Chapter 7.7, Problem 2PE

Interpretation Introduction

Interpretation:

The total number of orbitals that are possible for given principal quantum number four has to be identified.

Concept introduction:

Principal Quantum Number(n): In an atom, the electron energy mainly depends on principal quantum number.  The energy of an electron becomes lower when the value of n is smaller.  The orbital size also depends on n.  The size of orbital increases with increase in value of principal quantum number (n).  It relates to distance between electron and nucleus in particular orbital.

Angular Momentum Quantum Number(l): It helps to differentiate different shapes of orbitals for given n.  For a given n, there are n different shapes of orbitals are present and are denoted as l.  Angular momentum quantum number is also known as Azimuthal quantum number.  The possible values of angular momentum quantum number is between $\text{0}\text{to}\text{(n-1)}$.  If the n is $3$, then l value is $0,1,2$

Magnetic Quantum Number(${\text{m}}_{\text{l}}$): It helps to distinguish orbitals having various orientation in space.  Any integer between $\text{-l,}\text{(-l+1),}\mathrm{..}\text{0,}\mathrm{..}\text{(+l-1)},\text{+l}$ is the probable values of magnetic quantum number.  For s subshell the $\text{l}\text{=}\text{0}$, then ${\text{m}}_{\text{l}}$ is zero.  For p subshell the $\text{l}\text{=}1$, then ${\text{m}}_{\text{l}}=-1,0,+1$. 

Spin Quantum Number(${\text{m}}_{\text{s}}$): It refers to direction of spin of an electron in an orbital.  The possible values are $\text{+}\frac{\text{1}}{\text{2}}\text{or}\text{-}\frac{\text{1}}{\text{2}}$.