Electrons in the Atom

Thomson: discovered the electron Rutherford: electrons like planets

around the sun

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 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

410 nm

434 nm

486 nm

656 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: E = h= hc / Energy in the atom is quantized.

Bohr’s Model of the AtomBased on

Spectra of the atoms Rutherford’s nuclear atom Classical electrostatics (like charges

repulse, unlike charges attract) Planck’s Quantum Theory

Bohr’s Postulates1. 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 is:

2n1

hRΔE

4. 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

Bohr’s Model

Nucleus

Electron

Orbit

Energy Levels

Bohr’s ModelIn

crea

sing

ene

rgy

Nucleus

First

Second

Third

Fourth

Fifth

} 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:

Difference of energy between two levels

21nh

RE

)2

12

1(

fnin

hRE

The Bohr Model

• n is the energy level• for each energy level the energy is defined by

an equationE = -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:

E = Efinal - Einitial

E = -2.178 x 10-18 [Z2 (1/ nf2 - 1/ ni

2)],

Joules, but z =1. Therefore:

E = 2.178 x 10-18 ( 1/ ni2 - 1/ nf

2 ) 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

May fall down in steps Each with a different energy

Changing the energy

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.

Ultraviolet Visible Infrared

The Bohr Ring Atom 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.

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 Quantum Mechanical Model

The physics of the very small 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.

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

The Quantum Mechanical Model

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.

Moving Electron

Photon

Before

ElectronChanges velocity

Photon changes wavelength

After

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=, E = 1/2

mv2 and E = h We can get = h/mv The wavelength of a particle.

Matter is a Wave 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 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

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

1 s orbital for every energy level

Spherical shaped

Each s orbital can hold 2 electrons Called the 1s, 2s, 3s, etc.. orbitals.

S orbitals

P orbitals 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: nEnergy of sublevels: s<p<d<fNumber of orbitals in principal energy

level: n2

Number of electrons in any principal energy level: 2n2

Each orbital can have only 2 electrons