Quantum numbers

Question 1

What is the atomic theory in relation to quantum numbers?

Answer 1

The state (position and energy) of an electron can be described by a wave function composed of dimensionless parameters which equal the degrees of freedom.
		~The degrees of freedom of an electron = 4
~Thus, atomic theory states that the any electron in an atom can be completely described by 4 quantum numbers.

Question 2

What do the quantum numbers determine?

Answer 2

With the exception of the last quantum number ms (spin), the numbers determine the geometry and symmetry of the electron cloud.
~The electron cloud is a space around the nucleus in which the probability of finding an electron is high.

Question 3

Describe the Pauli Exclusion Principle

Answer 3

Pauli Exclusion Principle: no two electrons in a given atom can possess the same set of four quantum numbers. (i.e. each electron in a given atom has a unique set of quantum numbers and exist in the same quantum state)

Question 4

Describe the principle quantum number, n

Answer 4

Principle Quantum Number (n)
n = any positive integer 1, 2, 3, …
n describes the electron’s total energy and shell in which it can be found
~n = 1, 2, 3, 4, 5, 6, 7 corresponds to shell K, L, M, N, O, P, Q
The greater the value of n, the higher the energy level and radius of the electron’s orbit
Maximum # of e- in energy level (shell) n = 2n2

 *The difference in energy between two adjacent shells decreases with distance from the nucleus (1/n12 - 1/n22)
n= total energy electron
M= 9.11x10 -31
E0= 8.854x10 -12 FM-1
e= 1.6x10 -19 coloumbs

Question 5

Describe the orbital quantum number, l

Answer 5

Orbital Quantum Number (L)
For any given n, L is a number from 0 → n-1
It is determined by the angular momentum L where the magnitude of L =

Describes the subshell of the electron
Subshells s, p, d, f correspond to l values of 0, 1, 2, 3
Determines the shape of the orbital (s is spherical, p is bilobed, etc)
The max # of e- that can exist within a subshell = 4l + 2

Question 6

Describe the magnetic quantum number, ml

Answer 6

Magnetic Quantum Number (ml)
Possible values are –l to +l
~For any value of l, there will be 2l +1 possibilities of ml
ex: l=0, ssubshell, 1 possibility of ml → 1 orbital
ex: l=1, p subshell, 3 possibilities of ml → 3 orbitals (oriented in the x, y, and zaxes)
~For any value of n, there are n2 orbitals

Specifies the particular orbital within the subshell where an electron can be found
Determines the spatial orientation of the orbital
It also estimates the direction of vector L in an external magnetic field

Question 7

Describe the spin quantum number, s

Answer 7

Spin Quantum Number (ms)
+-1/2
Describes the spin of the electron due to its internal angular momentum (S)
In the presence of an external magnetic field, electrons orient themselves in one of two possible orientations corresponding to +-1/2
Two electrons within the same orbital must have opposite values of spin (paired e-)
~Parallel e- are electrons in different orbitals that possess the same value of ms

Question 8

Describe allowed and forbidden electron transitions

Answer 8

• Electron transitions may be probable or improbable (allowed vs. forbidden)
  ~allowed: transitions in which l changes by +-1
  ~forbidden: transitions in which l changes by more than +-1
  *During electron transitions n can vary arbitrarily