The number of electrons present in all the completely filled subshells having n=4 and s=+½ is _____. (Where n = principal quantum number and s = spin quantum number).
Correct Answer: 16
Approach Solution - 1
To determine the number of electrons present in all the completely filled subshells with principal quantum number n=4 and spin quantum number s=+½, we first identify the available subshells for n=4. These are 4s, 4p, 4d, and 4f.
Each subshell can hold a specific number of electrons:
- 4s: 2 electrons
- 4p: 6 electrons
- 4d: 10 electrons
- 4f: 14 electrons
Next, since we are only interested in electrons with s=+½, we consider half of those in each subshell:
| Subshell | Total Electrons | Electrons with s=+½ |
|---|---|---|
| 4s | 2 | 1 |
| 4p | 6 | 3 |
| 4d | 10 | 5 |
| 4f | 14 | 7 |
Summing these, the total number of electrons with s=+½ is 1+3+5+7=16.
This value fits the expected range of 16,16, confirming its correctness. Therefore, the number of electrons in all completely filled subshells with n=4 and s=+½ is 16.
Approach Solution -2
For n = 4, the possible subshells and their electron capacities are:
So, the total number of electrons is 16.
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