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Chapter 30: Problem 34

Which of the following subshell configurations are not allowed? For those that are not allowed, give the reason why. \((a) 3 s^{1}\) \(({b}) 2 {d}^{2}\) (c) 3\(s^{4} \quad\) (d) 4\(p^{8} \quad(\text { e }) 5 f^{12}\)

Short Answer

Expert verified
Configurations (b), (c), and (d) are not allowed due to subshell limitations.

Step by step solution

01

Understanding Subshells and Their Capacities

Each electron shell consists of subshells (s, p, d, f) with specific capacities. The s subshell can hold a maximum of 2 electrons, p can hold 6, d can hold 10, and f can hold 14 electrons.
02

Check Subshell Configuration (a)

For (a) 3\(s^{1}\), the 3s subshell can hold up to 2 electrons. Since it has only 1 electron, this configuration is allowed.
03

Check Subshell Configuration (b)

For (b) 2\(d^{2}\), the 2d subshell is non-existent as the second energy level only supports s and p subshells. Therefore, this configuration is not allowed.
04

Check Subshell Configuration (c)

For (c) 3\(s^{4}\), a maximum of 2 electrons can occupy the s subshell. Hence, with 4 electrons, this configuration is not allowed.
05

Check Subshell Configuration (d)

For (d) 4\(p^{8}\), the p subshell can hold a maximum of 6 electrons, so a configuration with 8 is not allowed.
06

Check Subshell Configuration (e)

For (e) 5\(f^{12}\), the f subshell can accommodate up to 14 electrons. Since it has 12, this configuration is allowed.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

s subshell
The "s subshell" is the simplest type of subshell found within electron shells. It is characterized by a spherical shape and can hold a maximum of 2 electrons. This is why configurations such as "3\(s^{1}\)" are allowed, as they fall under the 2-electron limit. The "s" in subshell implies simplicity, but it's vital to remember that each principal energy level begins by filling the s subshell first.
  • The first energy level (n=1) includes only the 1s subshell.
  • The second energy level (n=2) includes the 1s and 2s subshells.
However, when a configuration such as "3\(s^{4}\)" appears, it's immediately incorrect as the s subshell does not have the capacity to support 4 electrons, exceeding its limit by 2 electrons.
p subshell
The "p subshell" is more complex than the s subshell, capable of holding up to 6 electrons. The p orbitals are shaped like dumbbells and exist from the second energy level and beyond (not in the first energy level). This subshell gains three orbitals, each able to accommodate 2 electrons. So, configurations like "4\(p^{8}\)" are incorrect because they attempt to surpass the maximum of 6 electrons.Here's how the p subshell fits into electron configurations:
  • Energy levels n=2 and higher have p subshells.
  • Each level has 3 p orbitals.
Remember, reaching a configuration like "4\(p^{6}\)" accomplishes a full p subshell. Anything more than 6 leads to exceeding its accommodation capacity.
d subshell
When it comes to the "d subshell", it has the capacity to hold up to 10 electrons, making it more intricate than the s and p subshells. The d subshell begins appearing at the third principal energy level. There are 5 d orbitals, each capable of hosting 2 electrons.
  • d orbitals commence from energy level n=3
  • Each d subshell has 5 orbitals
A configuration like "2\(d^{2}\)" is flawed because the "d" subshells do not exist in the n=2 level at all. The correct manifestation of a filled d subshell configuration might be something like "3\(d^{10}\)", where the d subshell can accommodate up to 10 electrons fully.
f subshell
The "f subshell" is the most sophisticated, accommodating up to 14 electrons with its seven orbitals. The f subshells start to appear at energy levels n=4 and above, and as such, do not exist in the first three potential energy levels.These details are important for determining valid electron configurations:
  • An f subshell exists only from n=4 and above.
  • It consists of 7 orbitals.
Therefore, a configuration like "5\(f^{12}\)" is quite valid since it remains below the maximum threshold of 14 electrons. Anything beyond 14, however, is not feasible as it would overflow the f subshell's capacity.

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