The Nature of Light: Its Wave Nature

The Nature of Light: Its Wave NatureLight is a form of electromagnetic radiationmade of perpendicular waves, one for the electric field and one for the

magnetic field

All electromagnetic waves move through space at the same, constant speed 2.998 x 108 m/s in a vacuum = the speed of light, c

Characterizing Waves

The amplitude is the height of the wave the distance from node to crest or node to

trough

the amplitude is a measure of how intense the light is – the larger the amplitude, the brighter the light

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The wavelength () is a measure of the distance covered by the wave

the distance from one crest to the next (or the distance from one trough to the next, or the distance between alternate nodes)

For visible light, the wavelength is related to the color of light


The frequency () is the number of waves that pass a point in a given period of time

the number of waves = number of cycles

units are hertz (Hz) or cycles/second = s−1

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LIGHT!!!wavelength and frequency are proportional

wavelength frequency

wavelength and energy are proportional

wavelength energy

energy and frequency are proportional

energy frequency

Wavelength and Frequency

Wavelength and frequency of electromagnetic waves are inversely proportional

because the speed of light is constant, if we know wavelength we can find the frequency, and vice versa

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Calculate the wavelength of red light (nm) with a frequency of 4.62x1014 s−1

Calculate the wavelength (m) of a radio signal with a frequency of 106.5 MHz

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Color

The color of light is determined by its wavelength or frequency

White light is a mixture of all the colors of visible light a spectrumRedOrangeYellowGreenBlueViolet

When an object absorbs some of the wavelengths of white light and reflects others, it appears colored the observed color is predominantly the colors reflected

low frequency and energy

high frequency and energy

Electromagnetic waves are classified by their wavelengthRadio waves = > 0.01 m

4 2Microwaves = 1 10 m < < 1 10 m Infrared (IR)

5 4far IR = 1 10 m < < 1 10 m 6 5middle IR = 1 10 m < < 1 10 m

7 6near IR = 1 10 m < < 1 10 m 7 7Visible light = 4 10 m < < 8 10 m

.YO GR BIV

Ultraviolet (UV)7 7near UV = 2 10 m < < 4 10 m

8 7far UV = 1 10 m < < 2 10 m 10 8X-rays = 1 10 m < < 1 10 m

10Gamma rays = < 1 10 m

Types of Electromagnetic Radiation

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Interference

The interaction between waves is called interference

When waves interact so that they add to make a larger wave it is called constructive interferencewaves are in-phase

Interference

The interaction between waves is called interference

When waves interact so they cancel each other it is called destructive interferencewaves are out-of-phase

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Diffraction

When traveling waves encounter an obstacle or opening in a barrier that is about the same size as the wavelength, they bend around it – this is called diffractionTraveling particles do not diffract

https://www.youtube.com/watch?v=hRFQd_fkzws

The diffraction of light through two slits separated by a distance comparable to the wavelength results in an interference pattern of the diffracted waves

An interference pattern is a characteristic of all light waves

2-Slit Interference

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The Photoelectric Effect

Many metals emit electrons when a light shines on them. called the photoelectric effect

The Photoelectric Effect Many metals emit electrons when a light shines on them.

called the photoelectric effect

Classic wave theory said this effect was due to the light energy being transferred to the electron.

The energy of a wave is directly proportional to its amplitude and its frequency

If the wavelength of light is made shorter, more electrons should be ejected

Light waves’ intensity made brighter, more electrons should be ejected

Predicts that if a dim light were used there would be a lag time before electrons wereemitted to give the electrons time to absorbenough energy

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Experiments showed that a minimum energy was needed before

electrons would be emitted

called the binding energy, work function, or threshold frequency

no dependence on intensity

It was observed that high-energy light from a dim source caused

electron emission without any lag time


Einstein proposed that the light energy was delivered to the

atoms in packets, called quanta or photons

The energy of a photon of light is directly proportional to its

frequency and inversely to wavelength

the proportionality constant is called Planck’s Constant, (h) and

has the value 346.626 10 J sphoton

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Calculate the number of photons in a laser pulse with a wavelength of 337 nm and total energy 3.83 mJ

What is the frequency (MHz) of radiation required to supply 1.0x102 J from 8.5x1027 photons?

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One photon at the threshold frequency gives the electron just enough

energy for it to escape the atom

binding energy,

When irradiated with a shorter wavelength photon, the electron

absorbs more energy than is necessary to escape

This excess energy becomes kinetic energy of the ejected electron

1. No electrons would be ejected.

2. Electrons would be ejected, and they would have the same kinetic energy as those ejected by yellow light.

3. Electrons would be ejected, and they would have greater kinetic energy than those ejected by yellow light.

4. Electrons would be ejected, and they would have lower kinetic energy than those ejected by yellow light.

Suppose a metal will eject electrons from its surface when struck by yellow light. What will happen if the surface is struck with ultraviolet light?

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Spectra

When atoms or molecules absorb energy, that energy is often released

as light energy

fireworks, neon lights, etc.

When that emitted light is passed through a prism, a pattern of

particular wavelengths of light is seen that is unique to that type of

atom or molecule – the pattern is called an emission spectrum

non-continuous

can be used to identify the material

The Bohr Model of the Atom The energy of the atom is quantized, and the amount of energy in the atom is

related to the electron’s position quantized means that the atom could only have very specific amounts of energy

The electron’s positions within the atom (energy levels) are called stationary states Each state is associated with a fixed circular orbit of the electron around the nucleus. The higher the energy level, the farther the orbit is from the nucleus.

The first orbit, the lowest energy state, is called the ground state.

The atom changes to another stationary state only by absorbing or emitting a photon. Photon energy (h) equals the difference between two energy states.

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nucleus

Emission Spectra

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1234

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Which is a higher energy transition?

65 or 32

53 or 31

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Rydberg’s Spectrum Analysis

Rydberg developed an equation involved an inverse square of integers that could describe the spectrum of hydrogen.

low high2 2

1 1 1R

n n

What is the wavelength (nm) of light based on an electron transition from n = 4 to n = 2?

71.096776 10R

m

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Wave Behavior of Electronsde Broglie proposed that particles could have wave-like character

Predicted that the wavelength of a particle was inversely proportional to its momentum

Because an electron is so small, its wave character is significant

hλ =

mv

hcE =

2E = mc

2hc = mc

h

= mc

h = planks constant

J s2

2s

kg m

s

m = mass of particle v = velocity

kgm

s

What is the wavelength of an electron traveling at 2.65 x 106 m/s. (mass e– = 9.109x10–31 kg)

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Determine your wavelength if you are walking at a pace of 2.68 m/s. (1 kg = 2.20 lb)

The matter-wave of the electron occupies the space near the nucleus and is continuously influenced by it.

The Schrödinger wave equation allows us to solve for the energy states associated with a particular atomic orbital.

The square of the wave function () gives the probability density, a measure of the probability of finding an electron of a particular energy in a particular region of the atom.

Ψ ΨH E

2 2 2 2

2 2 2, , Ψ , , Ψ

8 e

hV x y z x y z E

m x y z

The Quantum Mechanical Model of the Atom

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Probability & Radial Distribution Functions

2 is the probability density the probability of finding an electron at a particular point in space decreases as you move away from the nucleus

The Radial Distribution function represents the total probability at a certain distance from the nucleusmaximum at most probable radius

Nodes in the functions are where the probability drops to 0

The probability density function represents the probability of finding an electron at a particular point in space

The Radial Distribution function represents the total probability at a certain distance from the nucleus

Probability Density Function

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The radial distribution function represents the totalprobability of finding an electron within a thin spherical shell at a distance r from the nucleus

The probability at a point decreases with increasing distance from the nucleus, but the volume of the spherical shell increases

The net result is a plot that indicates the most probable distance of the electron in a 1s orbital of H is 52.9 pm

Radial Distribution Functions

Solutions to the Wave Function,

Calculations show that the size, shape, and orientation in space of an

orbital are determined to be three integer terms in the wave function

These integers are called quantum numbers

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Characterizes the energy of the electron in a particular orbital and the size of that orbital

corresponds to Bohr’s energy level

n can be any integer 1

The larger the value of n, ______________________________the orbital has

The larger the value of n, ____________________________________ orbital

Greater relative distance from the nucleus

As n gets larger, the amount of energy between orbitals ___________________

Energies are ____________________________________________

an electron would have E = 0 when it just escapes the atom

Principal Quantum Number, n

Principal Quantum Number, n

• The energies of individual energy levels in the hydrogen atom (and therefore the energy changes between levels) can be calculated.

2

1nE hcR

n

What is the energy of a photon of light based on an electron transition from n = 4 to n = 2?

2 2

1 1

final initial

E hcRn n

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Principal Energy Levels in Hydrogen

Angular Momentum Quantum Number, l The angular momentum quantum number determines the shape of the orbital

l can have integer values from 0 to (n – 1)

Each l is called by a particular letter that designates the shape of the orbital

s (spherical) orbitals are spherical

p (principal) orbitals are like two balloons tied at the knots

d (diffuse) orbitals are mainly like four balloons tied at the knot

f (fundamental) orbitals are mainly like eight balloons tied at the knot

principal (n) quantum number possible angular momentum (l) quantum number(s)1

2

3

4

5

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Magnetic Quantum Number, ml

The magnetic quantum number is an integer that specifies the orientation of the orbital the direction in space the orbital is aligned relative to the other orbitals

Values are integers from _________________________ including zero

Gives the number of orbitals of a particular shapewhen l = 2, the values of ml are −2, −1, 0, +1, +2; which means there are five

orbitals with l = 2

l = 0, s Shaped Orbitals

Each principal energy level n 1 has one s shaped orbital

Lowest energy orbital in a principal energy state

Spherical

ml = _________

Number of nodes = (n – 1)

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2sn = 2,l = 0

3sn = 3,l = 0

2s and 3s

l = 1, p Shaped OrbitalsEach principal energy state n 2 has a set of three p orbitals

ml = _______________

Each of the three orbitals points along a different axis

px, py, pz

2nd lowest energy orbitals in a principal energy state

Two-lobed

One node at the nucleus, total of n nodes

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l = 1, p Shaped Orbitals

l = 2, d Shaped Orbitals

Each principal energy state n 3 has a set of five d orbitals ml = ____________________________

Four of the five orbitals are aligned in a different plane

the fifth is aligned with the z axis,

3rd lowest energy orbitals in a principal energy level

Mainly four-lobed one is two-lobed with a toroid

Planar nodes higher principal levels also have spherical nodes

2zd

2 2xy yz xz x yd , d , d , d

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l = 2, d Shaped Orbitals

l = 3, f Shaped Orbitals

Each principal energy state n 4 has a set of seven f orbitals

ml = ___________________________

4th lowest energy orbitals in a principal energy state

Mainly eight-lobed

some two-lobed with a toroid

Planar nodes

higher principal levels also have spherical nodes

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l = 3, f Shaped Orbitals

n

l

ml

Quantum Numbers Summary (for now…)

QUANTUMNUMBER CALLEDNAME WHAT

ALLOWEDVALUES

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Give the name, magnetic quantum numbers, and number of orbitals for each sublevel with the following quantum numbers:

(a) n = 3, l = 2

sublevelname

possible ml

valuesnumber of

orbitals

(b) n = 2, l = 0

(c) n = 5, l = 1

(d) n = 4, l = 3

Quantum Numbers

Electron Sub-Levels

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Spin Quantum Number, ms

The spin quantum number for electrons is a half-integer that specifies the direction of electron spin in the orbital.

Spin is a fundamental property of all electrons and all electrons have the same amount of spin. Property of the electron, not the orbitalNot included in Schrödinger’s equation

The orientation of the electron spin is quantized, it can only be either ___________________________

Values are ________________________________!

Each electron in any atom is described completely by a set of four quantum numbers n, l, ml describe the orbital

ms describes the electron spin in the orbital

Pauli’s exclusion principle states that no two electrons in the same atom can have the same four quantum numbers.

An atomic orbital can hold a maximum of two electrons and they must have opposing spins.

n = 3, l = 2 (d) possible ml – 2, –1, 0, +1, +2

each of these can hold two electrons of opposite spin

Quantum Numbers: n, l, ml , and ms

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The number orbitals in a sublevel determines the maximum number of electrons in the sublevel:

Quantum Numbers: n, l, ml , and ms

s sublevel (l = ), has orbital (ml = ); therefor it can hold electrons ( )

p sublevel (l = ), has orbitals (ml = ); therefor it can hold electrons

d sublevel (l = ), has orbitals (ml = ); therefor it can hold electrons

f sublevel (l = ), has orbitals (ml = ); therefor it can hold e–

g sublevel (l = ), has orbitals (ml = ); therefor it can hold electrons

For hydrogen atoms, all orbitals within a principal energy level (n) have the same energy.

Orbitals with the same energy are called degenerate

Hydrogen’s single electron bouncing around doesn’t have a lot of options of where to jump and where to fall, so not very many spectral lines (only four in the visible range).

Add even ONE more electron and things get ugly.

Proton-electron interactions are essentially the only things affecting the energy of the orbitals within the principal energy levels

Energy Levels of Electrons in the Hydrogen Atom

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Multielectron Systems

Schrödinger’s equation calculations for multielectron atoms cannot be exactly solved.

Approximate solutions show the orbitals to be “hydrogen-like”Now have to worry about electron-electron interactionsCauses energy splitting of the sublevels

Multielectron Systems In general, energies of sublevels increase as n increases (1 < 2 < 3…) In general, energies of sublevels increase as l increases (s < p < d < f). As n increases, some sublevels overlap.

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The aufbau principle: electrons are always placed in the lowest energy sublevel available. (doesn’t always work so well)

The Pauli exclusion principle: each orbital may contain a maximum of 2 e– , which must have opposite spins.

Hund’s rule: when orbitals of equal energy are available, the lowest energy electron configuration has the maximum number of unpaired electrons with parallel spins.

Orbital Box Diagrams

available orbitals ml =


next lowest energy l =

lowest energy l =

next lowest energy n =


lowest energy l =

lowest energy n =

Follow aufbau, Pauli, and Hund to fill boxes (orbitals) with arrows (electrons)

orbital box diagram for: nitrogen!

Quantum #s for last e–?


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lowest energy n =

lowest energy l =



lowest energy l =





orbital box diagram for: Ne! Quantum #s for last e–?


lowest energy n =

lowest energy l =



lowest energy l =





lowest energy l =





orbital box diagram for: chlorine! Quantum #s for last e–?


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Follow aufbau, Pauli, and Hund to fill boxes (orbitals) with arrows (electrons)orbital box diagram for: iron!


lowest energy l = lowest energy n =


next lowest energy n = lowest energy l =

available orbitals ml = next lowest energy l =


next lowest energy n = lowest energy l =

available orbitals ml = next lowest energy l =


nl


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Follow aufbau, Pauli, and Hund to fill boxes (orbitals) with arrows (electrons)26 electrons


orbital box diagram for: iron! Quantum #s for last e–?

next lowest energy n = next lowest energy l =


lowest energy n = 1lowest energy l = 0 (s)

available orbitals ml = 0next lowest energy n = 2

lowest energy l = 0 (s)available orbitals ml = 0

next lowest energy l = 1 (p)available orbitals ml = –1, 0, +1

next lowest energy n = 3lowest energy l = 0 (s)

available orbitals ml = 0next lowest energy l = 1 (p)

available orbitals ml = –1, 0, +1next lowest energy n =

lowest energy l = available orbitals ml =

1s0

2s0

2p–1 0 +1

3s0

3p –1 0 +1

Electron Configuration

1s0

2s0

2p–1 0 +1

3s0

3p –1 0 +1

4s0

3d–1 0 +1–2 +2

electron configuration for: iron!


orbital box diagram for: iron! 26 electrons

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4s0

3d–1 0 +1–2 +2

[Ar]

electron configuration for: iron!

Electron ConfigurationFollow aufbau, Pauli, and Hund to fill boxes (orbitals) with arrows (electrons)

orbital box diagram for: iron! 26 electrons

Orbital Box DiagramsFollow aufbau, Pauli, and Hund to fill boxes (orbitals) with arrows (electrons)

orbital box diagram for: copper!lowest energy n =

lowest energy l =available orbitals ml =

next lowest energy n =lowest energy l =

available orbitals ml =next lowest energy l =

available orbitals ml =next lowest energy n =

lowest energy l =available orbitals ml =

next lowest energy l =available orbitals ml =

next lowest energy n =lowest energy l =

available orbitals ml =next lowest energy n =

next lowest energy l =available orbitals ml =

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Multielectron Systems

The energies of atomic orbitals are affected by

nuclear charge (Z)

A higher nuclear charge increases nucleus-electron

interactions and lowers sublevel energy.

Multielectron Systems The energies of atomic orbitals are affected by shielding by other electrons Reduces the full nuclear charge to an effective nuclear charge (Zeff). Electrons in same energy level have a small effect on Zeff

Each electron added to an energy level decreases effect of added proton

Z for H = 1, Zeff in 1s = 1.00 100%

, Zeff in 1s = 1.688Z for He = 2 84.4%

Increase

Z for Li = 3, Zeff in 2s = 1.279

, Zeff in 2s = 1.912Z for Be = 4 4.36%

, Zeff in 2s = 2.576Z for B = 5 3.16%

, Zeff in 2s = 3.217Z for C = 6 1.66%

, Zeff in 2s = 3.847Z for N = 7 1.01%

, Zeff in 2s = 4.492Z for O = 8 0.94%

, Zeff in 2s = 5.128Z for F = 9 0.63%

, Zeff in 2s = 5.758Z for Ne = 10 0.43%

51.89%

55.04%

56.71%

57.72%

58.66%

59.28%

59.72%

47.53%

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Multielectron Systems The energies of atomic orbitals are affected by shielding by other electrons Reduces the full nuclear charge to an effective nuclear charge (Zeff). Each energy level between nucleus and outer electrons has large effect

Change

Z for Rb = 37, Zeff in 1s = 36.208

, Zeff in 2s = 27.157Z for Rb = 37 –24.46%

, Zeff in 3s = 21.843Z for Rb = 37 –14.36%

, Zeff in 4s = 12.388Z for Rb = 37 –25.55%

, Zeff in 5s = 4.985Z for Rb = 37 –20.01%

73.40%

59.04%

33.48%

13.47%

97.86%

Multielectron Systems The energies of atomic orbitals are affected by shielding by other electrons Reduces the full nuclear charge to an effective nuclear charge (Zeff). Each energy level between nucleus and outer electrons has large effect

Change perproton

Z for H = 1, Zeff in outer (1s) = 1.000

, Zeff in outer (2s) = 1.279Z for Li = 3 0.1395

, Zeff in outer (3s) = 2.507Z for Na = 11 0.1535

, Zeff in outer (4s) = 3.495Z for K = 19 0.1235

, Zeff in outer (5s) = 4.985Z for Rb = 37 0.0828

42.63%

22.79%

18.39%

13.47%

100%

PercentZeff

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Multielectron SystemsThe energies of atomic orbitals are affected by nuclear charge (Z) A higher nuclear charge _____________ nucleus-electron attractions and __________

energy.

The closeness to the nucleus ___________ nucleus-electron attractions and __________ energy

shielding by other electrons Shielding by other electrons reduces the full nuclear charge to an effective nuclear charge

(Zeff), which ___________ nucleus-electron attractions and __________ energy

Zeff is _________________________________________________________

________________________________________________________________

Effective Nuclear Charge

Moving left to right across the periodic table Adding electrons increases electron repulsion, __________________ to the nucleus (Zeff)

Adding protons increases attraction, ___________________ to the nucleus (Zeff)

In general, increased _________and attraction to the nucleus (Zeff) gets bigger left to right

Moving down the periodic table Adding shells between outer electrons and nucleus increases shielding, ______________

_______________ to the nucleus (Zeff)

Adding protons increases attraction, ___________________ to the nucleus (Zeff)

Increased ______________and attraction to the nucleus (Zeff) gets smaller top to bottom

Effective nuclear charge explains most of periodic trends

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Periodic Trends: Atomic Radii

Moving left to right across the periodic table

Attraction of electrons to nucleus (Zeff) increases, pulling them in more tightly.

Moving down the periodic table

Attraction of electrons to nucleus (Zeff) decreases, holding them more loosely.


THESE ARE JUST TRENDS!!!

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Using the periodic trend for atomic radii, put each of the following groups in order if decreasing atomic radius

Ca, Mg, Sr K, Ga, Ca Br, Rb, Kr Sr, Ca, Rb

Periodic Trends: Ionization Energy Ionization energy: the energy required to completely remove a single electron from

an atom or ion in the gas phase. Typically give in kJ/mol

Each IE is for the removal of a single electron Ca Ca+ + 1 e– IE1

Ca+ Ca2+ + 1 e– IE2

Ca2+ Ca3+ + 1 e– IE3

Each e– is harder to remove than the previous IE3 > IE2 > IE1

Atoms with a low IE tend to form cations.

Atoms with a high IE tend to form anions except the noble gases

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Periodic Trends: Ionization Energy

Moving left to right across the periodic table Attraction of electrons to nucleus (Zeff) increases, holding electrons more tightly (harder to remove).

Moving down the periodic table Attraction of electrons to nucleus (Zeff) decreases, holding them more loosely (easier to remove).


THESE ARE JUST TRENDS!!!

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Using the periodic trend for ionization energy, put each of the following groups in order if decreasing first ionization energy

Kr, He, Ar Sb, Te, Sn K, Ca, Rb I, Xe, Cs

Periodic Trends: Successive Ionization Energies

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Periodic Trends: Successive Ionization Energies

Name the Period 3 element with the following ionization energies (in kJ/mol)

IE1 IE2 IE3 IE4 IE5 IE6

1012 1903 2910 4956 6278 22,230

Periodic Trends: Electron Affinity

Electron Affinity is the energy change involved in adding one

electron to gaseous atom or ion.

Typically give in kJ/mol

Mostly negative values for first EA

The more negative the EA, the more favorable it is to add an e–.

Atoms with a low EA tend to

Atoms with a high EA tend to

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Moving left to right across the periodic table EA generally gets more negative (larger value), so mostly

Moving down the periodic table EA generally gets less negative (smaller value), so mostly


• NO, SERIOUSLY, THESE ARE JUST TRENDS!!!

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Reactive nonmetals have high IEs and highly negative EAs. Attract electrons strongly and tend to form negative ions in ionic compounds.

Reactive metals have low IEs and slightly negative EAs. Lose electrons easily and tend to form positive ions in ionic compounds.

Noble gases have very high IEs and slightly positive EAs.Tend to neither lose nor gain electrons.

Ionization Energy and Electron Affinity

Periodic Trends: Ionic RadiusMoving left to right across the periodic table Cations: Formed by the loss of electron(s) but maintain the number of protons, so cations

are SMALLER than the original neutral atom, and ions get SMALLER LEFT TO RIGHTdue to increasing Zeff.

Anions: Formed by the gain of electron(s) but maintain the number of protons, so anions are LARGER than the original neutral atom, but ions still get SMALLER LEFT TORIGHT due to increasing Zeff.

Moving down the periodic table For both cations and anions, ionic radius INCREASES TOP TO BOTTOM due to

decreasing Zeff.

For an isoelectric series (same electron configuration), ionic radius decreaseswith increasing number of protons

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Periodic Trends: Ionic Radius

METALS

Typically shiny solids

Moderate to high melting points

Good conductors of heat

Good conductors of electricity

Malleable and ductile

Tend to lose electrons to form cations

Easily oxidized and are generally strong reducing agents.

NONMETALS

Typically dull if solid

Really low to really high melting points

Poor conductors of heat

Do not conduct electricity

Brittle if solid

Tend to gain electrons to form anions

Easily reduced and are generally strong oxidizing agents.

Periodic Trends: Metallic Behavior

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Periodic Trends: Metallic BehaviorMoving left to right across the periodic table Elements cross over from being metals to being nonmetals, so

Moving down the periodic table Elements lower ionization energies, so

Periodic Trends

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The Nature of Light: Its Wave Nature

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