has 18 core electrons as well (same as scandium), so:
Z_eff ≈ 19 − 18 = +1
This means potassium’s single 4s electron experiences a much weaker nuclear pull than scandium’s valence electrons. As a result, scandium’s valence electrons are held more tightly than those of potassium.
This is consistent with periodic trends. Across a period, effective nuclear charge increases, and electrons are held more tightly. Therefore, scandium (to the right of potassium in Period 4) holds its valence electrons more strongly.
