Atomic orbitals

Question 1

pauli principle

Answer 1

the Pauli principle states that two or more identical fermions cannot simultaneously occupy the same quantum state inside a quantum system.

Question 2

aufbau principle

Answer 2

filled in increasing energy

Question 3

Hunds rule

Answer 3

E- enter in empty orbitals before they pair up and share same orbital

Question 4

What is an orbital?

Answer 4

• Orbitals describe where the electrons can be found in the atom.
• The electrons behave like waves and so are spread out in the atom

Question 5

Can an orbital be considered as ?

Answer 5

They are wavefunctions, i.e. mathematical functions of x, y, z coordinates describing the waves

Question 6

The orbital wavefunctions are normally denoted by

Answer 6

The orbital wavefunctions are normally denoted by (x,y,z) or (x,y,z) #

Question 7

Electron density ()

Answer 7

• Regions where an electron is most likely to be found are said to have high electron density.
• Regions where an electron is unlikely to be found have low electron density.
  *

Question 8

the electron density at any location

Answer 8

The square of the orbital wavefunction gives the electron density at any location (x,y,z):
(x,y,z) = 2
(x,y,z)
*

Question 9

The probability of finding an electron in a small volume V at any location

Answer 9

The probability of finding an electron in a small volume V at any location (x,y,z) is:
P(x,y,z) = (x,y,z) V = 2
(x,y,z) V

Question 10

The quantum numbers tell us about:

Answer 10

(i) the energy of the orbital (larger n generally means higher energy)
(ii) the size of the orbital (larger n generally means a larger orbital)
(iii) the type of orbital (s, p, d, f)
(iv) the direction(s) in which an orbital points (i.e. the orientation of the orbital)

Question 11

The orbital energies in an H atom depend only

Answer 11

on the principal quantum number n #
* For an H atom, different orbitals with the same value of n have the same energy (they are

Question 12

s, p, d,f

Answer 12

• These types of orbital have different values of the orbital angular momentum quantum number

Question 13

shapes of orbitals

Answer 13

electron density is zero at nodes
* An angular node is a node encountered as we go around the orbital (e.g. from top to bottom)
* The number of angular nodes in the orbital is equal to the value of the l quantum number

Question 14

radial
distance

Question 15

angular
dependence

Question 16

graph types

Answer 16

the plots show the radial dependence R(r) of the orbitals and the radial distribution functions (RDFs)

Question 17

The RDFs

Answer 17

The RDFs show how the electron density varies with distance from the nucleus and are related to the
squares of the orbital wavefunctions #

Question 18

Shapes of atomic orbitals

Answer 18

The different radial dependence can be seen in the plots of 2p and 3p orbitals (not to scale)

The full shapes of atomic orbitals combine the radial and angular parts

Question 19

iso-surface

Answer 19

Instead we draw an iso-surface joining points of equal probability and enclosing say 90% of the electron density

Question 20

The 2s orbital always fills before the 2p orbital because

Answer 20

The 2s orbital always fills before the 2p orbital because in atoms with more than one electron, the 2s orbital is lower in energy than 2p

Question 21

Why is the 2s orbital lower than the 2p orbital in multi-electron atoms?

Answer 21

n atoms like Li, Be, B and C, the 1s orbitals are filled
and lie closest to the positively charged nucleus.
We refer to the filled 1s orbital as a core orbital and the
1s electrons as core electrons.
These core electrons shield electrons further out from
‘feeling’ some of the positive charge on the nucleus.
The RDFs show that a 2s electron has a greater
probability of penetrating through the 1s core than does
the 2p electron.
Hence, the 2s electron can spend some of its time inbetween the 1s electrons and the nucleus.
On average, a 2s electron feels a larger net positive
charge than a 2p electron and hence is lower in energy.
We say that the 2s electron feels a greater effective
nuclear charge (Zeff) than the 2p electron

Question 22

For the n = 3 orbitals, the energy ordering is 3s < 3p < 3d in multi-electron atoms

Answer 22

In atoms like Na, Mg, Al, Si, P, S, Cl, and Ar, the core
electrons are now in the filled 1s2
2s2
2p6
orbitals.
These filled core orbitals shield the 3s, 3p and 3d
electrons from some of the nuclear charge.
The 3s orbital penetrates through the core orbitals more
than the 3p, which in turn penetrates more than the 3d
orbital.
Hence the 3s electron feels a greater Zeff than 3p which in
turn feels a greater Zeff than 3d. The energy ordering is 3s < 3p < 3d.
Hence, the 3s orbital fills before the 3p which fills before
the 3d.