QJEEM24Ch2514: JEE Main 2024 Chemistry - Class 11 JEEM24Ch2514 Solution: The number of electrons present in all the completely filled…

To determine the number of electrons with a spin quantum number of $s=+\frac{1}{2}$ in all completely filled subshells with principal quantum number $n=4$ , we must first identify the subshells in the n=4 shell and then calculate the electrons with the specified spin.

The n=4 shell has the following subshells and their capacity for electrons:

• $4s$ subshell can hold 2 electrons
• $4p$ subshell can hold 6 electrons
• $4d$ subshell can hold 10 electrons
• $4f$ subshell can hold 14 electrons

In quantum mechanics, each orbital within these subshells can hold 2 electrons, each with opposite spins ( $+\frac{1}{2}$ and $-\frac{1}{2}$ ). Thus, in a completely filled subshell, half of the electrons will have a spin quantum number of $+\frac{1}{2}$ :

• In $4s$ , 1 out of 2 electrons will have $s=+\frac{1}{2}$
• In $4p$ , 3 out of 6 electrons will have $s=+\frac{1}{2}$
• In $4d$ , 5 out of 10 electrons will have $s=+\frac{1}{2}$
• In $4f$ , 7 out of 14 electrons will have $s=+\frac{1}{2}$

Adding these together: $1 + 3 + 5 + 7 = 16$ electrons with $s=+\frac{1}{2}$ in all completely filled subshells with $n=4$ .