Atomic Physics – Part 1 To accompany Pearson Physics PowerPoint presentation by R. Schultz...

Atomic Physics – Part 1Atomic Physics – Part 1

To accompany To accompany Pearson PhysicsPearson Physics

PowerPoint presentation by R. [email protected]

15.1 The Discovery of the Electron15.1 The Discovery of the Electron

Cathode rays – major item of interest near Cathode rays – major item of interest near the end of the 1800’s – what were they?the end of the 1800’s – what were they?

Emr? Charged particles? Neutral Emr? Charged particles? Neutral particles?particles?

Path deflection caused by both electric Path deflection caused by both electric (parallel to field) and magnetic (parallel to field) and magnetic (perpendicular to field) fields (perpendicular to field) fields


Conclusion: negatively charged particlesConclusion: negatively charged particles

J.J. Thomson, 1897, measured J.J. Thomson, 1897, measured charge to charge to mass ratiomass ratio of a cathode particles using the of a cathode particles using the apparatus shown:apparatus shown: particles accelerated

from C to A

focused by B

deflected by magnetic field from coil

straightened by electric field between D and E


Thomson found Thomson found q/mq/m for cathode ray for cathode ray particles to be 1.76 x 10particles to be 1.76 x 101111 C/kg C/kg

This is close to 2000 x This is close to 2000 x q/mq/m for a hydrogen for a hydrogen ionion

Thomson’s conclusion: cathode-ray Thomson’s conclusion: cathode-ray particles (today called electrons) are particles (today called electrons) are approximately 1/2000 the mass of a approximately 1/2000 the mass of a hydrogen ion (today called protons)hydrogen ion (today called protons)


Since Thomson didn’t know the charge or Since Thomson didn’t know the charge or mass of these particles couldn’t usemass of these particles couldn’t use

to determine their speedto determine their speed

He balanced so that particle He balanced so that particle path was undeflectedpath was undeflected

212qV mv

versus e mF F


Then, Then,

Using only a magnetic field, Using only a magnetic field,

e mF F

q E qvB

Ev

B

2

m cF F

vqvB m

rq vm Br


Examples: Examples: Practice Problem 1Practice Problem 1, page 756, page 756

Practice Problem 1Practice Problem 1, page 758, page 758

446.0 10

2.4 102.50

NC m

s

Ev

TB

681.0 10

1.0 101.0 0.0100

ms C

kgq vm Br T m


The Mass Spectrometer uses the principles The Mass Spectrometer uses the principles behind Thomson’s experiment to measure behind Thomson’s experiment to measure the charge to mass ratio of compoundsthe charge to mass ratio of compounds

Read Read Then, Now and FutureThen, Now and Future, page 759, page 759


The Thomson Raisin-bun model of the The Thomson Raisin-bun model of the atomatom

Recalling that Thomson concluded Recalling that Thomson concluded electrons were approximately 1/2000 the electrons were approximately 1/2000 the mass of equivalent amount of positive mass of equivalent amount of positive charge, he concluded that atom was a charge, he concluded that atom was a mass of (+) charge, taking up almost total mass of (+) charge, taking up almost total volume of atom, with tiny, near massless, volume of atom, with tiny, near massless, electrons embedded in itelectrons embedded in it

Like raisins in a bun – Like raisins in a bun –

Thomson Raisin Bun ModelThomson Raisin Bun Model


Thomson quotationThomson quotation

Check and ReflectCheck and Reflect page 760, questions 3, 7 page 760, questions 3, 7

SNAPSNAP booklet, page 274, questions 1, 3, 4, booklet, page 274, questions 1, 3, 4, 7, 9, 11, 13, 167, 9, 11, 13, 16

15.2 Quantization of Charge15.2 Quantization of Charge

Millikan Oil-Drop ExperimentMillikan Oil-Drop Experiment

oil droplets sprayed into chamber

fall into region of strong electric field

voltage across plates adjusted until gravity is balanced

Millikan’s actual apparatus still at CalTech


Because of air resistance actual analysis is Because of air resistance actual analysis is more complex than that presented heremore complex than that presented here

We will stick with the analysis required for We will stick with the analysis required for this coursethis course


Example: Example: Practice Problem 1Practice Problem 1, page 763, page 763

25 14

19

19

19

5.0 10 2.4 10 9.81

4.7 10

4.7 103

1.60 10

e g

N mC s

Ce

F F

E m g

kg

q

q

q C

Ce


In some problems you will need to use the In some problems you will need to use the density of the oil and radius of droplet to density of the oil and radius of droplet to find its massfind its mass

mass = density x volumemass = density x volume

34Volume of sphere =

3r


SNAPSNAP booklet, page 280, questions 1, 2, 3, booklet, page 280, questions 1, 2, 3, 7, 8, 10 7, 8, 10

15.3 The Discovery of the Nucleus15.3 The Discovery of the Nucleus

Discuss Discuss QuickLab 15-3,QuickLab 15-3, page 766 page 766

The Rutherford ExperimentThe Rutherford Experiment


ResultsResults

most alpha particles (helium nuclei) passed most alpha particles (helium nuclei) passed through gold foil with scattering of 1º or through gold foil with scattering of 1º or lessless

A small number were scattered backwards A small number were scattered backwards (at angles greater than 140º)(at angles greater than 140º)


Not predicted by Thomson raisin bun modelNot predicted by Thomson raisin bun model

Because of low density of mass and Because of low density of mass and positive charge in Thomson Raisin Bun positive charge in Thomson Raisin Bun model, alpha particles (model, alpha particles (αα particles) particles) expected to blast right through bunexpected to blast right through bun

Even direct collisions with electrons Even direct collisions with electrons (raisins) should cause little scattering(raisins) should cause little scattering


Conclusion: Positive charge and mass not Conclusion: Positive charge and mass not distributed throughout whole atom, but distributed throughout whole atom, but concentrated in a tiny fraction of total concentrated in a tiny fraction of total volume – the nucleusvolume – the nucleus

Atom radius approximately 10Atom radius approximately 10-10-10 m m

Nucleus radius approximately 10Nucleus radius approximately 10-14-14 m m

Volume to volume – like an ant in a football Volume to volume – like an ant in a football fieldfield

Atom mostly empty space!


Rutherford’s famous quotation – the Rutherford’s famous quotation – the scattering “was almost as incredible as if scattering “was almost as incredible as if you had fired a 15-inch shell at a piece of you had fired a 15-inch shell at a piece of tissue paper and it came back and hit tissue paper and it came back and hit you!”you!”


Rutherford’s Planetary Model of the atomRutherford’s Planetary Model of the atom

Review example 15.5, page 769Review example 15.5, page 769

Do and discuss Do and discuss Check and ReflectCheck and Reflect, page , page 770, questions 1, 2, 4, and 5770, questions 1, 2, 4, and 5

Note if this diagram was to scale, nucleus would be too small to be visible

15.4 The Bohr Model of the Atom15.4 The Bohr Model of the Atom

Problem with Rutherford model:Problem with Rutherford model:

Recall that accelerating charges produce Recall that accelerating charges produce electromagnetic waveselectromagnetic waves

Electrons orbiting nucleus undergo Electrons orbiting nucleus undergo continuous centripetal accelerationcontinuous centripetal acceleration

Atom would give off emr, lose energy, and Atom would give off emr, lose energy, and electrons spiral into nucleus in small electrons spiral into nucleus in small fraction of a second!fraction of a second!


Fraunhofer, 1814, noticed dark lines in the Fraunhofer, 1814, noticed dark lines in the solar spectrumsolar spectrum

Further study of the spectra led to the Further study of the spectra led to the following generalizations:following generalizations:


•• Hot dense material (e.g. a glowing solid) Hot dense material (e.g. a glowing solid) produces continuous spectrum with no produces continuous spectrum with no bright or dark linesbright or dark lines

•• Hot gas at low pressure: Hot gas at low pressure: emissionemission, bright , bright line spectrum, characteristic of elementline spectrum, characteristic of element


•• Cool gas at low pressure with light Cool gas at low pressure with light shone through it, shone through it, absorptionabsorption, dark , dark line spectrumline spectrum

Dark lines of absorption spectrum Dark lines of absorption spectrum occur at the same frequencies as occur at the same frequencies as the bright line spectrum for the the bright line spectrum for the same gassame gas


Fraunhofer lines on solar spectrum later Fraunhofer lines on solar spectrum later realized to be absorption spectra of all of realized to be absorption spectra of all of the gases in the cooler outer atmosphere the gases in the cooler outer atmosphere of the Sunof the Sun

Elements identified by comparing Elements identified by comparing individual elements’ spectra with lines on individual elements’ spectra with lines on the solar spectrumthe solar spectrum


Hydrogen’s emission spectrum had been Hydrogen’s emission spectrum had been analyzed by Balmer, a mathematician, in analyzed by Balmer, a mathematician, in 18851885

Balmer noticed a pattern and formulated Balmer noticed a pattern and formulated an equation to predict wavelengths emittedan equation to predict wavelengths emitted

2 2

1 1 1 n= 3, 4, 5, .....

2 Rydberg's constant for hydrogen

H

H

Rn

R

you won’t do calculations with this formula on the diploma exam


Bohr realized that emitted wavelengths of Bohr realized that emitted wavelengths of light were due to differences between light were due to differences between quantized energy levels in hydrogen atomquantized energy levels in hydrogen atom

He postulated mathematically that:He postulated mathematically that:

• • Electrons were allowed to orbit nucleus Electrons were allowed to orbit nucleus at at certain allowed radii (no others), called certain allowed radii (no others), called stationary states,stationary states, without emission of without emission of radiation radiation


• • Electrons in each Electrons in each stationary statestationary state orbit orbit had ahad a fixed amount of energy – the closer to fixed amount of energy – the closer to the the nucleus, the lower the energy (energy nucleus, the lower the energy (energy was was quantized) quantized)

• • Electrons can move from one Electrons can move from one stationary stationary statestate to another by giving off or absorbing to another by giving off or absorbing energyenergy in the form of EMR (remember the in the form of EMR (remember the spectrum spectrum of hydrogen) of hydrogen)


Allowed radii for hydrogen:Allowed radii for hydrogen:

Allowed energy for hydrogen:Allowed energy for hydrogen:

11 25.29 10nr m n Don’t need to know for test

2

13.6n

eVE

nDon’t need to know for test

-13.6 eV is ground state (n=1) for hydrogen

n=2 and higher called “excited states”


View emission spectrum of hydrogenView emission spectrum of hydrogen

hydrogen tube

metre stick

diffraction grating

view hydrogen tube through grating

see spectral lines on top of metre stick


Discuss Discuss Check and ReflectCheck and Reflect, page 780, , page 780, questions 2, 4, 8, 10questions 2, 4, 8, 10

You should know in a non-quantitative You should know in a non-quantitative manner, the Bohr model of the atom: what manner, the Bohr model of the atom: what are the basic features, how does it get are the basic features, how does it get around the difficulty in the Rutherford around the difficulty in the Rutherford model, how does it explain the spectrum of model, how does it explain the spectrum of hydrogenhydrogen

You should be familiar with the three types You should be familiar with the three types of spectra, and how to produce eachof spectra, and how to produce each

15.5 The Quantum Model of the Atom15.5 The Quantum Model of the Atom

Bohr’s model accurately predicts Bohr’s model accurately predicts hydrogen’s spectral lines, size of the hydrogen’s spectral lines, size of the unexcited atom, and ionization energyunexcited atom, and ionization energy

Shortcomings:Shortcomings:

Doesn’t explain Doesn’t explain whywhy energy is quantized or energy is quantized or how electrons can orbit a specific radii and how electrons can orbit a specific radii and notnot emit emr emit emr

Doesn’t work completely for anything but Doesn’t work completely for anything but hydrogenhydrogen


Doesn’t explain why spectral lines are split Doesn’t explain why spectral lines are split by a magnetic field (Zeeman Effect)by a magnetic field (Zeeman Effect)


Recall De Broglie – previous chapter – Recall De Broglie – previous chapter – wavelength of particles:wavelength of particles:

Extend the idea – the allowed orbits for Extend the idea – the allowed orbits for hydrogen are the right size so that each is hydrogen are the right size so that each is a whole number of “standing electron a whole number of “standing electron waves”waves”

hmv

other orbital radii can’t exist because they won’t allow a whole # of standing waves


Schrödinger, 1926, wrote a wave function Schrödinger, 1926, wrote a wave function (called the psi (called the psi ““ΨΨ”” function) to describe function) to describe electron waveselectron waves

ΨΨ 22 for a point is proportional to the for a point is proportional to the

probability of finding an electron at that probability of finding an electron at that pointpoint

OrbitalsOrbitals – probability distributions for – probability distributions for electrons of different energieselectrons of different energies


Quantum indeterminancy: in the quantum Quantum indeterminancy: in the quantum mechanical model, electrons don’t orbit the mechanical model, electrons don’t orbit the nucleus at defined orbits, they don’t have nucleus at defined orbits, they don’t have a precise locationa precise location

Einstein and also Schrödinger himself, had Einstein and also Schrödinger himself, had difficulty accepting this interpretation of difficulty accepting this interpretation of the modelthe model

Interesting reading – The Schrödinger’s cat Interesting reading – The Schrödinger’s cat paradoxparadox

Atomic Physics – Part 1 To accompany Pearson Physics PowerPoint presentation by R. Schultz...

Documents

Transcript of Atomic Physics – Part 1 To accompany Pearson Physics PowerPoint presentation by R. Schultz...