Electronic configuration of an element 13 in the subsidiary energy level is

Analysis

The question asks for the electronic configuration of an element with an atomic number ($Z$) of 13. In chemistry, the atomic number represents the total number of protons (and electrons in a neutral atom). Therefore, we need to distribute 13 electrons into the various energy levels and subshells following the Aufbau principle.

Concept: The Aufbau Principle

The Aufbau principle states that electrons fill atomic orbitals in order of increasing energy levels. The order of filling is: $1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \dots$

• s-orbitals can hold a maximum of 2 electrons.
• p-orbitals can hold a maximum of 6 electrons.

Step-by-Step Solution

To find the configuration for $Z = 13$, we fill the orbitals until we reach a total of 13 electrons:

1. 1s orbital: Holds 2 electrons ($1s^2$). Remaining: $13 - 2 = 11$.
2. 2s orbital: Holds 2 electrons ($2s^2$). Remaining: $11 - 2 = 9$.
3. 2p orbital: Holds 6 electrons ($2p^6$). Remaining: $9 - 6 = 3$.
4. 3s orbital: Holds 2 electrons ($3s^2$). Remaining: $3 - 2 = 1$.
5. 3p orbital: Holds the final 1 electron ($3p^1$).

Putting it all together, we get: $1s^2 2s^2 2p^6 3s^2 3p^1$

Comparison with Options

• Option A: $1s^2 2s^2 2p^6 3s^2 3p^1$ (Total = 13) - Matches our calculation.
• Option B: $1s^2 2s^2 2p^4 3p^1 3s^1$ (Total = 10) - Incorrect.
• Option C: $1s^2 2s^2 2p^6 3s^2 3p^3$ (Total = 15) - Incorrect.
• Option D: $1s^1 2s^2 2p^6 3s^2 3p^4$ (Total = 15) - Incorrect.

Exam Tip

When writing electronic configurations, always remember the "2-8-3" rule for the main shells (K, L, M). For element 13, the shells are 2, 8, and 3. If you look at the subshells in Option A, the 3rd shell ($3s^2 3p^1$) contains $2 + 1 = 3$ electrons, which matches the valence electrons of Group 13 elements. This is a quick way to verify your answer!