Atomic Structure and the Periodic Table

Question 1

What is the Rydberg formula for the H atom

Answer 1

v = - c Ry (1/n(1)^2 - 1/n(2)^2)
where v = frequency
c = speed of light
Ry = rydberg constant
n(1) = quantum number of first energy level
n(2) = “ “ second energy level

Question 2

What is the Born Interpretation

Answer 2

wavefunction is amplitude of the wave
square of the modulus of the wavefunction is proportional to the probability density
the probability for a spherically symmetric orbital is the probability density x the volume element (4 pi r^2)

Question 3

what does separation of variables give for the wavefunction

Answer 3

the wavefunction expressed as a product of the radial wavefunction (n,l) and the angular wavefunction (l,m)

Question 4

What is a radial distribution function

Answer 4

P(r) = 4 pi r^2 x Ψ^2

for spherically symmetric (otherwise use the volume element, dτ)

Question 5

what is an angular node (nodal plane)

Answer 5

The planes or planar areas around the nucleus where the probability of finding an electron is zero

Question 6

what is a radial node

Answer 6

point where the radial wavefunction passes through zero such that there is no electron density at the node but there is surrounding it

Question 7

how many radial nodes does an orbital have?

Answer 7

nodes = n - l - 1

Question 8

how many angular nodes for l = 0

Answer 8

none

Question 9

how many angular nodes for l = 1

Answer 9

1

Question 10

how many angular nodes for l = 2

Answer 10

2

Question 11

how is the “boundary surface” of an orbital defined

Answer 11

the surface which contains the region for which there is a 90% probability of finding an electron

Question 12

what is the pauli (exclusion) principle

Answer 12

No two electrons in the same atom can have the same 4 quantum numbers: n,l,ml and ms

Question 13

what is hund’s rule

Answer 13

the ground state electronic configuration of an atom or ion has the maximum number of electrons with parallel spin

i.e. when filling degenerate orbitals, electrons are added with parallel spins before being paired

Question 14

what is the aufbau principle

Answer 14

building up the electronic configuration of atom is done by filling the lowest energy orbitals first

Question 15

what is the central field approximatiion

Answer 15

the total atomic wavefunction is written as a product of single-electron wavefunctions - i.e. each electron is thought of as moving in a purely central potential and having a wavefunction akin to hydrogenic orbital (experiencing Zeff)

Question 16

what is exchange energy

Answer 16

each pair of electrons with parallel spins leads to a lowering of the electronic energy of the atom

Question 17

What is multiplicity?

Answer 17

multiplicity is related to the number of unpaired electrons and is given by the expression 2S+1
where a pair of electrons with opposite spin has S=0 but if they have parallel spin in different orbitals S = 1

hund’s rule of maximum multiplicity states that the ground state of an atom will be the one having the greatest multiplicity

Question 18

what is the name for the ground states S = 0, 1/2, and 1

Answer 18

S = 0 is singlet
S = 1/2 is a doublet
S = 1 is a triplet etc

Question 19

What is the definition of electronegativity (Pauling)

Answer 19

the power of an atom when in a molecule to attract electrons (density) to itself

Question 20

put the orbitals in order of decreasing shielding ability

Answer 20

s > p > d > f

Question 21

what is the expression for the ionisation energy?

Answer 21

IE = (Zeff/n)^2

Question 22

what is “shielding”

Answer 22

Shielding is a consequence of electron-electron repulsion whereby electrons in different subshells prevent each other from experiencing the effect of the full nuclear charge, Z
This is as a result of the different penetrating abilities of different orbitals - the more penetrating an orbital, the less shielding it experiences

Question 23

give the formula of the rydberg formula for the H atom which includes the rydberg constant for the H atom

Answer 23

v = 1/λ = R(H) (1/nf^2 - 1/ni^2)

λ is wavelength
v is frequency
R(H) is rydberg constant for H atom
n(f) is the lower energy level
n(i) is the higher energy level

Question 24

what are the different series of the emission spectrum for hydrogen

Answer 24

wavelengths in different regions of the electromagnetic spectrum correspond to electronic transitions to different n(lower).
UV light: n=1, Lyman series
visible light: n=2, Balmer series (look for λ ~ 650 for n = 3 -> n=2 transition)
infrared light: n = 3, Paschen series

Question 25

define an atomic orbital

Answer 25

The atomic orbital is the solution to the Schrödinger equation for an electron in an atom, for which the square of the wavefunction is the probability density of finding an electron at a point in space surrounding the nucleus

Question 26

what is penetration in terms of orbitals