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Chemistry is all around us

Everything you hear, see, smell, taste, and touch involves chemistry and chemicals (matter).

And hearing, seeing, tasting, and touching all involve intricate series of chemical reactions and interactions in

your body…(acs.org)

In more formal terms chemistry is the study of matter and the changes it can undergo.

What is matter?

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What is matter composed of?

What are atoms made of?

What are protons, neutrons, and electrons made of?

https://phet.colorado.edu/sims/html/build-an-atom/latest/build-an-atom_en.html

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Democritus (c. 460–c. 370 B.C.) proposed that matter was made of discrete indivisible particles. He called his particles atomon,

meaning "cannot be cut."

His ideas were largely ignored until the scientific revolution of

the 16th, 17th, and 18th centuries.

The Atom

Lavoisier 1774 - Law of conservation of mass:The total mass of substances present after a chemical reaction is the same as the total mass of substances before the reaction

Proust 1799 - Law of definite proportions:All samples of a compound have the same composition-the same proportions by mass of the constituent elements.

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Conservation of Mass

Each element is composed of small particles called atoms.

Atoms are neither created nor destroyedin chemical reactions.

All atoms of a given element are identical.

Compounds are formed when atoms of more than one elementcombine.

Dalton’s Atomic Theory

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While atoms were thought to be indivisible, that all changed when J(oseph) J(ohn) Thomson (1856–1940) discovered the electron in 1897.

Ernest Rutherford (1871–1937) showed that the electrons occupied a region of space surrounding the tiny nucleus.

Figuring out just how those electrons behaved required the development of quantum mechanics, a theory in which electrons are treated as wavelike.

Radioactivity

Radioactivity is the spontaneous emission of radiation from a substance.

X-rays and g-rays are high-energy light.

a-particles are a stream of helium nuclei,

He2+.

b-particles are a stream of high speed

electrons that originate in the nucleus.

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2-3 The Nuclear Atom

Geiger and Rutherford1909

The a-particle experiment

Most of the mass and all of the positive charge is concentrated in a small region called the nucleus .

There are as many electrons outside the nucleus as there are units of positive charge on the nucleus

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The Nuclear Atom

Rutherfordprotons 1919

James Chadwickneutrons 1932

Atomic Diameter 10-8 cm Nuclear diameter 10-13 cm

Nuclear Structure

1 Å

Particle Mass Electric Charge

kg amu Coulombs (e)Electron 9.1094 10-31 0.00054858 –1.6022 10-19 –1Proton 1.6726 10-27 1.0073 +1.6022 10-19 +1Neutron 1.6749 10-27 1.0087 0 0

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Scale of Atoms

Useful units:

1 amu (atomic mass unit) = 1.66054 10-27 kg

1 pm (picometer) = 1 10-12 m

1 Å (Angstrom) = 1 10-10 m = 100 pm = 1 10-8

cm

The heaviest atom has a mass of only 4.8 10-22 gand a diameter of only 5 10-10 m.

Biggest atom is 240 amu and is 50 Å across.

Typical C-C bond length 154 pm (1.54 Å)

Molecular models are 1 Å /inch or about 0.4 Å /cm

EM Radiation

Low

High

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Frequency, Wavelength and Velocity

• Frequency () in Hertz—Hz or s-1.

• Wavelength (λ) in meters—m.

• cm m nm Ă pm

(10-2 m) (10-6 m) (10-9 m) (10-10 m) (10-12 m)

• Velocity (c)—2.997925 108 m s-1.

c = λ λ = c/ = c/λ

Electromagnetic Spectrum

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Constructive and Destructive Interference

Examples of Interference

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Refraction of Light

Slide 10 of 50 General Chemistry: Chapter 8 Prentice-Hall © 2007

9-2 Atomic Spectra

Slide 11 of 50 General Chemistry: Chapter 8 Prentice-Hall © 2007

(a) (b) (c) (d) (e)

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Atomic Spectra

Helium

Hydrogen

Harry Potter and an Uncertain World

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It is not possible to know the exact

position or path the electron takes with in

these orbitals.

The 1s orbital is represented by drawing a sphere about nucleus within which e-

spends 90% of its time, 90% probability contour.

Three 2p orbitals, as far apart as possible

Professor Heisenberg…Why do you say it is impossible to know where an electron is within

its orbit?

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Hermione told me using physics I can predict where the quaffle will be at any time after it is thrown. This has greatly improved my skills as

keeper on the University quidditch team.

Quaffle Bluger

I’m great and so is physics.

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Both Professor J.J. Thomson and Professor Millikan say an electron is a particle.

Cathode ray tube

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Properties of cathode rays

Electron m/e = -5.6857 10-9 g coulomb-1

Charge on the electron

Robert Millikan showed ionized oil drops can be balanced against the pull of gravity by an electric field.

The charge is an integral multiple of the electronic charge, e.

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An electron is a particle in an orbit…like a planet. If we know the momentum of a planet, we can predict where it will be at any future

time. If electrons are in orbits can’t we us the same method with them?

Ron I think you’ve been hit in the head with a bluger to many times. He said orbital not orbit.

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Heisenberg’s Uncertainty Principle –

It is not possible to simultaneously know the exact position and momentum of a

particle.uncertainty in position

uncertainty in momentum

Intrigued by their meeting with Professor Heisenberg, the three

rush of to Physical Potions Lab and try to

demonstrate the uncertainty principle.

As they are leaving they run into Professor de

Broglie. He had overheard their discussion with

Professor Heisenberg.Professor de Broglie

also explains that electron behave like waves and particle

similar to the photon.

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Calculate of e- in 1st orbit of H, using Bohr’s velocity

h = 6.626 x 10-34 Kg m2 s-1 (same as Js)

m of e- = 9.11 x 10-31 Kg

u (velocity) of e- = 2.19 x 106 ms-1

= 3.32 x 10-10 m = 0.332 nm

= h/mu

de Broglie – e- behave as a wave.

Harry, Hermione and Ron come up with a couple of experiments to demonstrate that electrons can behave

like waves and thus the uncertainty principle would apply to them.

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Diode laser Adustable slit

Photodetector

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If I put Prof. Schrödinger’s cat in a box…

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Heisenberg’s Uncertainty Principle –not possible to simultaneously know the exact position and momentum of a particle.

Bohr model, 1st orbit has radius = 52.9 pm (picometer = 10-12 m), circumference = 0.332 nm.

Same as just calculated for the e-.

When n = 1, one wavelength in standing wave.

When n = 2, two wavelengths in standing wave, etc.

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Only certain allowed wavelengths and energies.

Wave must have integral number of wavelengths about circle.

If number of waves not integral, wave self-destructs.

Wave motion in restricted systems.

Figure 7.13

Schrödinger equation enables one to calculate allowed energy levels for e- .

The allowed energy levels are the same as in the Bohr model.

Enables one to calculate the probability of finding the e-

at any particular point in the atom or the amplitude of the wave at any point.

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Quantum mechanics, Schrödinger equation, treats e-

as a standing wave

EH

),,(),,(),,(8 2

2

2

2

2

2

2

2

zyxEzyxzyxVdz

d

dy

d

dx

d

m

h

e

Where E is the energy of the atom, is called a wave function and H is the Hamiltonian operator

The complete form of the Schrödinger equation:

),,(),,(),,(8 2

2

2

2

2

2

2

2

zyxEzyxzyxVdz

d

dy

d

dx

d

m

h

e

The complete form of the Schrödinger equation:

),,(),,(4

sin

1

sin

11

2

0

2

2

2

22

2

2

2

2

2

rErr

e

rr

rrr

rr

n

– wavefunction Me – electron’s mass

E – total quantized energy V – potential energy of point (x, y, z)

In Cartesian coordinates

In Spherical coordinates

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0

r

y

x

z

z

y

x

Cartesian coordinates Spherical coordinates

N

Potential energy of an electron (attraction between the e- and the nucleus).

Kinetic energy of an electron (the energy of the moving e-).

Wave properties of an e-.

What is included in the Schrödinger equation?

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),,(),,(4

sin

1

sin

11

2

0

2

2

2

22

2

2

2

2

2

rErr

e

rr

rrr

rr

n

Focus on the solutions

The solutions to the Schrödinger equation answer

the following questions:

What is the energy of the electron?

Where is the electron most likely to exist?

The probability of finding the electron (electron density).

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),()(),,( YrRr

Wavefunction Radial part

(how far?)

Angular part

(Where?)

We don’t care where the electron is.

We want to know how far it is away from the nucleus.

1 for an s orbital

),,( rFirst low energy solution

e

a

zR s

23

0

1 2

Exponential Decay

Don’t worry about where this comes from.

Constants

z – the charge on the nucleus (1 for hydrogen)

a0 – the Bohr radius ≈ 0.53Å

σ = zr/a0

The farther from the nucleus, the lower the likelihood of finding the electron.

21s

r

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Figure 7.16Electron probability in the ground-state H atom.

Figures A and B - Electron density (probability of finding e- at a single point) vs. radius for the 1s orbital

2

1

24 sRr

Bohr radius≈

0.53Å

Higher e-

density

Lower e-

density

The 1s orbital is represented by drawing a sphere about nucleus within which e- spends 90% of its time, 90% probability contour.

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2

23

0

2 222

1

e

a

zR s

If σ = 2, then this term

goes to zero and ψ2 goes

to zero.

Somewhere there is a node, the electron

cannot be found at this

radius.

N

Potential energy of an electron (attraction between the e- and the nucleus).

Kinetic energy of an electron (the energy of the moving e-).

Wave properties of an e-.

What is included in the Schrödinger equation?

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Orbital – region of space where the e- is likely to be foundDifferent orbitals have different sizes, shapes and orientationsEach orbital is identified by 3 quantum numbers (n, l, ml)

n = principal quantum no. = 1, 2, 3, etc.determines energy and size of orbital n = 1is lowest energy and smallest size

l = angular momentum quantum no. = 0, 1, 2, . . ., (n – 1)determines shape of orbital

ml = magnetic quantum no. = -l … 0 … +l(integers, determines orientation of orbital)

n=1

n=2 n=2

n=3 n=3

n=4 n=4

n=5 n=5n=6 n=6

h

h

h

h

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l Shape of orbital

0 s

1 p

2 d

3 f

Total no. orbitals/shell = n2

n l ml No. of

orbitals

Sublevel

1 0 0 1 1s

2 0 0 1 2s

1 +1,0,-1 3 2p

3 0 0 1 3s

1 +1,0,-1 3 3p

2 +2,+1,0,-1,-2 5 3d

4 0 0 1 4s

1 +1,0,-1 3 4p

2 +2,+1,0,-1,-2 5 4d

3 +3,+2,+1,0,-1,-2,-3 7 4f

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Figure 7.17

1s 2s

Radial probability plot – 1 peak for the 1s, 2

peaks for the 2s.

2s orbital is also spherical, but it

contains 2 layers.

3s

Radial probability plot –3 peaks for

the 3s.

The 3s orbital contains 3 layers.

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),()(),,( YrRr

Wavefunction Radial part

(how far?)

Angular part

(Where?)

If not one, what is the shape?

cos4

3

sinsin4

3

cossin4

31

4

10

21

21

21

21

Pz

Py

Px

s

Y

Y

Yl

Yl

Angular part describes the

shape.

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Figure 7.18

The 2p orbitals.

Lowest energy p orbital, 2p, has a single peak in the radial probability plot.

Single peak slightly closer to the nucleus than the larger peak in the 2s plot.

Figure 8.5

Figure 7.18The 2p orbitals.

Three 2p orbitals shapes.

Each orbital centered along different axis (x, y, z)

Px, Py, Pz

2Pz orbital, e- wave has no amplitude on the xy plane, called a nodal plane

Three 2p orbitals, as far apart as possible

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H atoms, and only H, 2s and 2p have same energy

Energy depends only on n.

In the 3p orbital, the e- spends the most time outside the 2p region, but some time in the 2p region.

In the third shell, there is two peaks on the radial probability plot.

Figure 7.19 The 3d orbitals.

The lowest energy d orbital is a 3d.

Radial probability plot – single peak

Composite of the five 3d orbitals

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Figure 7.19 continued

Five 3d orbitals: 3dxy, 3dxz, 3dyz, 3dx2

-y2, and 3dz

2

Total no. orbitals/shell = n2

n l ml No. of

orbitals

Sublevel

1 0 0 1 1s

2 0 0 1 2s

1 +1,0,-1 3 2p

3 0 0 1 3s

1 +1,0,-1 3 3p

2 +2,+1,0,-1,-2 5 3d

4 0 0 1 4s

1 +1,0,-1 3 4p

2 +2,+1,0,-1,-2 5 4d

3 +3,+2,+1,0,-1,-2,-3 7 4f

Shapes of orbitals

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Chapter 8Atoms with more than one electron

Electrons located in orbitals similar to those found in H atom

Same 3 quantum numbers are needed to identify an orbital:n identifies orbit or shell e- is inl identifies type of orbital or subshell e- is in,

e.g. s, p, dml identifies a particular orbital within a subshell

To uniquely identify an e-, a 4th quantum no.

is needed,

ms = spin quantum number = +1/2 or –1/2

Electron behaves as a spinning charge.

clockwise or counterclockwise

Acts like a tiny magnet and generates a magnetic field.

+1/2 -1/2

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Pauli exclusion principle – no two e- in same atom can have same four quantum numbers.

Maximum of two e- in an orbital. First three quantum numbers are the same, but

must have opposite spins. The two e-s in the same orbital are “paired”. Their magnetic fields cancel each other.

e-’s occupy orbitals with lowest energies

In the H atom, the energy of the orbital depends only on n or the shell it is in.

In many-electron atoms, the energy of orbital depends on n and l.

Within a shell, the energy of an orbital increases as l increases.

Orbitals that have same n and l values, i.e., are in the same subshell have the same energy (e.g. 2px, 2py, 2pz all have same energy).