Answer :
Sure! Let’s determine the effective nuclear charge (denoted as [tex]\( Z_{\text{eff}} \)[/tex]) for a [tex]\(2p\)[/tex] electron in a nitrogen atom step-by-step.
1. Start with the atomic number:
The atomic number ([tex]\( Z \)[/tex]) of nitrogen is 7. This means a nitrogen atom has 7 protons in its nucleus and 7 electrons surrounding it.
2. Identify the electrons in the inner shells:
The electron configuration of nitrogen is [tex]\( 1s^2 2s^2 2p^3 \)[/tex]. [tex]\(1s^2\)[/tex] represents the electrons in the innermost shell.
- The number of electrons in the [tex]\(1s\)[/tex] shell is 2. These are inner-shell electrons.
3. Determine the shielding effect:
- Electrons in the same shell (the [tex]\(2s\)[/tex] and [tex]\(2p\)[/tex] electrons) partially shield each other from the nucleus’s positive charge.
- Inner-shell electrons shield outer-shell electrons more effectively and are given a higher shielding constant.
For simplicity, we use typical shielding constants:
- Each inner-shell (1s) electron shields outer electrons by 0.35 (Slater’s rules).
- Each electron in the same shell contributes 0.85 towards shielding.
4. Calculate the total shielding effect:
- Inner-shell contribution: [tex]\( 2 \times 0.35 = 0.70 \)[/tex]
- Contribution from other electrons in the same shell (2s and 2p): Since there are 4 electrons in the n=2 shell (2 in 2s and 2 in 2p besides the electron we are considering), we get [tex]\( 4 \times 0.85 = 3.40 \)[/tex].
Total shielding effect = [tex]\( 0.70 + 3.40 = 4.10 \)[/tex].
5. Calculate the effective nuclear charge ([tex]\( Z_{\text{eff}} \)[/tex]):
[tex]\( Z_{\text{eff}} = Z - \text{Shielding effect} \)[/tex].
- Here, [tex]\( Z = 7 \)[/tex] and the shielding effect is 4.10.
Effective nuclear charge = [tex]\( 7 - 4.10 = 2.90 \)[/tex].
Therefore, the effective nuclear charge [tex]\( Z_{\text{eff}} \)[/tex] for a [tex]\(2p\)[/tex] electron in a nitrogen atom is approximately 2.90.
1. Start with the atomic number:
The atomic number ([tex]\( Z \)[/tex]) of nitrogen is 7. This means a nitrogen atom has 7 protons in its nucleus and 7 electrons surrounding it.
2. Identify the electrons in the inner shells:
The electron configuration of nitrogen is [tex]\( 1s^2 2s^2 2p^3 \)[/tex]. [tex]\(1s^2\)[/tex] represents the electrons in the innermost shell.
- The number of electrons in the [tex]\(1s\)[/tex] shell is 2. These are inner-shell electrons.
3. Determine the shielding effect:
- Electrons in the same shell (the [tex]\(2s\)[/tex] and [tex]\(2p\)[/tex] electrons) partially shield each other from the nucleus’s positive charge.
- Inner-shell electrons shield outer-shell electrons more effectively and are given a higher shielding constant.
For simplicity, we use typical shielding constants:
- Each inner-shell (1s) electron shields outer electrons by 0.35 (Slater’s rules).
- Each electron in the same shell contributes 0.85 towards shielding.
4. Calculate the total shielding effect:
- Inner-shell contribution: [tex]\( 2 \times 0.35 = 0.70 \)[/tex]
- Contribution from other electrons in the same shell (2s and 2p): Since there are 4 electrons in the n=2 shell (2 in 2s and 2 in 2p besides the electron we are considering), we get [tex]\( 4 \times 0.85 = 3.40 \)[/tex].
Total shielding effect = [tex]\( 0.70 + 3.40 = 4.10 \)[/tex].
5. Calculate the effective nuclear charge ([tex]\( Z_{\text{eff}} \)[/tex]):
[tex]\( Z_{\text{eff}} = Z - \text{Shielding effect} \)[/tex].
- Here, [tex]\( Z = 7 \)[/tex] and the shielding effect is 4.10.
Effective nuclear charge = [tex]\( 7 - 4.10 = 2.90 \)[/tex].
Therefore, the effective nuclear charge [tex]\( Z_{\text{eff}} \)[/tex] for a [tex]\(2p\)[/tex] electron in a nitrogen atom is approximately 2.90.
