To determine the correct electron configuration for carbon, we should first recognize that carbon has an atomic number of 6, meaning it has 6 electrons. These electrons will fill the available atomic orbitals in the order of increasing energy levels according to the Aufbau principle.
Here’s a detailed breakdown of how the electrons fill the orbitals:
1. 1s Orbital: The first two electrons will occupy the 1s orbital. This orbital can hold up to 2 electrons.
[tex]\[
1s^2
\][/tex]
2. 2s Orbital: The next two electrons will fill the 2s orbital. This orbital also can hold up to 2 electrons.
[tex]\[
2s^2
\][/tex]
3. 2p Orbital: The remaining two electrons will go into the 2p orbital. The 2p subshell can hold a maximum of 6 electrons, but since carbon only has two more electrons left, they will occupy the 2p orbital.
[tex]\[
2p^2
\][/tex]
Putting all this together, the electron configuration for carbon is:
[tex]\[
1s^2 2s^2 2p^2
\][/tex]
Now let's examine each option to find the correct match:
A. [tex]\(1s^2 2s^2 2p^6\)[/tex] - This configuration has 10 electrons, which doesn't match the atomic number of carbon (6 electrons). Therefore, this option is incorrect.
B. [tex]\(1s^2 2s^2 2p^4\)[/tex] - This configuration has 8 electrons, which also does not match the atomic number of carbon. Thus, this option is incorrect.
C. [tex]\(1s^2 2s^2 2p^2\)[/tex] - This configuration correctly represents 6 electrons fitting within the described orbitals. This matches carbon’s atomic number, so this option is correct.
D. [tex]\(1s^2 2s^2\)[/tex] - This configuration only accounts for 4 electrons. Since carbon has 6 electrons, this option is incorrect.
Based on this detailed breakdown, the correct electron configuration for carbon (atomic number 6) is:
[tex]\[
\boxed{1s^2 2s^2 2p^2}
\][/tex]
Therefore, the correct answer is option C.
