Electrons in Atoms

Quantum Mechanics Model

Standards

• 3221.1.1 Compare and contrast the major models of the atom

• 3221.1.5 Represent an electron’s location in the quantum mechanical model of an atom in terms of shapes of electron clouds, relative energies of orbitals, and the number of electrons possible in the s, p, d, and f orbitals.

Evolution of Atomic Models

So far we have described the atom as a nucleus of protons and neutrons surrounded by electrons—this works well for a simple explanation, but it does not explain certain properties of elements, such as why metals give off a characteristic color when heated in a flame—or why lasers give off a particular wavelength(s)

Review• Democritus– “atomos” indivisible

• John Dalton– Created first atomic theory (worked for about 50 yrs)

1. All elements composed of atoms2. Atoms of the same element are identical. The atoms of one

element are different from atoms of a different element.3. Atoms of different elements combine in simple, whole-

number ratios to form compounds4. Chemical reactions occur when atoms are separated,

joined, or rearranged. Atoms of one element are never changed to atoms of another element as a result of a chemical reaction

Review (cont’d)• JJ Thomson– Discovered electron via cathode-ray tube experiment– Plum Pudding Model

• Ernest Rutherford– Proposed nuclear atom—electrons surround a dense

nucleus, leaving lots of empty space– Did not describe the number of protons or electrons or

how they were arranged

Review (cont’d)• Niels Bohr– Student of Rutherford– Planetary Model: electrons are in circular orbits around

the nucleus, much like planets orbit the sun

From Classical Physics to Quantum Theory

-early models could not account for stability of molecules—What forces hold the atom together?

-The properties of atoms and molecules are NOT governed by the same laws that work so well for larger objects

Max Plank• Discovered that atoms and molecules emit energy only in

discrete quantities, or quanta– Physicists had always assumed that energy is continuous,

which meant that any amount of energy could be released in the radiation process

• Wave: vibrating disturbance by which energy is transmitted– Speed of the wave depends on the type of wave and the

nature of the medium through which it is travelling (air, water, vacuum)

More terms:• Wavelength(λ): distance between identical points on

successive waves (measured in m)• Frequency(ν): number of waves that pass a particular

point in one second (measured in Hz)• Amplitude: vertical distance from the midline of a

wave to the peak or trough• Wavelength and frequency are INVERSELY

proportional

Properties of waves• Speed (u)= wavelength * frequency

u= λν• Electromagnetic radiation: all types of radiant energy

(travels in waves through space)– Speed of light (c) = 3.00 x 108 m/s

Electromagnetic Radiation

• gamma rays have the shortest wavelength and highest frequency

• Radio waves have the longest wavelength and lowest frequency

Plank’s Quantum Theory• Quantum: smallest amount of energy that can be

emitted (or absorbed) in the form of electromagnetic radiation

E = hνh= Plank’s constant (6.63 x 10-34 J*s)

• Energy is always emitted in whole number multiples of hν

• Examples of quantization: eggs laid by hens, cats deliver integral numbers of kittens...

The Photoelectric Effect• Electrons are ejected from

the surface of certain metals exposed to light of at least a certain minimum frequency– Number of electrons ejected

was proportional to the intensity (or brightness) of the light, but the energies of the ejected electrons were not

– could not be explained by wave theory of light

Albert Einstein• 1905: Einstein suggested that a beam of light is a

stream of particles, called photons• Photon: a particle of electromagnetic radiation

having NO mass and carrying a quantum of energy• Using Plank’s theory, Einstein deduced that each

photon must possess energy E, given by the equation E = hν

• Explained the photoelectric effect!!

ExplanationElectrons are held in metal by attractive forces, and so to remove them from the metal, we must employ light of a sufficiently high frequency (which corresponds to sufficiently high energy) to break them free. Shining a beam of light onto a metal surface can be thought of as shooting a beam of particles—photons—at the metal atoms.

Explanation (cont’d)If the frequency of the photons is such that hv is equal to the binding energy of the electrons in the metal, then the light will have just enough energy to knock the electrons loose. If we use light of a higher frequency, then not only will the electrons be knocked loose, but they will acquire some kinetic energy.

Effects of Einstein• Einstein’s particle theory of light explained the

photoelectric effect, but it was not consistent with the known wave behavior of light

• Dual wave-particle nature: possesses both particlelike and wavelike properties

Question: What is meant by “red-hot” or “white-hot?” Give examples

• The visible glow is the portion of the emission spectrum that is sense by the eye.

• The warmth of the same iron bar represents another portion of its emission spectrum—the infrared region.

History of Emission Spectra

• 17th century—sometime around the apple tree—Newton showed that sunlight is composed of various color components that can be recombined to produce white light

• Emission spectra: either continuous or line spectra of radiation emitted by substances

How it Works…• The emission spectrum of a substance can be seen

by energizing a sample of material either with thermal energy or with some other form of energy (such as a high-voltage electrical energy for gaseous substances)

• Every element has a unique emission spectrum– Like atomic number, this is a “finger-print”

Emission Spectra

Atomic Emission Spectra Video

• http://www.brightstorm.com/science/chemistry/the-atom/atomic-emission-spectra/

2 types of emission spectra

• Continuous Spectra: all wavelengths of light are represented in the spectra– Sun, heated solids (e.g. iron)

• Line Spectra: light is emitted only at certain wavelengths– GASES

Why Bohr’s Model?• Niels Bohr offered his model in 1913 as a theoretical

explanation of the emission spectrum of the hydrogen atom.

• The “planetary” idea was already widely accepted in the scientific community because it related to something already “understood”

• Positive and negative attraction balanced by centripetal motion of electrons in orbits (Remember—Chadwick has not discovered the neutron, yet…1932)

Bohr’s Model• Energy level: region around the nucleus where the

electron is likely to be moving• These energy levels are like rungs on a ladder—just

like you cannot stand between rungs on a ladder, electrons cannot be between energy levels

Energy in atoms is quantized• Quantum: amount of energy needed to move an

electron from its present energy level to the next higher level– Electrons that have moved to a higher energy level are

said to be excited– Ground state: lowest possible energy state for an

electron

Bohr Model (cont’d)• “quantum leap” comes from describing this sudden

movement of electrons from one energy level to the next

• The higher the energy level, the farther the electron is from the nucleus

• The energy levels are not the same distance apart—the farther from the nucleus an energy level is, the less energy is required to move it to a higher energy level (How much energy is in the nucleus of an atom???)

Energy-State Diagram for Hydrogen

Hydrogen spectral series

Problems with Bohr’s Model

1. Only true for hydrogen (only has one electron)

2. Does not explain the chemical behavior of atoms.

The Dual Nature of the Electron

• Louis de Broglie (1924)If light waves can behave like a stream of particles (photons), then perhaps particles (e.g. electrons) can possess wave properties

De Broglie (cont’d)• Electrons bound to the nucleus behave like standing

waves.• Standing waves: (stationery) because they do not

travel along the string– “plucking” a guitar string–Nodes: points along the string that DON’T MOVE• Amplitude at these points is zero

De Broglie continuedWhere are the nodes?

The greater the frequency of vibration, the shorter the wavelength of the standing wave and the greater the number of nodes.

Based on this, if electrons behave like waves, they would only exist at specific frequencies.

Other Wave Properties of Electrons

• Diffraction: bending of a wave as it passes by the edge of an object or through a small opening

• Interference: occurs when waves overlap– Overlapping results in a reduction of energy in

some area and an increase of energy in others

The Heisenberg Uncertainty Principle

It is impossible to determine simultaneously both the position and

velocity of an electron or any other particle

Quantum Mechanical Model• Quantum theory: describes mathematically the

wave properties of electrons and other very small particles

• The Schrӧdinger Wave Equation: a mathematical formula that provides regions where electrons are likely to be located

• Orbital: three dimensional region around the nucleus that indicates the probable location of an electron– Have different shapes and sizes!!!

Atomic Orbitals and Quantum Numbers• Electrons in orbitals have quantized energies (What

is this formula???)• Quantum numbers: specify the properties of atomic

orbitals and the properties of electrons in orbitals– First three quantum numbers result from Schrodinger

equation– Fourth quantum number describes a fundamental state

of the electron that occupies the orbital

Principal Quantum Number• Indicates the main energy level (or shell) occupied

by the electron• Symbolized by the “n”• Values of n can only be positive integers—1, 2, 3…• n=1: occupies the first or lowest main energy level

and is located closest to the nucleus• The total number of orbitals that exist in a given

shell is = n2

Angular Momentum Quantum Number

• Indicates the shape of the orbital• Symbolized by l• For a specific main energy level, the number

of orbital shapes possible is equal to n• Possible values of l: 0…(n-1)

Shapes of Orbitals

Orbitals in Energy Levels

letter designation orbital shape # of electrons # 3-D orientations

s spherical 2 1

p dumbell-shaped 6 3

d clover (4-leaf) 10 5

f 14 7