Chapter 28, Problem 15P

To determine

Number of electrons.

Answer to Problem 15P

The answer is $\text{14}\text{electrons}$

Explanation of Solution

Given info: The principal quantum number $\text{n = 6}$

The orbital quantum number $l=3$

Formula used:

The principal quantum number $n$ can take on any integer value $\left(1,2,3,\mathrm{...}\right)$ and also, corresponds to the quantum number of the old Bohr theory. The orbital quantum number $l$ can take on values from $0$ to $\text{n-1}$ .

The magnetic quantum number, $m_l$ , can take on the integer values from $-l$ to $+l$

The spin quantum number, $m_s$ , can be $+\frac{1}{2}$ to $-\frac{1}{2}$

Calculation:

Note that the number of electrons in subshell will be easily determined by the value of $l$ .

For each $l$ , value of $m_l$ will range from $-l$ to $+l$ or $2l+1$ values.

Also, for each of these two values of $m_s$ . So, the total number for $l=3$ : $\text{N=}2\left(2l+1\right)$

Substitute all the values in expression $\text{N=}2\left(2l+1\right)$

  $\text{=}2\left[2\left(3\right)+1\right]$

  $\text{=14}\text{electrons}$

Conclusion:

The number of electrons is $14$ .