To determine the noble gas configuration for chromium (Cr), we need to consider its electron arrangement.
Chromium has an atomic number of 24, which means it has 24 electrons. We use the Aufbau principle, Hund's rule, and the Pauli exclusion principle to fill up the atomic orbitals with these 24 electrons.
The order in which the orbitals are filled is given by the following sequence:
1. [tex]\(1s\)[/tex]
2. [tex]\(2s\)[/tex]
3. [tex]\(2p\)[/tex]
4. [tex]\(3s\)[/tex]
5. [tex]\(3p\)[/tex]
6. [tex]\(4s\)[/tex]
7. [tex]\(3d\)[/tex]
8. [tex]\(4p\)[/tex], and so on.
For the noble gas configuration, we start by acknowledging that Argon (Ar) has an atomic number of 18, so it signifies filling up to the 3p orbital. The configuration of Argon is:
[tex]\[ [Ar] = 1s^2 2s^2 2p^6 3s^2 3p^6 = 18 \text{ electrons} \][/tex]
Now, since Argon accounts for 18 electrons, we need to distribute the remaining 6 electrons in Chromium beyond Argon:
[tex]\[ 24 - 18 = 6 \text{ electrons} \][/tex]
Next, these 6 electrons will populate the 4s and 3d orbitals. According to the typical filling order, you would expect the electrons to fill as follows:
[tex]\[ 4s^2 \][/tex] would be filled first, and then the remaining electrons:
[tex]\[ 3d^4 \][/tex]
However, chromium is an exception due to the additional stability provided by a half-filled d-subshell. Therefore, one electron from the 4s orbital is promoted to the 3d orbital to achieve a more stable half-filled 3d subshell:
[tex]\[ 4s^1 \][/tex]
[tex]\[ 3d^5 \][/tex]
Thus, the actual noble gas configuration for chromium is:
[tex]\[ [Ar] 4s^1 3d^5 \][/tex]
Looking at the provided options:
1. [tex]\([Ar] 4s^2 3d^1\)[/tex] — This would be the configuration for an element with an atomic number 21 (Scandium).
2. [tex]\([Ar] 4s^2 3d^4\)[/tex] — This configuration does not reflect the correct filling for chromium and is not preferred.
3. [tex]\([Ar] 4s^2 3d^6\)[/tex] — This would be the configuration for an element with an atomic number 26 (Iron).
4. [tex]\([Ar] 4s^2 3d^9\)[/tex] — This would be the configuration for an element with an atomic number 29 (Copper).
Therefore, the correct noble gas configuration for chromium (Cr) is:
[tex]\[ [Ar] 4s^1 3d^5 \][/tex]
So, the answer is not listed among the given options, but the correct noble gas configuration is indeed:
[tex]\[ [Ar] 4s^1 3d^5 \][/tex]
