unit_1_mod_1_atomic_structure_and_periodic_table.doc
-
Upload
pearl-lawrence -
Category
Documents
-
view
213 -
download
0
Transcript of unit_1_mod_1_atomic_structure_and_periodic_table.doc
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
1/20
ATOMIC STRUCTURE AND THE PERIODIC TABLE
Theoretical change with respect to Daltons atomic theory
1. In 1803, atomic theory was revived by John Daltona) matter is made up of tiny particles called atoms which cannot be created,
destroyed or split
b) all atoms of one element are identical:- same mass and same chemical
properties
c) a chemical reaction consists of rearranging atoms from one combination to
another.
d) When elements combine to form compounds, small whole numbers of atoms
form molecules.
However this was proved to be not entirely correct. Atoms have been spl
it as
well as created i.e. nuclear reactions. Also there are isotopes, meaning that not
all atoms of an element are identical.
Therefore theory was forced to CHANGE in regards to these observations
contradicting to the theory
put forward by Dalton.
The distribution of charge and mass in an atom
Particle Location Mass Charge
Electron Orbitals 1/1837 unit -1 unit
Proton Nucleus 1 unit +1 unit
Neutron Nucleus 1 unit 0
Atomic Structure page 1 of 20
A unit is one atomic mass unit = 1.67 x 10-27
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
2/20
Atomic Structure page 2 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
3/20
Terminology
Term
Definition
Atomic/proton number Number of protons in a nucleus of an atomNucleon/mass number Sum of the number of protons and neutrons in the
nucleus of an atom
Nuclide Any atomic species of which the proton number and
nucleon number are specified e.g. 126C and94B are
nuclides
Isotopes Nuclides of the same element or atoms of the same
element with different mass numbers
NB isotopes have the same chemical properties but
different physical propertiesRelative atomic mass Mass of an atom based on a scale such that the C-12
isotope has a mass of 12.00 units
relative atomic mass
= mass of 1 atom of an element x 12
mass of 1 atom of carbon-12
Atomic Structure page 3 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
4/20
Phenomenon of radioactivity
Radiation is the spontaneous decay of unstable atoms with the emission of either
alpha, beta or gamma radiation.
Alpha decay is a type ofradioactive decay in which anatomic nucleusemits an
alpha particle (two protons and two neutrons bound together into a particle
identical to a helium nucleus) and transforms (or 'decays') into an atom with a
mass number4 less andatomic number2 less.
For example:
although this is typically written as:
Beta decay is a type ofradioactive decay in which a fast moving ele
ctrons is
emitted. The new atom has no change in mass number but an atomic number
increases by 1.
Gamma rays orgamma-ray (denoted as ) are forms ofelectromagneticradiation(EMR) orlight emissions of a specific frequency produced from sub-
atomicparticle interaction, such aselectron-positron annihilationand
radioactive decay. There is no change in atomic or mass number of the atom.
Band of stability (n/p ratio)
Atomic Structure page 4 of 20
Most elements have isotopes. For stableisotopes, an interesting plot arises when
the number of neutrons is plotted versus
the number of protons.
Because the plot shows only the stable
isotopes, this graph is often called theNuclear Belt of Stability.
The plot indicates that lighter nuclides
(isotopes) are most stable when theneutron/proton ratio is 1/1. This is the
case with any nucleus that has up to 20protons.
As theatomic numberincreases beyond
20, a different trend becomesapparent. In this range, it appears that a
stable nucleusis able to accommodatemore neutrons. Stable isotopes have a
higherneutrontoprotonratio, rising to1.5/1 for elements having atomic
numbers between 20 and 83.
http://en.wikipedia.org/wiki/Radioactivityhttp://en.wikipedia.org/wiki/Radioactivityhttp://en.wikipedia.org/wiki/Atomic_nucleushttp://en.wikipedia.org/wiki/Atomic_nucleushttp://en.wikipedia.org/wiki/Atomic_nucleushttp://en.wikipedia.org/wiki/Alpha_particlehttp://en.wikipedia.org/wiki/Atomic_weighthttp://en.wikipedia.org/wiki/Atomic_numberhttp://en.wikipedia.org/wiki/Atomic_numberhttp://en.wikipedia.org/wiki/Radioactivehttp://en.wikipedia.org/wiki/Radioactivehttp://en.wikipedia.org/wiki/Gammahttp://en.wikipedia.org/wiki/Electromagnetic_radiationhttp://en.wikipedia.org/wiki/Electromagnetic_radiationhttp://en.wikipedia.org/wiki/Electromagnetic_radiationhttp://en.wikipedia.org/wiki/Electromagnetic_radiationhttp://en.wikipedia.org/wiki/Photonhttp://en.wikipedia.org/wiki/Atomhttp://en.wikipedia.org/wiki/Atomhttp://en.wikipedia.org/wiki/Atomhttp://en.wikipedia.org/wiki/Electron-positron_annihilationhttp://en.wikipedia.org/wiki/Electron-positron_annihilationhttp://en.wikipedia.org/wiki/Electron-positron_annihilationhttp://en.wikipedia.org/wiki/Radioactive_decayhttp://en.wikipedia.org/wiki/Radioactive_decayhttp://def%28%27/Glossary/glossaryterm.aspx?word=Graph%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Ratio%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Nucleus%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Atomic%20Number%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Atomic%20Number%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Atomic%20Number%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Nucleus%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Nucleus%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Neutron%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Neutron%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Neutron%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Proton%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Proton%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Proton%27,%20500,%20500);http://en.wikipedia.org/wiki/Atomic_nucleushttp://en.wikipedia.org/wiki/Alpha_particlehttp://en.wikipedia.org/wiki/Atomic_weighthttp://en.wikipedia.org/wiki/Atomic_numberhttp://en.wikipedia.org/wiki/Radioactivehttp://en.wikipedia.org/wiki/Gammahttp://en.wikipedia.org/wiki/Electromagnetic_radiationhttp://en.wikipedia.org/wiki/Electromagnetic_radiationhttp://en.wikipedia.org/wiki/Photonhttp://en.wikipedia.org/wiki/Atomhttp://en.wikipedia.org/wiki/Atomhttp://en.wikipedia.org/wiki/Electron-positron_annihilationhttp://en.wikipedia.org/wiki/Radioactive_decayhttp://def%28%27/Glossary/glossaryterm.aspx?word=Graph%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Ratio%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Nucleus%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Atomic%20Number%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Nucleus%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Neutron%27,%20500,%20500);http://def%28%27/Glossary/glossaryterm.aspx?word=Proton%27,%20500,%20500);http://en.wikipedia.org/wiki/Radioactivity -
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
5/20
Uses of radioisotopes
1. radiocarbon dating 2. smoke detectors
3. pacemakers 4. medical uses i.e. trac
ers or chemotherapy
5. irradiation in pest control
Calculations of relative atomic mass from isotopic data
Arof an element = sum of (abundances x mass number of all of the isotopes of
an element)
e.g.zirconium-90 51.5% zirconium-91 11.2% zirconium-92 17.1%
zirconium-94 17.4 % zirconium-96 2.8%
Arzirconium = (51.5 x 90) + (11.2 x 91) + (17.1 x 92) + (17.4 x 94) + (2.8 x 96)
= 9131.8
The average mass of these 100 atoms would be 9131.8 / 100 = 91.3 (to 3
significant figures).
91.3 is the relative atomic mass of zirconium.
Evidence of discrete energy levels using emission spectra
Atomic Structure page 5 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
6/20
An element's emission spectrum is the relative intensity ofelectromagnetic
radiation of each frequency it emits when it is heated (or more generally when it
is excited).
When the electronsin the elementare excited, they jump to higher energylevels. As the electrons leave the excited state and fall back down, energy is
emitted, the wavelength of which refers to the discrete lines of the emission
spectrum. If discrete energy levels were NOT present, no lines could EVER be
formed in an emission spectrum.
e.g. emission spectrum of hydrogen
Emission spectrum of hydrogen
When a gaseous hydrogen atom i
n its ground state is excited by an input of
energy, its electron is 'promoted' from the lowest energy level to one of higher
energy. The atom does not remain excited but re-emits energy aselectromagnetic radiation. This is as a result of an electron 'falling' from a higher
energy level to one of lower energy. This electron transition results in the release
of a photon from the atom of an amount of energy (E = h) equal to the
difference in energy of the electronic energy levels involved in the transition.
In a sample of gaseous hydrogen where there are many trillions of atoms all of
the possible electron transitions from higher to lower energy levels will take
place many times. A prism can now be used to separate the emitted
electromagnetic radiation into its component frequencies (wavelengths orenergies). These are then represented as spectral lines along an increasing
frequency scale to form an atomic emission spectrum.
Atomic Structure page 6 of 20
http://en.wikipedia.org/wiki/Electromagnetic_radiationhttp://en.wikipedia.org/wiki/Electromagnetic_radiationhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Light_emissionhttp://en.wikipedia.org/wiki/Heathttp://en.wikipedia.org/wiki/Electronshttp://en.wikipedia.org/wiki/Electronshttp://en.wikipedia.org/wiki/Chemical_elementhttp://en.wikipedia.org/wiki/Chemical_elementhttp://en.wikipedia.org/wiki/Electromagnetic_radiationhttp://en.wikipedia.org/wiki/Electromagnetic_radiationhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Light_emissionhttp://en.wikipedia.org/wiki/Heathttp://en.wikipedia.org/wiki/Electronshttp://en.wikipedia.org/wiki/Chemical_element -
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
7/20
Lyman series occurs when electrons drop from higher energy levels to the
ground state (n = 1), in this series, the most amount of energy is released and
thus the smallest wavelength and highest frequency. In the Balmer series, all
electrons drop to the n= 2 level, here energies released are not as high as in the
Lyman series. Remember energy is directly proportional to frequency butindirectly proportional
Note that within each series, the spectral lines get closer together with increasing
frequency. This suggests that the electronic energy levels get closer the more
distant they become from the nucleus of the atom.
No two elements have the same atomic emission spectrum; the atomic emission
spectrum of an element is like a fingerprint.
Atomic Structure page 7 of 20
Lyman series occurs when electrons drop
from higher energy levels to the ground
state (n = 1), in this series, the mostamount of energy is released and thus the
smallest wavelength and highest
frequency. In the Balmer series, all
electrons drop to the n= 2 level, here
energies released are not as high as in the
Lyman series. Remember energy is
directly proportional to frequency butindirectly proportional to wavelength.
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
8/20
Atomic orbitals
Quantum number Definition
First principal quantum number (n) This corresponds to the shell number
e.g. the 1st shell has n=1, 2nd shell has
n=2
1. Orbital volume of space in which there is a 95% chance of finding an
electron
2. Subshell a group of orbitals with the same energy i.e. they are
degenerate
e.g. 3p subshell which has 3 orbitals of the same energy
3. Shell a group of orbitals and/or subshells with the same principal quantumnumber. n =1 shell is called the K shell, n=2, the L shell, n=3 the M shell
etc.
Principal quantum number Types of orbitals/subshells present
in the shell
n=1 1s orbital
n=2 2s orbital and 2p subshell (which
contain THREE 2p orbitals)n=3 3s orbital, 3p subshell (THREE p
orbitals) and 3d subshell (FIVE d
orbitals)
The relative energies of s, p and d orbitals up to principal quantum
number 4
Note: The 4s orbital is LOWER than the 3d orbital. Therefore electrons will
enter the 4s orbital first before the 3d
Atomic Structure page 8 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
9/20
Shapes of atomic orbitals (s orbital and p orbital respectively)
Order of filling electrons in orbitals & sub-shells (electronic
configuration)
1s 2s 2p 3s 3p 4s 3d
Each orbital can hold only TWO electrons. Electrons
entering sub-shells
containing 2 or more orbitals enter and occupy the orbitals SINGLY
before pairing. An orbital of lower energy must be filled FIRST beforeelectrons enter an orbital of a higher energy level.
Element 1s 2s 2px 2py 2px 3s 3px 3py 3pz 4s 3d
1H 1
2He 2
3Li 2 1
4Be 2 2
5B 2 2 1
6C 2 2 1 1
7N 2 2 1 1 1
8O 2 2 2 1 1
9F 2 2 2 2 1
10Ne 2 2 2 2 211Na 2 2 2 2 2 1
19K 2 2 2 2 2 2 2 2 2 1
20Ca 2 2 2 2 2 2 2 2 2 2
Atomic Structure page 9 of 20
Remember for each p sub-
shell, there are 3 p orbitals in
x, y and z axis calledpx, py and pz. They are
perpendicular to each other.
They are of the same energy
level and are called
degenerate.
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
10/20
Element 1s 2s 2px 2py 2pz 3s 3px 3py 3pz 4s 3d
21Sc 2 2 2 2 2 2 2 2 2 2 1
22Ti 2 2 2 2 2 2 2 2 2 2 2
23V 2 2 2 2 2 2 2 2 2 2 324Cr* 2 2 2 2 2 2 2 2 2 1 5
25Mn 2 2 2 2 2 2 2 2 2 2 5
26Fe 2 2 2 2 2 2 2 2 2 2 5
27Co 2 2 2 2 2 2 2 2 2 2 7
28Ni 2 2 2 2 2 2 2 2 2 2 8
29Cu* 2 2 2 2 2 2 2 2 2 1 10
30Zn 2 2 2 2 2 2 2 2 2 2 10
* Indicates that the electronic configuration is not what is expected.
For Cr what would have been expected would be 3d
4 4s2, however, half
filled and totally filled shells/orbitals are very stable and thus more
preferred than any other configuration. Therefore the electrons half fill the
3d subshell with 5 electrons and half fill the 4s orbital with 1 electron.
For Cu, what would be expected was 3d
9 4s2, again the combination of atotally filled subshell and a half filled orbital is more stable than just a filled
orbital and a partly filled subshell. Therefore the electrons adopt the more
stable configuration.
Evidence of discrete energy levels using emission spectra
Based on information given above, it is shown that energy occupy different
orbitals or even-subshells and in essence occupy discrete energy levels.When elements undergo emission spectroscopy and produce an emission
spectrum, a series of lines are shown like the emission spectrum of hydrogen
shown below.
Atomic Structure page 10 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
11/20
But how are these lines explained and how do they show evidence of
discrete energy levels?
When the electronsin the elementabsorb energy, they move to higher energylevels and are no longer in the ground state (lowest energy state), they are
now in an excited state (state of higher energy). As the electrons release the
energy absorbed and leave the excited state to return to the ground state, the
excess energy is emitted, the wavelength of which refers to the discrete lines of
the emission spectrum. If discrete energy levels were NOT present, no lines
could EVERbe formed in an emission spectrum.
Emission spectrum of hydrogen
When a gaseous hydrogen atom in its ground state is excited by an input ofenergy, its electron is 'promoted' from the lowest energy level to one of
higher
energy (similar from moving from a lower rung in a ladder to a higher
rung). The atom does not remain excited but re-emits the excess energy as
electromagnetic radiation. This is as a result of an electron 'falling' from a higher
energy level to one of lower energy. This electron transition results in the release
of a photon from the atom of an amount of energy (E = hv) equal to the
difference in energy of the electronic energy levels involved in the transition.
Note E = energy, h = Plancks constant and v = frequency of wavelength ofradiation emitted
In a sample of gaseous hydrogen where there are many trillions of atoms all of
the possible electron transitions from higher to lower energy levels will take
place many times. A prism can now be used to separate the emitted
electromagnetic radiation into its component frequencies (wavelengths or
energies). These are then represented as spectral lines along an increasing
frequency scale to form an atomic emission spectrum.
Atomic Structure page 11 of 20
http://en.wikipedia.org/wiki/Electronshttp://en.wikipedia.org/wiki/Electronshttp://en.wikipedia.org/wiki/Chemical_elementhttp://en.wikipedia.org/wiki/Chemical_elementhttp://en.wikipedia.org/wiki/Electronshttp://en.wikipedia.org/wiki/Chemical_element -
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
12/20
In each spectra a group of lines are see together which is classified as a series.
There are 3 series which are of significance.
The Lyman series occurs when electrons drop from higher energy levels to the
ground state (n = 1), in this series, the most amount of energy is released andthus the smallest wavelength and highest frequency. This is why Lyman series
corresponds to the ultra-violet region (high energy)
The Balmer series occurs when electrons drop from higher energy levels to the
n = 2 level, here energies released are not as high as in the Lyman series. This
corresponds to the visible region of electromagnetic (EM) spectrum.
The Paschen series occurs when electrons drop from higher energy levels to then = 3 level. This corresponds to the infra-red region of electromagnetic (EM)
spectrum.
No two elements have the same atomic emission spectrum; the atomic
emission spectrum of an element is like a fingerprint.
Ionisation energy
It can be quoted more accurately as either 1st, 2nd, 3rd, 4th etc ionisation
energy. For our purposes, we will deal with the 1st ionisation energy.
The 1st ionisation energy is the energy required to remove a mole of
electrons from a mole of gaseous atoms to form a mole of gaseous
univalent ions. A (g) A+ (g) + e-
Trend of 1st ionisation energies
Ionisation energies
generally increase going across a period
Remember two factors must be considered: (1) proton number increases
sequentially going across a period i.e. greater nuclear attraction for the
outermost electron(s) and (2) number of electrons are also increasing.
Although the addition of electrons into the shell causes repulsion and thus
would increase the atomic radius, the predominant factor is the increasedeffective nuclear charge (which is the residual attraction of the nucleus
and the outermost electron(s) after shielding of the inner electrons) i.e. more
energy would be needed to remove the outermost electron(s). Thus
ionisation energy increases from left to right of a period
Atomic Structure page 12 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
13/20
Ionisation energies decreases going down a group
Although nuclear charge increases, the dominant factor is the increasing number
of shells between the nucleus and the outermost electron(s). This results in
increased shielding of the nuclear charge, therefore less attraction of the nucleusand the outermost electron(s) i.e. less energy needed to remove an outermost
electron. Thus ionisation energy decreases down a group.
Atypical behaviour seen in period 3 for Mg & Al AND P & S (period 3)
In period 3, Mg has E.C. of [Ne] 3s2, while Al has E.C. of [Ne] 3s2 3px1, in Al
the outermost electron (3p) is at a higher energy level than the outermost
electron in Mg (3s), therefore less energy is needed to remove it. Or using a
different explanation, the valence electron in Al experiences more shielding i.e.less nuclear attraction than one of the valence electrons in Mg i.e. less energy
needed to remove it from Al than for Mg.
In period 3 for P and S, the explanation needed is somewhat different. For P,
the E.C. is [Ne] 3s2 3p3, while for S the E.C. is [Ne] 3s2 3p4. In the 3p subshell of
P, the half-filled subshell represents a very stable configuration since it
represents a system of minimum repulsion as each electron occupies one orbital
singly. A lot of energy would be needed to disrupt this configuration. While in
S, 3p subshell experiences electron-electron repulsion in one of its orbital whichraises the energy of the system, therefore it is LESS stable and LESS energy
would be needed to remove one of the valence electrons.
Below is a diagram for the 1st ionisation energy of period 3 elements. Note
the circles show the areas of atypical behaviour
Atomic Structure page 13 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
14/20
Evidence of sub-shells using ionization data
The graph below shows the successive ionization energies for an atom of
sodium:
The electronic structure for sodium is 1s2 2s2 2p6 3s1.
The energy required to
remove the first electron is relatively low. This corresponds to the loss ofone 3s electron. To remove the second electron needs a much greater energy
because this electron is closer to the nucleus in a 2p orbital. There is a steady
increase in energy required as electrons are removed from 2p and then 2s
orbitals.
The removal of the tenth and eleventh electrons requires much greater
amounts of energy, because these electrons are closer to the nucleus in the 1s
orbital.
Large jumps in energy shown by the circles, indicate moving from one
principal quantum number to another. The smaller, more gradual increases
indicate going moving within subshells as the energies of the electrons will
slowly decrease resulting in more and more energy needed to remove them.
Atomic Structure page 14 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
15/20
How to derive group number of an element from successive ionization
energies
A large jump (usually an increase of 3 or more times the amount) between
two successive ionisation energies is typical of suddenly breaking in to an
inner level. You can use this to work out which group of the Periodic Table
an element is in from its successive ionisation energies.
Example 1 Magnesium (1s22s22p63s2) is shown with the following
successive ionisation energies:
Here the big jump occurs after the second ionisation energy. It means that
there are 2 electrons which are relatively easy to remove
(the 3s2 electrons),
while the third one is much more difficult (because it comes from an inner
level - closer to the nucleus and with less screening). Mg is therefore ingroup II
Example 2 Silicon (1s22s22p63s23px13py
1) is shown with the following
successive ionisation energies:
Here the big jump comes after the fourth electron has been removed. The
first 4 electrons are coming from the 3rd shell orbitals; the fifth from. Silicon
is therefore in group IV
To try on your own
Decide which group an atom is in if it has the following successive
ionisation energies:
END OF ATOMIC STRUCTURE
Atomic Structure page 15 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
16/20
Worksheet
1.Write the electronic configurations of the following atoms or ions
a) 20Ca..
b) 7N3-..
c) 26Fe2+..
d)29Cu..
2.
Atomic Structure page 16 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
17/20
3.
Atomic Structure page 17 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
18/20
Atomic Structure page 18 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
19/20
..
..
.
.
.
.
..
..
.
.
.
.
..
..
.
.
.
.
Atomic Structure page 19 of 20
-
7/30/2019 unit_1_mod_1_atomic_structure_and_periodic_table.doc
20/20
..
..
.
.
.
.
..
..
.
.
Atomic Structure page 20 of 20