4: Electrons in atoms

Question 1

the wave equation

Answer 1

c=fλ

speed of light = frequency * wavelength
note frequency often written as v rather than f

Question 2

equation for energy of photons

Answer 2

E = hf or hv
h is Planck’s constant

Question 3

equation relating energy of photons to wavelength

Answer 3

combine c=fλ and E=hf
E = h (c/λ)
inversely proportional

Question 4

define atomic orbital

Answer 4

energy levels which electrons occupy

Question 5

each orbital can accommodate …

Answer 5

two electrons
spin up / spin down

Question 6

names of shells in order

Answer 6

K (1s)
L (2s, three 2p)
M (3s, five 3d, three 3p)

Question 7

describe photoelectron spectroscopy

Answer 7

measure energy levels of e- in atoms/molecules

photons (fixed frequency) ionise e- from sample, energy of these e- measured

energy of photon = energy of ionised e- + ionisation energy of e-

Question 8

how does quantum mechanics model an energy level?

Answer 8

as a wavefunction predicted by theory

Question 9

what is the Born interpretation of a wave function?

Answer 9

small box hovering in space - probability of finding an e- in here proportional to the SQUARE of wavefunction at this point
(greater value, greater prob)

Question 10

what is the square of the wave function known as?

Answer 10

the probability density

Question 11

probability of e- being in box = (eqn)

Answer 11

(wave function)^2 x volume of box

hence why wf^2 known as prob DENSITY
mass = density x volume

Question 12

what are spherical polar coordinates?

Answer 12

coordinates expressing position in space relative to nucleus
r (radius), θ (angle from z axis) and φ (angle from x axis)
angles are like latitude / longitude

Question 13

method to calculate the total probability of finding the e- at a set distance from the nucleus

Answer 13

image a thin spherical shell radius r

use probability eqn (prob in shell = wf^2 x vol shell)

Question 14

what is the radial distribution function (RDF)?

Answer 14

RDF = wf^2 x 4πr^2

where 4πr^2 is the eqn for the surface area of the sphere shell

Question 15

eqn prob e- in shell using RDF

Answer 15

prob = RDF x thickness of shell

bc shell assumed to be thin, so volume of shell = surface area x thickness
RDF = wf^2 x surface area

Question 16

what is the Bohr radius?

Answer 16

plot RDF vs radius for 1s orbital
from zero, peak at 53pm, tail to the right
maximum is the Bohr radius, the same as the lowest energy orbit in the Bohr model

Question 17

three quantum numbers

Answer 17

principle (n)
orbital angular momentum (l)
magnetic (ml)

Question 18

what does the principle quantum number determine, what values can it take?

Answer 18

positive integers n = 1, 2…
determines the ENERGY of the orbital

Question 19

equation for energy of the orbital

Answer 19

En = -R/(n^2)
where R is the Rydberg constant

note that energy is NEGATIVE, measured from energy of ionised e-

Question 20

letters for n=1, 2, 3

Answer 20

K, L, M shells

Question 21

values the orbital angular momentum number (l) can take

Answer 21

integers from n-1 to 0

eg. n=2, l=1,0

Question 22

letters representing l=0, l=1, l=2

Answer 22

s, p, d respectively
hence 2p, 3d etc

Question 23

what do n and l tell us about the orbital

Answer 23

its three-dimensional shape

Question 24

values the magnetic quantum number can take

Answer 24

integers from +l to -l

eg. l=1, m=1,0,-1

Question 25

what does m tell us

Answer 25

the orientation of the orbital in space

Question 26

describe 1s orbital in terms of n, l, m

Answer 26

K shell n=1
hence l=0 and m=0
hence only one orbital, wave function is spherical, RDF has a single maximum at Bohr radius

Question 27

describe the 2s orbital in terms of n, l and m

Answer 27

in the L shell with n=2
l can be 0,1 so for 2s, l=0 and m=0

Question 28

define radial node in terms of wave function

Answer 28

a radial node occurs where the wave function is zero

so graph wf vs radius crosses the x axis

Question 29

where is the radial node of the 2s orbital located?

Answer 29

graph wave function vs Bohr radii shows curve crosses x-axis (so wf=0) at 2 Bohr radii

Question 30

describe the general shape of 1s and 2s orbitals (actually all s orbitals)

Answer 30

m=0 for both so shape doesn’t depend on θ or Φ
l=0 so no angular nodes
only depends on radius so spherical

Question 31

describe 2p orbitals in terms of quantum numbers

Answer 31

n=2, l=1 so m= -1, 0, 1
hence three possible orbitals which depend on angles θ and Φ

Question 32

define nodal plane / angular node

Answer 32

a plane in which the wf=0 at some angle

Question 33

the wf of an orbital is the product of two parts, called…

Answer 33

the angular part (with angle θ)
the radial part (generally ne^-mr)

Question 34

the n=2 orbital wave functions have the same ___ part but different ___ parts

Answer 34

the same radial part (2s and all 2p)
but different angular parts (2p)

Question 35

T or F: in hydrogen, the 2s and three 2p orbitals have exactly the same energy

Answer 35

T, because energy depends only of the value of principle quantum number, n

Question 36

define degenerate

Answer 36

distinct orbitals which have the same energy

Question 37

in what case will the 2s and 2p orbitals be degenerate?

Answer 37

In H which only has one e- present, the L shell has 4 degenerate orbitals
but in atoms w more than 1 e-, they are not

Question 38

the general rules for # of radial and angular nodes

Answer 38

number of angular nodes (nodal planes) = l
number of radial nodes = n - l - 1

hence total number of radial and angular nodes is n-1

Question 39

how many 3d orbitals are there?

Answer 39

five.
n=3, l=2 (l=0 is 3s, l=1 is 3p), so m= -2, -1, 0, 1, 2
hence five total

Question 40

what is orbital approximation?

Answer 40

make a multi-electron atom like a one-electron atom

multiple e-‘s mean e-e- repulsion
hence alter the nuclear charge to Z(eff) from actual value to “effective” value

Question 41

what two things does changing Z(eff) do?

Answer 41

affects energy of orbitals
affects SIZE of orbitals (inversely)

Question 42

what does the energy of an orbital depend on?

Answer 42

1. Principle quantum number
2. Effective nuclear charge (actual nuclear charge and e-e- repulsion)

Question 43

what is screening?

Answer 43

basically the inner electrons blocking the outer electrons and influencing the effective nuclear charge experienced

Question 44

what does it mean when the 2s is said to be more penetrating than the 2p?

Answer 44

higher probability of the 2s electron being inside the air occupied by 1s, hence penetrating the screen and experiencing a greater nuclear charge

Question 45

in general the ordering of the orbitals depends on …

Answer 45

the degree of penetration
with lower value of l being more penetrating and hence lower in energy

Question 46

generally, the polarity of a bond depends on …

Answer 46

the relative energies of the atomic orbitals of the two atoms involved

generally the lowest energy will end up with the partial negative charge, more electronegative

ELECTRONEGATIVITY IS A CONSEQUENCE OF ORBITAL ENERGIES