To determine the correct electron configuration for zinc, we need to consider the distribution of electrons in atomic orbitals according to the principles of quantum mechanics. Zinc has an atomic number of 30, which means it has 30 electrons.
Let's analyze each given option step-by-step:
1. First option:
[tex]\[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^8\][/tex]
- Summing the electrons:
[tex]\[
1s^2 = 2, \, 2s^2 = 2, \, 2p^6 = 6, \, 3s^2 = 2, \, 3p^6 = 6, \, 4s^2 = 2, \, 3d^8 = 8
\][/tex]
[tex]\[
2 + 2 + 6 + 2 + 6 + 2 + 8 = 28 \text{ electrons}
\][/tex]
- This adds up to 28 electrons, which is incorrect as zinc has 30 electrons.
2. Second option:
[tex]\[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1 \, 3d^{10}\][/tex]
- Summing the electrons:
[tex]\[
1s^2 = 2, \, 2s^2 = 2, \, 2p^6 = 6, \, 3s^2 = 2, \, 3p^6 = 6, \, 4s^1 = 1, \, 3d^{10} = 10
\][/tex]
[tex]\[
2 + 2 + 6 + 2 + 6 + 1 + 10 = 29 \text{ electrons}
\][/tex]
- This adds up to 29 electrons, which is incorrect as zinc has 30 electrons.
3. Third option:
[tex]\[1s^2 \, 2s^2 \, 2p^5 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10}\][/tex]
- Summing the electrons:
[tex]\[
1s^2 = 2, \, 2s^2 = 2, \, 2p^5 = 5, \, 3s^2 = 2, \, 3p^6 = 6, \, 4s^2 = 2, \, 3d^{10} = 10
\][/tex]
[tex]\[
2 + 2 + 5 + 2 + 6 + 2 + 10 = 29 \text{ electrons}
\][/tex]
- This adds up to 29 electrons, which is incorrect as zinc has 30 electrons.
4. Fourth option:
[tex]\[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10}\][/tex]
- Summing the electrons:
[tex]\[
1s^2 = 2, \, 2s^2 = 2, \, 2p^6 = 6, \, 3s^2 = 2, \, 3p^6 = 6, \, 4s^2 = 2, \, 3d^{10} = 10
\][/tex]
[tex]\[
2 + 2 + 6 + 2 + 6 + 2 + 10 = 30 \text{ electrons}
\][/tex]
- This adds up to 30 electrons, which is correct for zinc.
Therefore, the correct electron configuration for zinc is given in the fourth option:
[tex]\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \][/tex]
So, the correct choice is:
4
