Final answer:
The correct screening constant for bromine using Slater's Rules should be 27.7, based on the contribution values from each group of electrons according to their respective shielding effect. Thus, the answer provided by the student, which was 28.9, was incorrect due to a miscalculation related to the contribution of the 4p electrons.
Step-by-step explanation:
The question concerns the calculation of the screening constant (also known as the Slater's constant) for a bromine atom using Slater's Rules. According to the rules, electrons in the same group and other electrons within the inner shells contribute differently to shielding. A potential oversight in the calculation occurs when attributing the shielding effect of the outermost electrons.
We know that bromine's electronic configuration is as follows: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁵. Applying Slater's Rules, we obtain contributions from different electrons to the screening constant as follows:
For 1s electrons: 2 (from 2 1s electrons)
For 2s and 2p electrons: 8 (from 2s² + 2p⁶)
For 3s and 3p electrons: 8 x 0.85 = 6.8 (from 3s² + 3p⁶)
For 4s and 3d electrons: 10 x 0.85 + 2 x 1 = 9.5 (from 4s² + 3d¹⁰)
For 4p electrons: 4 x 0.35 = 1.4 (from the four 4p electrons that are not the electron in question)
Adding these together:
2 + 8 + 6.8 + 9.5 + 1.4 = 27.7. Therefore, the correct screening constant for bromine should be 27.7, indicating the answer given in the student's materials is correct.