3.3

Question 1

Shrodingers equation

Answer 1

• The wavefunction for the electron
  -Electron’s trajectory as a function of position
  -Is the probability density for the electron

Now you can calculate the energy of all electrons!

Question 2

Quantum theory of Atoms

Answer 2

• Wavefunctions for electrons in atoms are called atomic
orbitals
• Each orbital describes the probability density
(electron density, electron distribution) for the
electron
• For hydrogen, energies (E) are the same as the Bohr
model
• Size, shape and orientation of each orbital are
determined be three integers called quantum numbers
✓principal quantum number, n _Level
✓orbital (angular momentum) quantum number, l_Shape
✓magnetic quantum number, ml_orientation

Question 3

Principle Quantum Number, n

Answer 3

Same as Bohr’s energy level
• Can be any integer  1
• The larger the value of n, the
higher the energy of the electron
• As n gets larger, energy
difference between orbitals gets
smaller
• Also called the electron shell or
electron level

Question 4

Orbital-l

Answer 4

Orbital quantum number (l) determines the shape of the orbital
✓ integer values from 0 to (n – 1)
✓ each value of l also designated by a letter
➢ l = 0: s orbital
➢ l = 1: p orbital
➢ l = 2: d orbital
➢ l = 3: f orbital
✓ orbitals with same n and lvalues also called electron subshell or electron sublevel
✓ number of sublevels in a givenlevel = n

Question 5

Magnetic Quantum - ml

Answer 5

Magnetic quantum number (ml) determines the orientation of the orbital
✓ integer values from –l to +l
✓ number of orbitals in a givensublevel = 2l + 1

Question 6

Plotting s Orbitals

Answer 6

y2 is maximum at nucleus, decrease
with increasing distance
• Isosurface: a 3D shape, where the
surface represents all points of a
particular value of the wavefunction
✓ 90% probability surface (electron is inside
90% of the time) is spherical

Question 7

The 3d Orbitals

Answer 7

• There are five 3d orbitals:
✓dxy, dyz, dxz, and dx2–y2 orbitals are
four-lobed
➢have 2 angular nodes that are planes
✓dz2, which is two-lobed with a toroid
➢has two nodal cones

Question 8

The 3p Orbitals

Answer 8

The 3p orbitals have one angular node
• And one spherical node

Question 9

The 2p Orbitals

Answer 9

Each of the three 2p orbitals point along a different axis
✓ 2px, 2py, 2pz
✓ do not exactly correspond to ml = -1, 0, +1
• Two-lobed
• Each 2p orbital has a nodal plane or angular node
✓ 2px: the yz-plane
✓ 2py: the xz-plane
✓ 2pz: the xy-plane

Question 10

Whaat i need to know

Answer 10

The 3D shapes of the s- and p-orbitals
✓for n = 1 to 5
• The 3D shapes of the 3d- and 4d-orbitals
• The possible values of n, l, and ml and the letter designations of l (s, p, d, f)
• The number angular nodes and spherical nodes for any given orbital
✓number of angular nodes = l
✓number of spherical nodes = n – l – 1
✓total number of nodes = n – 1
• Your new best friend is:

Question 11

Pauli Exclusion Principle

Answer 11

1925, Pauli Exclusion Principle: no two electrons
in an atom may have the same set of 4 quantum
numbers
• 2 electrons in same orbital have same values of
n, l, and ml → ms must differ
• An orbital can only hold 2 electrons, must have
opposite spins
• Maximum number of electrons in a sublevel:
✓s sublevel has 1 orbital →2 electrons
✓p sublevel has 3 orbitals →6 electrons
✓d sublevel has 5 orbitals →10 electrons
✓f sublevel has 7 orbitals →14 electrons