lectures 17 & 18 atomic physics chapter 29

Lectures 17 & 18Atomic Physics

Chapter 29

July 25, 2012 Chapter 29 - Atomic Physics 2

AtomsAtoms● Matter is made up of atoms● Atoms are made of...

Protons: +e Electrons: -e Neutrons: no charge

● Discovered well after classical physics was developed (Late 1800's) Early thoughts were that atoms were the smallest units of matter

(hadn't discovered protons, electrons, etc.) Newton's Laws don't seem to work for atoms

Quantum Theory needed to explain

● Why do different elements have different properties? Arrangement of Periodic Table


● Electrons were the first building-block particle to be discovered

Electricity

● The model suggested that the positive charge of the atom is distributed as a “pudding” with electrons suspended throughout the “pudding”

● A neutral atom has zero total electric charge

● An atom must contain a precise amount of positive “pudding”

● How was that accomplished?

● Physicists studied how atoms collide with other atomic-scale particles

● Experiments carried out by Rutherford, Geiger and Marsden

Plum Pudding ModelPlum Pudding Model


● Fire alpha particles at thin Gold foil

alpha particle = He2+

Didn't know that at the time

● Expected the relatively massive alpha particles would pass freely through the plum-pudding atom

● A small number of alpha particles were actually deflected through very large angles

Some bounced backward

Rutheford ExperimentRutheford Experiment


● Rutherford realized that all the positive charge in an atom must be concentrated in a very small volume

The mass and density of the positive charge was about the same as the alpha particle

● Most alpha particles missed this dense region and passed through the atom

● Occasionally an alpha particle collided with the dense region, giving it a large deflection

● He concluded that atoms contain a nucleus that is positively charged and has a mass much greater than that of the electron

● Electrons in orbit around nucleus? Planetary Model Problem: Electrons should crash into nucleus

Model will have to be adjusted

Planetary ModelPlanetary Model


Details of NucleusDetails of Nucleus● Contains Protons

Charge of proton +e Electron -e e = 1.602 x 10-19 C

Z – Atomic Number Number of Protons in

nucleus➢ Also the number of

electrons if the atom is neutral

Every element has a different atomic number

● Contains Neutrons Discovered in 1930s Protons are attracted to

Neutrons Strong Force Otherwise they would fly away

from nucleus

A – Mass Number A = Z + N N is the number of neutrons

Number of neutrons doesn't affect properties of element

Affects stability of nucleus (Ch.30)


● The planetary model of the hydrogen atom is shown

● Contains one proton and one electron

● The electric force supplies a centripetal force

● Apply centripetal force Speed is

Assume r is about .1 nm (from Chemistry)

kev

mr=

2

Energy of Orbiting ElectronEnergy of Orbiting Electron


● This speed corresponds to a kinetic energy of the electron of 1.2 x 10-18 J = 7.5 eV

● This is close to the measured ionization energy of the hydrogen atom of 13.6 eV The ionization energy is the energy required to

remove an electron from an atom in the gas phase● The electron also has potential energy

The change in potential energy when the atom is ionized is 14 eV

Planetary Model was close on some things

Energy of Orbiting Electron, cont.Energy of Orbiting Electron, cont.

Δ PE=−k e2

∞ −(−k e2

r )


How to fix Planetary Model?How to fix Planetary Model?● Quantum Theory

Electron has a wavefunction and Newton's laws are modified

Each possible wavefunction corresponds to a different quantized energy level

Energy is gained or lost when the energy level changes

There is a lowest allowed energy – the electron will not crash into the nucleus

● Proof? Atomic Spectra Initially seen as colors missing from sunlight


● The sun’s spectrum shows sharp dips superimposed on the smooth blackbody curve

Smooth curve follows Wein's Law● The dips are called lines because of their appearance● The dips show up as dark lines● The locations of the dips indicate the wavelengths at which the light

intensity is lower than the expected blackbody value

Sun's SpectraSun's Spectra

Put light through diffraction grating


● When light from a pure blackbody source passes through a gas, atoms in the gas absorb light at certain wavelengths

● The values of the wavelengths have been confirmed in the laboratory

● Dark lines missing from a white light spectrum are called absorption lines

● You can also excite a gas and see what colors it gives off – emission lines

Gas Cell Demo

Emission lines line up with absorption lines

Absorption and EmissionAbsorption and Emission


● The pattern of spectral lines is different for each element

● Questions: Why do the lines occur at specific

wavelengths? Why do absorption and emission lines occur

at the same wavelength? What determines the pattern of

wavelengths? Why are the wavelengths different for

different elements?

Why do the lines exist?Why do the lines exist?


● The energy of a photon is Ephoton = h ƒ● Energy is conserved

Energy of the photon is the difference in the energy of the atom before and after emission or absorption

● The energy of an atom is quantized Only specific energies are allowed

● The energy of an absorbed or emitted photon is equal to the difference in energy between two discrete atomic energy levels

● The wavelength (or frequency) of the line gives the spacing between the atom’s energy levels

● Explained the experimental evidence of discrete spectral lines

Atomic Energy LevelsAtomic Energy Levels


● Experiments showed that Rutherford’s planetary model of the atom did not work

● Niels Bohr invented another model called the Bohr model

● Although not perfect, this model included ideas of quantum theory Based on Rutherford’s planetary model How do we introduce the idea of quantization and

discrete energy levels? Quantize angular momentum and apply it to the

planetary model Apply to Hydrogen

Bohr's Model of the atomBohr's Model of the atom


● To determine the allowed values of r, Bohr proposed that the orbital angular momentum of the electron could only have certain values

n = 1, 2, 3, … is an integer and h is Planck’s constant

● Combining this with the orbital motion of the electron, the radii of allowed orbits can be found

π2

hnL =

=

22

22

4 mke

hnr

π

Bohr's ResultBohr's Result


● The only variable is n The other terms in the equation for r are constants

● The orbital radius of an electron in a hydrogen atom can have only these values Shows the orbital radii are quantized

● The smallest value of r corresponds to n = 1 This is called the Bohr radius of the hydrogen

atom and is the smallest orbit allowed in the Bohr model

For n = 1, r = 0.053 nm

Bohr's RadiusBohr's Radius


● The energies corresponding to the allowed values of r can also be calculated

● The only variable is n, which is an integer and can have values n = 1, 2, 3, …

● Therefore, the energy levels in the hydrogen atom are also quantized

● For the hydrogen atom, this becomes

tot elec

π k e mE KE PE

h n

= + = − ÷

2 2 4

2 2

2 1

tot

. eVE

n= − 2

13 6

Bohr's Energy LevelsBohr's Energy Levels


● Each allowed orbit is a quantum state of the electron● E1 is the ground state

The state of lowest possible energy for the atom● Other states are excited states● Photons are emitted when electrons fall from higher to lower

states● When photons are absorbed, the electron undergoes a

transition to a higher state

Absorption and Emission LinesAbsorption and Emission Lines


● The negative energies come from the convention that PEelec = 0 when the electron is infinitely far from the proton

● The energy required to take the electron from the ground state and remove it from the atom is the ionization energy

● The arrows show some possible transitions leading to emissions of photons

● Spectra observed in 1880's Observations were used to

predict where other lines would occur

Bohr was the first to offer an explanation

Only partly correct

Hydrogen Energy LevelsHydrogen Energy Levels


● The highest photon energy available in a hydrogen atom is in the ultraviolet part of the electromagnetic spectrum

● Other atoms can emit much more energetic photons● May applications use X-ray photons obtained from an

electron transition from E2 to E1 in heavier atoms Larger Z means more spacing between energy levels

This are called K X-rays See table 29.1 for the energy of K X-rays produced by

some elements

X-RaysX-Rays


● If an absorbed photon has more energy than is needed to ionize an atom, the extra energy goes into the kinetic energy of the ejected electron

Unbound states aren't quantized

Like photoelectric effect KE = hf – 13.6 eV

● This final energy can have a range of values and so the absorbed energy can have a range of values

● This produces a continuous spectrum

Continuous spectraContinuous spectra


● The allowed electron orbits in the Bohr model correspond to standing waves that fit into the orbital circumference

● Since the circumference has to be an integer number of wavelengths, 2 π r = n λ = n (h / mv)

● This leads to Bohr’s condition for angular momentum De Broglie correctly explains why Bohr's assumption was true

Bohr and De BroglieBohr and De Broglie


● The Bohr model was successful for atoms with one electron H, He+, etc.

● The model does not correctly explain the properties of atoms or ions that contain two or more electrons

● Physicists concluded that the Bohr model is not the correct quantum theory It was a “transition theory” that help pave the way

from Newton’s mechanics to modern quantum mechanics

Problems with Bohr's ModelProblems with Bohr's Model


● Modern quantum mechanics depends on the ideas of wave functions and probability densities instead of mechanical ideas of position and motion

● To solve a problem in quantum mechanics, you use Schrödinger’s equations Bohr started from classical mechanics and made a

“lucky guess” The real solution gives the wave function, including its

dependence on position and time● Four quantum numbers are required for a full

description of the electron in an atom Bohr’s model used only one

Modern Quantum MechanicsModern Quantum Mechanics


Atomic Quantum NumbersAtomic Quantum Numbers


What Do they Mean?What Do they Mean?● Principle Quantum Number – n

n = 0, 1, 2, 3, … Roughly the same as Bohr's

quantum number Gives information on:

Position of Electron➢ Average Distance from nucleus

Energy state of the atom

● Orbital Quantum Number – l n = 0, 1, 2, … , n – 1 Orbital Angular Momentum of

Electron Gives information on:

Position of Electron➢ Shape of Orbital

Energy state of atom

● Spin Quantum number – s s = +½, -½ “Rotational Angular Momentum” of

Electron No evidence that electron actually

rotates Just a point particle

Only detected with magnetic fields

● Magnetic Quantum Number – m m = - l, … , l (2l + 1 states) Direction of angular momentum Gives information on:

Shape of Orbital Only detected in presence of

magnetic field No affect on energy state atom

Ok, so why do these matter?


l quantum numberl quantum number● For historical reasons the l quantum number is

often labeled with a letter instead of a number l = 0 → s l = 1 → p l = 2 → d l = 3 → f l = 4 → g … h, i, j, k, l, … All ground state atoms only have electrons with

l = 3 or less (s, p, d, or f) At least until we get atoms with Z ≈ 140


Electron CloudsElectron CloudsDepends on n, l, and m


http://www.nature.com/news/2010/101117/full/468355a.html

Anti-HydrogenAnti-Hydrogen

http://www.nature.com/news/2010/101117/full/468355a.html


● The electron energy levels of multielectron atoms follow the same pattern as hydrogen Use the same quantum numbers

● The electron distributions are also similar● There are two main differences between

hydrogen and multielectron atoms The values of the electron energies are different

for different atoms The spatial extent of the electron probability clouds

varies from element to element

Multielectron AtomsMultielectron Atoms


Pauli Exclusion PrinciplePauli Exclusion Principle● Every electron in atom must have a different set of

quantum numbers No two can have the same all four the same

At least one must be different Because Electrons are Spin ½

Ground state of hydrogen is... n =1 l = 0 m = 0 s = +½ or -½

Shorthand Notation – 1s1 (nlnumber between 1 and 4l+2) Carbon

Z = 6 1s22s22p2


● The direction of the arrow represents the electron’s spin● In C, the He electrons have different spins and obey the

Pauli exclusion principle

Section 29.5

Electrical DistributionElectrical Distribution


Electron Configuration of Some ElementsElectron Configuration of Some Elements


● The energy of each level depends mainly on the value of n

● In multielectron atoms, the order of energy levels is more complicated

● For shells higher than n = 2, the energies of subshells from different shells being to overlap

● In general, the energy levels fill with electrons in the following order:

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f

Filling Energy LevelsFilling Energy Levels

Note: This does not come after 3pTransition Metals

Lanthanides and Actinides


Order of Energy LevelsOrder of Energy Levels


● How many electrons are in an atom with electrons filled up to 4s?A) 20B) 18 C) 16 D) 12E) 42

Quiz!Quiz!


Periodic tablePeriodic tables1

s2 p1s2 p2 p3 p4 p5

p6

d1 d2 d3 d5 d5 d6 d7 d8 d10 d10

See book

n


● Quantum theory explains why the periodic table has its structure

● The periodic table was developed by Dmitry Mendeleyev in the late 1860’s

● Mendeleyev and other chemists had noticed that many elements could be grouped according to their chemical properties

● Mendeleyev organized his table by grouping related elements in the same column

His organization ended up reflecting the quantum numbers of the electrons

● His table had a number of “holes” because many elements had not yet been discovered

Chemical Properties of ElementsChemical Properties of Elements


● Mendeleyev could not explain why the regularities in the periodic table occurred

● The electron energy levels and the electron configuration of the atom are responsible for its chemical properties

● When an atom participates in a chemical reaction, some of its electrons combine with electrons from other atoms to form chemical bonds

● The bonding electrons are those occupying the highest energy levels

Chemical Properties, cont.Chemical Properties, cont.


● The electron that forms bonds with other atoms is a valence electron

● When a shell has all possible states filled it forms a closed shell

● Elements in the same column in the periodic table have the same number of valence electrons

Very similar chemical properties

● The last column in the periodic table contains elements with completely filled shells These elements are largely inert They almost never participate in chemical reactions

Electron ShellsElectron Shells


● Atomic clocks are used as global and US time standards● The clocks are based on the accurate measurements of

certain spectral line frequencies● Cs atoms are popular● One second is now defined as the time it takes a cesium clock

to complete 9,192,631,770 ticks

Section 29.7

Applications: Atomic ClocksApplications: Atomic Clocks


Fluorescent BulbsFluorescent Bulbs

● This type of bulb uses gas of atoms in a glass container● An electric current is passed through the gas● This produces ions and high-energy electrons● The electrons, ions, and neutral atoms undergo many collisions,

causing many of the atoms to be in an excited state● These atoms decay back to their ground state and emit light● Much more efficient than incandescent bulbs

Blackbody radiation generates requires lots of heating Fluorescent bulbs generate little heat

Applications: Fluorescent light bulbsApplications: Fluorescent light bulbs


● Lasers depend on the coherent emission of light by many atoms, all at the same frequency

● In spontaneous emission, each atom emits photons independently of the other atoms It is impossible to predict when it will emit a photon The photons are radiated randomly in all directions

● In a laser, an atom undergoes a transition and emits a photon in the presence of many other photons that have energies equal to the atom’s transition energy

● A process known as stimulated emission causes the light emitted by this atom to propagate in the same direction and with the same phase as surrounding light waves

Applications: LasersApplications: Lasers


● Laser is an acronym for Light Amplification by Stimulated Emission of Radiation

● The light from a laser is thus a coherent source● Mirrors are located at the ends of the bulb (laser tube)● One of the mirrors lets a small amount of the light pass through and leave

the laser● HeNe laser

Helium Neon Stimulate a transition in Neon

Many other systems Not all atomic But all can be described in terms of quantum energy levels

Lasers, cont.Lasers, cont.


● Quantum mechanics is needed in the regime of electrons and atoms since Newton’s mechanics fails in that area

● Newton’s laws work very well in the classical regime

● Quantum theory can be applied to macroscopic objects, giving results that are virtually identical to Newton’s mechanics

● Classical objects have extremely short wavelengths, making the quantum theory description in terms of particle-waves unnecessary

Quantum vs. Newton's MechanicsQuantum vs. Newton's Mechanics


● Physicists are actively studying the area where quantum mechanics and Newtonian mechanics meet

● One question concerns the quantum behavior of living organisms such as viruses

Shall ever the twain meet?Shall ever the twain meet?

lectures 17 & 18 atomic physics chapter 29

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