Question

(a) how many sub-shells are associated with $\mathrm{n}=4$? (b) how many electrons will be present in the sub-shells having ${\mathrm{m}}_{\mathrm{s}}$value of $-1/2\mathrm{for}\mathrm{n}=4?$

Answer 1

Orbital:

• An orbital is a function that describes the wave-like behaviour of an electron.
• An atomic orbital is a space where the probability of the electron is the highest

Subshell:

• A subshell is a pathway followed by the electrons moving within the shell.
• There are four types of subshells.$\mathrm{s},\mathrm{p},\mathrm{d},\mathrm{and}\mathrm{f}$are the subshells.

(a) Number of sub-shells associated with n = 4:

• A given value of $‘\mathrm{n}’,‘\mathrm{l}’$can have values from zero to $(\mathrm{n}–1).\mathrm{i}.\mathrm{e}.,0,1,2,3$
• The four sub-shells are associated with $\mathrm{n}=4$, are $\mathrm{s},\mathrm{p},\mathrm{d},\mathrm{and}\mathrm{f}.$
• Where,

$$\begin{gathered} \mathrm{l}=0:4\mathrm{s}-\mathrm{subshell} \\ \mathrm{l}=1:4\mathrm{p}-\mathrm{subshell} \\ \mathrm{l}=2:4\mathrm{d}-\mathrm{subshell} \\ \mathrm{l}=3:4\mathrm{f}-\mathrm{subshell} \end{gathered}$$

(b) The number of electrons in the sub-shells having an m_s value of -1/2 for n = 4:

• The number of orbitals will be $={\mathrm{n}}^2$
• The number of orbitals $=16.$
• Two electrons will go to each orbital with spins $-1/2\mathrm{and}+1/2$

∴ Hence the number of electrons having spin $-1/2$ will be$16.$