Download Quantum Atom PPT - River Dell Regional School District

Electrons in the Atom
Thomson: discovered the electron
 Rutherford: electrons like planets
around the sun
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Experiments: bright – line spectra of
the elements
Atomic Spectrum
The colors tell us about the
structure of electrons in atoms
Electromagnetic Spectrum
Complete range of wavelengths and
frequencies (gamma to radio)
 Mostly invisible to human eye
 Substances can either absorb or emit
different radiations

Continuous Spectrum
Display of colors that are merging into
each other. Rainbow, visible light,
heated gases emit continuous
spectrum.
 The range of frequencies present in
light.
 White light has a continuous spectrum.
 A rainbow.

Prism and White Light

White light is
made up of all the
colors of the
visible spectrum.

Passing it through
a prism separates
it.
Continuous
spectrum
Line Spectrum
(Discontinuous)

Images appear as narrow colored lines
separated by dark regions.
Bright Line Spectra: gases at low
temperature emit lines of colors.
 Each line corresponds to a particular
wavelength emitted by the atom.

If the Light is not White
By heating a gas
with electricity we
can get it to give
off colors.
 Passing this light
through a prism
produces the
bright line
spectrum

Bright line
spectra
Atomic Spectrum
Each element
gives off its own
characteristic
colors.
 Can be used to
identify the atom.
 How we know
what stars are
made of.

Atomic
fingerprints
• These are called
discontinuous
spectra
• Or line spectra
• Unique to each
element.
• These are
emission spectra
• The light is
emitted given off.
An Explanation of Atomic Spectra
NIELS BOHR
explained only the
Hydrogen Spectra
Hydrogen spectrum
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Emission spectrum: these are the colors
hydrogen emits when excited by energy.
Called a line spectrum.
There are just a few discrete lines showing
in the visible spectrum
656 nm
434 nm
410 nm
486 nm
What this means
Only certain energies are allowed for
the electrons in hydrogen atom.
 The atom can absorb or emit only
certain energies (packets-photons,
quanta).
 Use Planck’s: DE = hn = hc / l
 Energy in the atom is quantized.

Bohr’s Model of the Atom
Based on

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Spectra of the atoms
Rutherford’s nuclear atom
Classical electrostatics (like charges
repulse, unlike charges attract)
Planck’s Quantum Theory
Bohr’s Postulates
1. Atoms consist of central nucleus.
2. Only certain circular orbits are
allowed. Radius of orbit
proportional to 1/n2
3. Electron in an orbit has a definite
amount of energy. It is quantized.
It is in a stationary state. Its energy
1
is:
ΔE   R 
h n2
Energy of the electron at infinity (when
it is totally removed from the atom) is
equal to zero.
5. Energy is emitted or absorbed when
electrons JUMP from orbit to orbit
(lower to higher: energy is absorbed;
higher to lower: energy is emitted).
In- between stages are forbidden
 ΔE > 0 , energy is absorbed
 ΔE < 0, energy is emitted
4.
Bohr’s Model
Nucleus
Electron
Orbit
Energy Levels
Bohr’s Model
Increasing energy
Fifth
Fourth
Third
Second
First
Nucleus
Further away
from the
nucleus means
more energy.
 There is no “in
between”
energy
 Energy Levels

Bohr’s Model – Equations
• Energy of electron in an orbit:
1
DE  R 
h n2
Difference of energy between two levels
1
1
DE  R (

)
h n2 n 2
i
f
The Bohr Model
• n is the energy level
• for each energy level the energy is defined by
an equation
E = -2.178 x 10-18 J (Z2 / n2 )
• Z is the nuclear charge, which is +1 for
hydrogen; Rh is Rydberg constant equal to
2.178 x 10-18 J .
• n = 1 is called the ground state
• when the electron is removed, n =  and
• ΔE = 0 of the electron.
Energy for Electron Transitions
• When the electron moves from one energy
level to another, the change in energy is:
 DE = Efinal - Einitial
DE = -2.178 x 10-18 [Z2 (1/ nf2 - 1/ ni2)],
Joules, but z =1. Therefore:
DE = 2.178 x 10-18 ( 1/ ni2 - 1/ nf2 ) Joules
Examples

Calculate the energy needed to move
an electron from its ground state
(n=1) to the third energy level.

Calculate the energy released when
an electron moves from n= 5 to n=2 in
a hydrogen atom.
Changing the energy
 Let’s
look at a hydrogen atom
Changing the energy

Heat or electricity or light can move the electron up
energy levels. Energy is being absorbed
Changing the energy

As the electron falls back to ground state it
gives the energy back as light. Energy is
being emitted
Changing the energy
May fall down in steps
 Each with a different energy

Ultraviolet
Visible
Infrared
 Further the electrons fall, more energy,
higher frequency.
 This is simplified picture
 the orbitals also have different energies
inside energy levels (more about it later)
 All the electrons can move around.
The Bohr Ring Atom
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Could not explain that only certain
energies were allowed.
He called these allowed energies energy
levels.
Putting Energy into the atom moved the
electron away from the nucleus.
From ground state to excited state
(energy is absorbed).
When it returns to ground state it gives off
light of a certain packet of energy.
The Bohr Model
Doesn’t work.
 Only works for hydrogen atoms.
 Electrons don’t move in circles.
 The quantization of energy is right,
but not because they are circling like
planets.

The Quantum Mechanical Model
of the Atom
A totally new approach.
 De Broglie (1892-1987) said:
 matter could be like a wave.
Matter waves are standing waves.
The vibrations of the wave are like
of a stringed instrument.

DeBroglie Waves
De Broglie Waves Simulations

http://www.launc.tased.edu.au/online/
sciences/physics/debrhydr.html
What’s possible?
You can only have a standing wave if
you have complete waves.
 There are only certain allowed waves.
 In the atom there are certain allowed
waves called electrons.
 1925 Erwin Schrödinger described the
wave function of the electron.
 Much math but what is important are
the solutions.

The Quantum Mechanical
Model
Things that are very small
behave differently from things
big enough to see.
 The quantum mechanical
model is a mathematical
solution
 It is not like anything you can
see.

The physics of the very small
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Quantum mechanics explains how the
very small behaves.
Classic physics is what you get when you
add up the effects of millions of packages
(Newtonian Physics).
Quantum mechanics is based on
probability because we cannot see the
particles and they are many of them
moving randomly.
The Quantum Mechanical Model
Has energy levels for
electrons.
 Orbits are not circular. They are not
uniquely defined. There is no definite
path for the motion of the electron.
 The model predicts the probability of
finding an electron a certain distance
from the nucleus. The space is defined
by the solution of Schrödinger equation.
 Orbitals are found in energy levels.

The Quantum Mechanical
Model
The atom is found
inside a blurry
“electron cloud”
 A area where there is
a chance of finding
an electron.
 Draw a line at 90 %
probability

Heisenberg Uncertainty Principle
It is impossible to know exactly the
speed and velocity of a particle.
 The better we know one, the less we
know the other.
 The act of measuring changes the
properties.

Heisenberg Uncertainty Principle
Introduces the Unknown Factor
 To
measure where a electron is, we
use light.
 But the light moves the electron
 And hitting the electron changes
the frequency of the light.
 Therefore we are never sure where
the electron is.
Before
Photon
Moving
Electron
After
Photon
changes
wavelength
Electron
Changes
velocity
Duality of Matter and Light
Light behaves as a wave (Young +
others)
 Light behaves as stream of particles
(Einstein)
 Matter behaves as a particle
(ancients + Newton)
 Matter behaves as waves (deBroglie)

What is light
Light is a particle - it comes in chunks.
 Light is a wave- we can measure its
wave length and it behaves as a wave
 If we combine E=mc2 , c=ln, E = 1/2
mv2 and E = hn
 We can get l = h/mv
 The wavelength of a particle.
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Matter is a Wave
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Does not apply to large objects
Things bigger that an atom
A baseball has a wavelength of about 10-32
m when moving 30 m/s. Too small to
measure.

An electron at the same speed has a
wavelength of 10-3 cm

Big enough to measure.
Schrödinger Equation
Treats electrons as waves and particles.
 Solution of equation determine the
probable energy of the electron (energy
level)
 Solutions come in form of set of
quantum numbers. Each set
determines an orbital.
 Orbital: the 90% probability space for
finding a given electron.

Atomic Orbitals
Wave function corresponding to a
particular set of three quantum numbers
(n, l, and ml)
 Within each energy level the complex
math of Schrödinger's equation
describes several shapes.
 Regions where there is a high
probability of finding an electron.

The Wave Mechanical Model of
the Atom
The atom has two parts:
 A dense nucleus in which most of the mass is
concentrated
 Energy levels that contain orbitals in which
electrons are placed
 Each electron is described by four quantum
numbers: (n, l, m, s)
 The quantum numbers (n, l, m) are solutions of
Schrödinger equation
 The quantum number (s) added for the spin of
the electron.
Schrödinger’s Equation
Solutions to Schrödinger’s
Equation
Solutions of the Schrödinger
Equation
The solution of Schrödinger equation
yields three quantum numbers:
 N, principal quantum number
 l, orbital quantum number
 ml, magnetic quantum number

Quantum Numbers: the Principal
Quantum Number n
n, Principal quantum number
n values = 1, 2, 3,.. whole numbers
 Designates the radial distance of the
electron cloud and the probability
where the electron can be found.
 In plain language: it is the size of the
electron cloud.

Orbital Quantum Number, l
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Orbital quantum number designated with letter l
Also called sublevel
Indicates the shape of the electron cloud
Can have values of l = 0, 1, 2,….(n-1);
When l = 0, called s-sublevel; l = 1, p-sublevel;
l=2, d-sublevel; l=3, f-sublevel
Example: n=3, l = 0, 1, 2;
n = 2, l = 0 or 1; n=3, l can be 0 and 1
Each sublevel has different energy.
Arranged by order of energy: least to most
Magnetic Quantum Number,
ml
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Designated with the letter ml
Determines the direction in space of the
particular orbital.
Example: px, py, pz; orbitals line along the
x, y, and z axis respectively
Values: ml = -l,…0…+l
The orbitals are located in different parts of
the sublevel.
Example: l=2; then ml = -2, -1, 0, +1, +2
Number of Orbitals in Each
Sublevel
Sublevel
# of orbitals
# of electrons
s
1
2
p
3
6
d
5
10
f
7
14
S orbitals
1 s orbital for
every
energy
level
 Spherical
shaped
 Each s orbital can hold 2 electrons
 Called the 1s, 2s, 3s, etc.. orbitals.

P orbitals
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Start at the second energy level
3 different directions
3 different shapes
Each can hold 2 electrons
P Orbitals
d orbitals
Start at the second energy level
 5 different shapes
 Each can hold 2 electrons

F orbitals
Start at the fourth energy level
 Have seven different shapes
 2 electrons per shape

F orbitals
Quantum Spin Number
Designated also by letter s. (Can be
confusing)
 Values +1/2 or -1/2
 Each electron can spin clockwise and
counterclockwise.

The Solution of Schrödinger
Equation
Summary:
Number of sublevels in principal energy
level: n
Energy of sublevels: s<p<d<f
Number of orbitals in principal energy
level: n2
Number of electrons in any principal
energy level: 2n2
Each orbital can have only 2 electrons