__Key Terms in this Particular Section include:__

__Quantum numbers __

Each orbital is characterized with a certain series of numbers

__Principle quantum number (____n__)

the quantum number relating to the size and energy of an orbital; it can have any positive integer.

__Angular momentum quantum number (____l____)__

the quantum number relating to the shape of an atomic orbital, which can assume an integral value from 0 to n-1 for each value of n

__Magnetic quantum number (____ml____) __

the quantum number relating to the orientation of an orbital in space relative to the other orbitals with the same l quantum numbers. It can have integral values between l and -l including zero.

__Subshell____ __

a set of orbitals with a given azimuthal quantum number.

__Electron spin __

the electron’s magnetic moment with two possible orientations when the atom is placed in an external magnetic field

__Electron spin quantum number __

__a quantum number representing one of the two possible values of the electron spin; either +½ or -½ __

__Pauli exclusion principle __

in a given atom, no two electrons can have the same set of four quantum numbers

__Descriptions of Quantum Numbers__

__Principal quantum number (____n____)__

- has any integer value starting from 1. This represents the principal energy level of the atom in which the electron is located=2 0and is related to the average distance of the electron from the nucleus. Angular momentum quantum number (l)

-designates the sublevel of the electron and also represents the shape of the orbitals in the sublevel. l may have any number from 0 up to 1 less than the current value of n. (l = 0, … n-1)

s → 0

p → 1

d → 2

f → 3

This chart shows the relationship between orbitals, angular momentum numbers and magnetic quantum numbers

__Magnetic quantum number (ml)__

any integer, including 0 from -l, to +l (ml = -l,…,0,…+l). This designates the orientation of an orbital in space. Spin quantum number (ms) -

may be either +½ or -½. This represents the “spin” of an electron. For electrons to pair up within an orbital, one electron must have a +½ value and the other a value of -½. This is required to satisfy the Pauli’s Exclusion Principle.

__Pauli’s Exclusion Principle__

No two electrons in the same atom may have the same four quantum numbers.

Relationship between the angular momentum number and the letters used to represent each.

Is the following set of quantum numbers allowed?

n=3, l=3, ml=0 ms=½

No. Because the maximum value of l is n-1=2. Therefore l cannot be 3. n=3 indicates that it’s in the third period. ml=0 is allowed because it is between -l and l. ms=½ shows that the electron has an upward spin.

__PRACTICE__

Is the following set of quantum numbers allowed?

n=1, l=0, ml=0 ms=½

(Answer: yes, because it is possible to have an s orbital at n =1. ml can always equal to 0 and ms is either +1/2 or -1/2.)

Is the following set of quantum numbers allowed?

n=3, l=2, ml=1 ms=0

(Answer: no because the spin can only be either positive or negative 1/2.)