Electrons in the Atom l Thomson: discovered the electron l Rutherford: electrons like planets around the sun l Experiments: bright – line spectra of the elements

Atomic Spectrum The colors tell us about the structure of electrons in atoms

Electromagnetic Spectrum l Complete range of wavelengths and frequencies (gamma to radio) l Mostly invisible to human eye l Substances can either absorb or emit different radiations

Continuous Spectrum l Display of colors that are merging into each other. Rainbow, visible light, heated gases emit continuous spectrum. l The range of frequencies present in light. l White light has a continuous spectrum. l A rainbow.

Prism and White Light l White light is made up of all the colors of the visible spectrum. l Passing it through a prism separates it. Continuous spectrum

Line Spectrum (Discontinuous) l Images appear as narrow colored lines separated by dark regions. l Bright Line Spectra: gases at low temperature emit lines of colors. l Each line corresponds to a particular wavelength emitted by the atom.

If the Light is not White l By heating a gas with electricity we can get it to give off colors. l Passing this light through a prism produces the bright line spectrum Bright line spectra

Atomic Spectrum l Each element gives off its own characteristic colors. l Can be used to identify the atom. l 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 l Emission spectrum: these are the colors hydrogen emits when excited by energy. l Called a line spectrum. l There are just a few discrete lines showing in the visible spectrum 410 nm 434 nm 486 nm 656 nm

What this means l Only certain energies are allowed for the electrons in hydrogen atom. l The atom can absorb or emit only certain energies (packets-photons, quanta). Use Planck’s:  E = h  = hc / l Energy in the atom is quantized.

Bohr’s Model of the Atom Based on l Spectra of the atoms l Rutherford’s nuclear atom l Classical electrostatics (like charges repulse, unlike charges attract) l 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/n 2 3.Electron in an orbit has a definite amount of energy. It is quantized. It is in a stationary state. Its energy is:

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 Model Increasing energy Nucleus First Second Third Fourth Fifth } l Further away from the nucleus means more energy. l There is no “in between” energy l Energy Levels

Bohr’s Model – Equations Energy of electron in an orbit: Difference of energy between two levels

The Bohr Model n is the energy level for each energy level the energy is defined by an equation E = x J (Z 2 / n 2 ) Z is the nuclear charge, which is +1 for hydrogen; R h is Rydberg constant equal to x 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 = E final - E initial  E = x [Z 2 (1/ n f 2 - 1/ n i 2 )], Joules, but z =1. Therefore:  E = x ( 1/ n i 2 - 1/ n f 2 ) Joules

Examples l Calculate the energy needed to move an electron from its ground state (n=1) to the third energy level. l Calculate the energy released when an electron moves from n= 5 to n=2 in a hydrogen atom.

Changing the energy l Let’s look at a hydrogen atom

Changing the energy l Heat or electricity or light can move the electron up energy levels. Energy is being absorbed

Changing the energy l As the electron falls back to ground state it gives the energy back as light. Energy is being emitted

l May fall down in steps l Each with a different energy Changing the energy

l Further the electrons fall, more energy, higher frequency. l This is simplified picture l the orbitals also have different energies inside energy levels (more about it later) l All the electrons can move around. Ultraviolet Visible Infrared

The Bohr Ring Atom l Could not explain that only certain energies were allowed. l He called these allowed energies energy levels. l Putting Energy into the atom moved the electron away from the nucleus. l From ground state to excited state (energy is absorbed). l When it returns to ground state it gives off light of a certain packet of energy.

The Bohr Model l Doesn’t work. l Only works for hydrogen atoms. l Electrons don’t move in circles. l The quantization of energy is right, but not because they are circling like planets.

The Quantum Mechanical Model of the Atom l A totally new approach. l De Broglie ( ) 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 l sciences/physics/debrhydr.html sciences/physics/debrhydr.html

What’s possible? l You can only have a standing wave if you have complete waves. l There are only certain allowed waves. l In the atom there are certain allowed waves called electrons. l 1925 Erwin Schrödinger described the wave function of the electron. l Much math but what is important are the solutions.

l Things that are very small behave differently from things big enough to see. l The quantum mechanical model is a mathematical solution l It is not like anything you can see. The Quantum Mechanical Model

The physics of the very small l Quantum mechanics explains how the very small behaves. l Classic physics is what you get when you add up the effects of millions of packages (Newtonian Physics). l Quantum mechanics is based on probability because we cannot see the particles and they are many of them moving randomly.

l Has energy levels for electrons. l Orbits are not circular. They are not uniquely defined. There is no definite path for the motion of the electron. l 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. l Orbitals are found in energy levels. The Quantum Mechanical Model

l The atom is found inside a blurry “electron cloud” l A area where there is a chance of finding an electron. l Draw a line at 90 % probability The Quantum Mechanical Model

Heisenberg Uncertainty Principle l It is impossible to know exactly the speed and velocity of a particle. l The better we know one, the less we know the other. l The act of measuring changes the properties.

Heisenberg Uncertainty Principle Introduces the Unknown Factor l To measure where a electron is, we use light. l But the light moves the electron l And hitting the electron changes the frequency of the light. l Therefore we are never sure where the electron is.

Moving Electron Photon Before Electron Changes velocity Photon changes wavelength After

Duality of Matter and Light l Light behaves as a wave (Young + others) l Light behaves as stream of particles (Einstein) l Matter behaves as a particle (ancients + Newton) l Matter behaves as waves (deBroglie)

What is light l Light is a particle - it comes in chunks. l Light is a wave- we can measure its wave length and it behaves as a wave If we combine E=mc 2, c=ln, E = 1/2 mv 2 and E = hn We can get l = h/mv l The wavelength of a particle.

Matter is a Wave l Does not apply to large objects l Things bigger that an atom l A baseball has a wavelength of about m when moving 30 m/s. Too small to measure. l An electron at the same speed has a wavelength of cm l Big enough to measure.

Schrödinger Equation l Treats electrons as waves and particles. l Solution of equation determine the probable energy of the electron (energy level) l Solutions come in form of set of quantum numbers. Each set determines an orbital. l Orbital: the 90% probability space for finding a given electron.

Atomic Orbitals l Wave function corresponding to a particular set of three quantum numbers (n, l, and m l ) l Within each energy level the complex math of Schrödinger's equation describes several shapes. l Regions where there is a high probability of finding an electron.

The Wave Mechanical Model of the Atom The atom has two parts: l A dense nucleus in which most of the mass is concentrated l Energy levels that contain orbitals in which electrons are placed l Each electron is described by four quantum numbers: (n, l, m, s) l The quantum numbers (n, l, m) are solutions of Schrödinger equation l The quantum number (s) added for the spin of the electron.

Schrödinger’s Equation

Solutions to Schrödinger’s Equation

Solutions of the Schrödinger Equation l The solution of Schrödinger equation yields three quantum numbers: l N, principal quantum number l l, orbital quantum number l m l, magnetic quantum number

Quantum Numbers: the Principal Quantum Number n n, Principal quantum number l n values = 1, 2, 3,.. whole numbers l Designates the radial distance of the electron cloud and the probability where the electron can be found. l In plain language: it is the size of the electron cloud.

Orbital Quantum Number, l l Orbital quantum number designated with letter l l Also called sublevel l Indicates the shape of the electron cloud l Can have values of l = 0, 1, 2,….(n-1); l When l = 0, called s-sublevel; l = 1, p-sublevel; l=2, d-sublevel; l=3, f-sublevel l Example: n=3, l = 0, 1, 2; n = 2, l = 0 or 1; n=3, l can be 0 and 1 l Each sublevel has different energy. l Arranged by order of energy: least to most

Magnetic Quantum Number, m l l Designated with the letter m l l Determines the direction in space of the particular orbital. l Example: p x, p y, p z ; orbitals line along the x, y, and z axis respectively l Values: m l = -l,…0…+l l The orbitals are located in different parts of the sublevel. l Example: l=2; then ml = -2, -1, 0, +1, +2

Number of Orbitals in Each Sublevel Sublevel# of orbitals# of electrons s12 p36 d510 f714

l 1 s orbital for every energy level l Spherical shaped l Each s orbital can hold 2 electrons l Called the 1s, 2s, 3s, etc.. orbitals. S orbitals

P orbitals l Start at the second energy level l 3 different directions l 3 different shapes l Each can hold 2 electrons

P Orbitals

d orbitals l Start at the second energy level l 5 different shapes l Each can hold 2 electrons

F orbitals l Start at the fourth energy level l Have seven different shapes l 2 electrons per shape

F orbitals

Quantum Spin Number l Designated also by letter s. (Can be confusing) l Values +1/2 or -1/2 l 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: n 2 Number of electrons in any principal energy level: 2n 2 Each orbital can have only 2 electrons