Wilhelm Conrad Röntgen - Northwestern...

X rays

Röntgen

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Rutherford

Experimentalconfirmation

Isotopes

Nucleus: properties

Radioactivity

Decay chains

Radiactive decay

Radioactive dating

Dating the earth

Patterson: lead

Ionizing radiation

Wilhelm Conrad Röntgen

• Wilhelm ConradRöntgen: starting in1888, Professor andDirector of thePhysical Institute atUniversitätWürzburg.Apartment on thesecond floor!

• By 1895,experimenting withthicker-walledLenard tubes (calledHittorf-Crookestubes)

Wilhelm Röntgen (1845–1923)

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Nov. 8, 1895• Friday afternoon: notices

glow of fluorescent screeneven though cathode raysare not emerging. Flickerswith fluctuations of tubedischarge.

• Strikes a match—it wasbarium platinocyanidescreen—but some distancefrom tube, and with blackpaper in between.

• Assistant comes into room to get some equipment; Röntgen isoblivious.

• Called to dinner several times; at little and in almost completesilence before returning to lab.

• Continues for several weeks in solitary puzzlement. To good friendBoveri: “I have discovered something interesting, but I do not knowwhether or not my observations are correct.”

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Observations. . .

• Noticed shadow of wire onscreen, so tested penetration ofrays through various objects.

• Try a lead brick. Opaque,but. . . shadow of bones in hiswrist?

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Bertha’s hand

Yo, Bertha! Put your hand here for 15 minutes. It will be really cool. . .

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Publishing with trepidation

• First observed phenomena onNov. 8, 1895.

• Drops a manuscript off forTransactions of the WürzburgPhysical Medical Society onSaturday, Dec. 28, 1895.

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Printing

• Handwritten manuscript droppedoff on Saturday, Dec. 28, 1895.

• Printed version in journal availableon Wednesday, New Year’s Day,1896.

• Röntgen mails reprint and somephotos to several respectedphysicists. “Now the devil will beto pay!”

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Sensational!• Headline in

ViennaPress,January 5;LondonDailyChronicle onJanuary 6.

• First reportreplicatingtheexperiments:New YorkElectricalEngineer,January 8.

• Röntgen wins first Nobel Prize in Physics in 1901, but does notgive a public lecture!

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Immediate use!Michael Pupin, Columbia University, Feb. 1896

A later, better image af-ter Pupin put a phospho-rescent coating on top ofthe film. Same patient, ordid pellets move?

“This is of the hand of a gentleman resident in New York, who, while ona hunting trip in England a few months ago, was so unfortunate as todischarge his gun into his right hand, no less than forty shot lodging inthe palm and fingers. The hand has since healed completely; but the shotremain in it, the doctors being unable to remove them, because unable todetermine their exact location. The result is that the hand is almostuseless, and often painful.”—Cleveland Moffett, McClure’s Magazine,April 1896

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Dating the earth

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Going overboard

Mihran Kassabian, Philadelphia Hospital, 1903–1904: brain irradiationto treat epilepsy. Two patients died, but epilepsy was reduced. . .

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Mihran Kassabian

Hands of Kassabian soon before his death in 1910. So as not to discredit the useof X-rays in medicine, it is said that he used an assumed name when he checkedinto the hospital to have some fingers amputated [Brown, Am. J. Roentgenology164, 1285 (1995)]

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Isotopes

Nucleus: properties

Radioactivity

Decay chains

Radiactive decay

Radioactive dating

Dating the earth

Patterson: lead

Ionizing radiation

Generating X rays

The general idea: get electrons from a hot filament (Coolidge at GeneralElectric, 1913), accelerate them over a high voltage difference, and slamthem into a metal target. Extract X rays at a shallow angle to reduceself-absorption.

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Isotopes

Nucleus: properties

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Radioactive dating

Dating the earth

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X-ray tubes

An x-ray tube in a dental x-ray machine:

Rotating anode tubes: spin the target to keep it from melting.

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Meanwhile. . . Radioactivity!

• Early 1896: Henri Becquerel noticedthat uranium compounds would fogphotographic plates–the discovery ofradioactivity.

• 1898: Marie Sklodowska Curiemeasures radioactivity by looking ationization of air. Unaffected bychemical binding, heat, etc.! HusbandPierre then joins research; theydiscover radium and polonium.

• Radioactive decay releases energies inthe MeV range!!!

• Becquerel, and Marie and Pierre Curieshare the 1903 Nobel Prize in Physics.Marie is awarded the 1911 NobelPrize in Chemistry.

Antoine HenriBecquerel

(1852–1908)

Marie Curie(1867–1934) and

Pierre Curie(1859–1906)

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Enter Rutherford: the alpha male

• Grew up on a farm in New Zealand,and studied at the University there.Applied for a graduate scholarship atCambridge and worked at home whileawaiting a reply. When thescholarship letter came (1894), hethrew down his shovel and said“That’s the last potato I will ever dig.”

• McGill University in Montreal,1898–1907. University of Manchester,1907–1919. Cavendish Professor atCambridge, 1919–1937.

• “All science is either physics or stampcollecting”

Ernest Rutherford(1871–1937; NobelPrize in Chemistry,1908)

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Discovery of the alpha particle

Rutherford at McGill in Montreal, 1905:• Fill thin-glass-wall tube with radon, which emits alpha particles

(α).• Surround that tube with another thick-walled, evacuated tube.• After a few days, helium identified in the outer tube by its

characteristic spectrum.• Alpha particles are helium nuclei (2 protons, 2 neutrons, or 4

2He2,using A

n XZ).• Other radioactive decay emissions: β− are electrons, γ are very

energetic photons.1908 Nobel Prize in Chemistry.

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Rutherford’s α apparatus

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Radioactivity: lots of energy!

• Rutherford and Soddy, 1903: “The energy of radioactive changemust therefore be at least twenty-thousand times, and may be amillion times, as great as the energy of any molecular change.”Remember that chemistry happens at ∼3–10 eV, while nucleardecays happen at 106 eV.

• Soddy in 1904: “If it [the energy of the nucleus] could be tappedand controlled what an agent it would be in shaping the world’sdestiny! The man who put his hand on the lever by which aparsimonious nature regulates so jealously the output of this storeof energy would possess a weapon by which he could destroy theearth if he chose.”

• Soddy continued: “The fact that we exist is a proof that [massiveenergetic release] did not occur; that it has not occurred is the bestpossible assurance that it never will. We may trust Nature to guardher secret.”

Quoted in Rhodes, The making of the atomic bomb

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Other gems fromwww.wikiquote.org

• “There is no likelihood man can ever tap the power of theatom.”—Robert Millikan, 1923.

• “There is not the slightest indication that nuclear energy will everbe obtainable. It would mean that the atom would have to beshattered at will.”—Albert Einstein, 1932.

• “The energy produced by the breaking down of the atom is a verypoor kind of thing. Anyone who expects a source of power fromthe transformation of these atoms is talking moonshine.”—ErnestRutherford, shortly after splitting the atom for the first time.

• “Nuclear-powered vacuum cleaners will probably be a reality in 10years.”—Alex Lewyt, president of vacuum cleaner company LewytCorp., in the New York Times in 1955.

plus• “It’s hard to make predictions—especially about the

future.”—attributed to Robert Storm Petersen.

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α backscattering?

• α particles travel at 90% of the speed of light, and have a mass ofabout 4/197 ' 0.020 that of gold nuclei but 8000 time that of anelectron.

• While at McGill, Rutherford had noticed significant scattering atlarge angles. That seemed odd. . .

• After receiving Nobel Prize, Rutherford is offered position atManchester in U.K. Wants to look into α scattering in more detail.

• Gold hammered to 2 µm thickness: about 104 atoms thick.• Rutherford assigns experiment to Ernest Marsden (age 20) and

Hans Geiger. They use a microscope focused on a ZnS screen toobserve flashes of light from single α particles.

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The experimentSet the Radium α emitter R and foil F to one angle. Sit in the dark forseveral minutes to become dark-adapted (Rutherford would tell stories).Stare into the microscope M and count flashes of light on the zinc sulfidescreen S for a long time. . .

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The unexpected

• Marsden and Geiger find significant scattering at large angles,including back towards the α particle source! Rutherford:“It was quite the most incredible event that has ever happened tome in my life. It was almost as incredible as if you fired a 15-inchshell at a piece of tissue paper and it came back and hit you. Onconsideration I realised that this scattering backwards must be theresult of a single collision, and when I made calculations I saw thatit was impossible to get anything of that order of magnitude unlessyou took a system in which the greatest part of the mass of theatom was concentrated in a minute nucleus.”

• Context: HMS Dreadnought (1906) with 12 inch guns. HMS QueenElizabeth (1913) with 15-inch guns: 1900 lb. shells, muzzlevelocity of 1700 mph, range of 11 miles!

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Re-examine the situation

• Conclusion: the nucleus is very small. When Rutherford figures itout (early 1911), he marches into Geiger’s office humming“Onward Christian Soldiers” and announces, “I know what theatom looks like!”

• With a point-like nucleus, electrons must be in some sort of orbitalmotion.

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Experimental confirmationAgreement between Rutherford’s theory and Marsden’s experiments(Krane Fig. 6.14):

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Figuring out the nucleus• From Rutherford, we know that the

nucleus is small (∼ 10−15 m) andpositively charged.

• From Bohr, we know that electronsare in orbitals outside the nucleus.

• Soddy and others carried outexaminations of chemical propertiesof radioactive atoms and their decayproducts. He proposes the existence ofisotopes (1910; Nobel Prize inChemistry, 1921).

• An atom can be described with AZXN ,

where Z is the charge (number ofprotons) which determines chemistry,and A is the weight (in proton masses).

• What does N = A− Z measure?Pairings of protons and electrons inthe nucleus?

Frederick Soddy(1877–1956; NobelPrize in Chemistry1921)

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Ionizing radiation

NeutronsChadwick, Cavendish Lab, 1932: discoveryof the neutron.

• α particles on 9Be leading to 13C.• Examine resulting radiation using a

gas detector and an oscilloscope!• Pulse height, and increase in signal

when hydrogen gas is placed in beampath, consistent with a neutron and notwith a photon.

James Chadwick(1891–1974; NobelPrize in Physics1935)

• “Up to the present, all the evidence is in favour of the neutron,while the quantum hypothesis [energetic photon] can only beupheld if the conservation of energy and momentum berelinquished at some point.”

• After three weeks of intense work using equipment whichresembled “a piece of discarded plumbing,” Chadwick mails aLetter to Nature, gives a talk on his discovery, and says “now Iwant to be chloroformed and put to bed for a fortnight.”

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Aston and mass spectrometers

• Inspired by J.J. Thomson’s apparatusfor measuring e/m of electrons.

• Find match of orthogonal electric andmagnetic forces giving no deflectionof a charged particle:

qvB = qE so v = E/B

Now measure curvature in a magneticfield:

mv2

r= qvB′ so m =

qBrv

=qBB′r

E

• Aston measures mass of 212 of whatwe now know are 287 stable isotopesat Cavendish Lab starting in 1919.

From Giancoli:

Francis Aston(1877-1945; NobelPrize in Chemistry

1922)

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Stable isotopesMasses of most isotopes are shown in Appendix B of Serway Stable andunstable isotopes (Serway Fig. 13.4; the plot shown here is Fig. 12.7 ofKrane Modern Physics which swaps the Z and N axes):

We will return to this in more detail in the liquid-drop model of thenucleus.

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Some properties of the nucleus

• Atomic mass unit: defined to be 1/12th the mass of a 12C atom.1 u=931.494 043 MeV/c2 = 1.66053886× 10−27 kg

• Proton: charge +1, mass 1.007 276 466 88 u or 938.272 029MeV/c2, spin + 1

2 .• Neutron: charge 0, mass 1.008 664 915 60 u or 939.565 360

MeV/c2, spin + 12

• Nuclear density is approximately constant for all nuclei, soA

(4/3)πR3 = constant or R = R0A1/3 with R0 ' 1.2× 10−15 m.

• There are three types of decay emissions: alpha (α are 42He nuclei),

beta (β are electrons and positrons), and gamma (γ: 0.1-10 MeVphotons).

• Nuclear density is very high! Roughly 1017 kg/m3

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The nucleus: summary

• The nucleus is made up of protons and neutrons. Nuclear density isquite constant constant, so R = R0A1/3 with R0 ' 1.2× 10−15 m.

• The number of protons Z determines electron orbitals, thuschemical behavior, thus element name and position in periodictable. But there are isotopes with the same proton number Z butdifferent neutron number N = A− Z. We write these as AElement,as in 14C and 12C for carbon with 8 or 6 neutrons, respectively.

• Some isotopes are stable, while others are not. Those that areunstable can undergo alpha decay (emission of 4

2He nuclei), betadecay (emission of electrons or positrons), and gamma decay(emission of >100 keV photons). ∆E = ∆mc2 applies.

• Number of nuclei remaining goes like N = N0e−λt, withλ = ln 2/t1/2. Also A = λN, with a common unit being the Curie:1 Ci=3.7× 1010 decays/second.

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Radioactivity• We cannot predict when any one nucleus will decay. We find,

however, that the rate of nuclei that decay is proportional to thenumber present (Serway Eq. 13.8):

dNdt

= −λN (1)

• The activity A = λN (or R = λN in Serway Eq. 13.10) is oftenexpressed in Curies:1 curie (Ci)=3.7× 1010 decays/second.

• Integrating Eq. 1 gives N = N0e−λt where N0 is the number ofnuclei present at t = 0. Since A ∝ N we also have A = A0e−λt.

• It is frequently useful to talk about a half-life, which is the timeover which half the nuclei decay:

N0

2= N0e−λt1/2 → t1/2 =

ln 2λ

=0.693λ

• Since A = λN, A ∝ 1/t1/2. That is, a source with a shorterhalf-life is “hotter.” (The general public automatically assumes thatlong half-lives are worse).

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A radioactive source• Consider a 1 µCi source of 137Cs:

13755 Cs→ β− +137

56 Ba

Note how we have preserved mass (at least approximately) andcharge.

• t1/2 = 30.17 years so

λ =ln 2t1/2

=0.693

(30.17 y) · (365 dy ) · (24 h

d ) · (3600 sh )

= 7.2×10−10 1sec

• Number of atoms is

N =Aλ

=(10−6 Ci) · (3.7× 1010 decays/s/Ci)

7.23× 10−10 s−1 = 5.1×1013 atoms

• Mass is

5.1× 1013 atoms6.02× 1023 atoms/mol

· 137 g/mol = 1.16× 10−8 g

though in fact we will see that A = 137 g/mol is not quite correct.

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Decay chains

Radioactive isotopes often involve a series of decays, and they caninclude branching:

Three natural heavy-element decay chains wind up producing differentisotopes of lead:23892 U→206

82 Pb (t1/2 = 4.47× 109 years)23592 U→207

82 Pb (t1/2 = 7.04× 108 years)23290 Th→208

82 Pb (t1/2 = 1.41× 109 years)

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Decay chains

We’ve outlined the basic single-step radioactive decay processes. In fact,radioactive isotopes often involve a series of decays, and they caninclude branching:

Three natural heavy-element decay chains wind up producing differentisotopes of lead:23892 U→206

82 Pb (t1/2 = 4.47× 109 years)23592 U→207

82 Pb (t1/2 = 7.04× 108 years)23290 Th→208

82 Pb (t1/2 = 1.41× 109 years)

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An example decay chainThe half-life of 235

92 U→20782 Pb is t1/2 = 7.04× 108 years

See also Serway Fig. 13.21.

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Radioactive dating• If we assume that we start out with all parent nuclei, we can

measure the ratio of daughter to parent nucleii (for example byusing a mass spectrometer) to determine the age of an object.

• Consider the case of carbon dating. 14C is created at a steady ratefrom 12C by cosmic ray irradiation of the atmosphere, leading to asteady ratio 14C/12C=1.3× 10−12.

• Note that carbon content of the atmosphere is increasing: CO2 hasgone from 280 ppmv in the year 1800, to 378 ppmv at the end ofthe year 2004. Methane or CH4 is also increasing in the atmospherealthough it is present in the atmosphere at only about 1.8 ppmv.However, the 14C/12C ratio should remain the same.

• Carbon in the atmosphere is taken up by plants which are theneaten by animals, so that everything gets about the same 14C/12Cratio. When something (you, a tree, or a rabbit) dies, it stopscycling carbon.

• We can measure the 14C/12C ratio in a mass spectrometer, but onlyif we can break apart all molecules (for example, rip the carbonsout of the amino acid glycine C2H5NO2).

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An example of using carbon dating• Example 13.11, Serway p. 490. To repeat our basic information:

t1/2 for 14C is 5730 years, or

λ =log(2)

t1/2=

0.6935730 y

1 y365 d

1 d24 h

1 h3600 s

= 3.83× 10−12 s−1,

and “fresh” carbon has the ratio 14C/12C=1.3× 10−12.• The intial number of 12C atoms is

25.0 g12.0 g/mol

6.02× 1023 atoms1 mol

= 1.26× 1024 atoms

The initial number of 14C atoms is1.3× 10−12 · 1.26× 1024 = 1.6× 1012 atoms.

• The activity of 25.0 g of “fresh” carbon due to its 14C mass fractionis thus

R0 = N0λ = (1.6×1012 atoms)·(3.83×10−12 s−1) = 6.13 decays/s

or 370 decays/minute.

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Carbon dating II

• Let’s say we measure an activity in “old” carbon of 250decays/minute. We have

RR0

=NλN0λ

= e−λt

because N = N0e−λt. Taking the logarithm of both sides gives

ln(R/R0) = −λt =ln 2t1/2

t

t = t1/2ln(R0/R)

ln 2= (5730 y)

ln(370/250)

ln 2= 3240 y

• Note that when R→ 0 we have problems; it’s hard to date backmore than about 10 half-lives.

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How old is the earth?

• James Ussher, Archbishop of Armagh (1581-1656): following thechronology of a literal reading of the book of Genesis, the earthwas created on the evening preceding October 23, 4004 BCE.

• Based on observed weathering rates of rocks, 19th centurygeologists estimated at least hundreds of millions of years.

• Fourier and Kelvin, ca. 1900: estimatecooling from the melt. 60 million years? Didnot account for radioactive heating in earth’score.

• Radioactive decay: use mass spectrometers tomeasure ratios 238U/206Pb, 235U/207Pb,232Th/208Pb to infer the age at which theradioactive isotopes were formed.

• Clair Patterson, CalTech: by measuring theseratios in meteorites, one can infer the age ofthe earth: 4.55 billion years. Oldest terrestrialrocks are ∼ 3.5 billion years old.

Clair CameronPatterson,1922–1995

http://www.nap.edu/html/biomems/cpatterson.html

X rays

Röntgen

Use and abuse

Generating X rays

Radioactivity

Rutherford


Isotopes

Nucleus: properties

Radioactivity

Decay chains

Radiactive decay

Radioactive dating

Dating the earth

Patterson: lead

Ionizing radiation

Patterson: get the lead out

• The care required to measure lead isotopes led Patterson to realizethat there was a huge increase in lead in the environment, and heeventualy found a 102–103× increase in human tissues over the lastcentury. The culprit? Tetra-ethyl lead which was used as ananti-knock compound in automotive gasoline beginning in 1921.Patterson devoted considerable efforts to eliminating this beginningin 1962.

• The person who had promoted the use of tetra-ethyl lead inautomotive fuels was Thomas Midgley (1889–1944). Workers atthe plants producing tetra-ethyl lead soon began to show severesymptoms of lead poisoning (including neurological degeneration,and several deaths), though Midgley held press conferences tosupposedly demonstrate the safety of the fuel additive.

X rays

Röntgen

Use and abuse

Generating X rays

Radioactivity

Rutherford


Isotopes

Nucleus: properties

Radioactivity

Decay chains

Radiactive decay

Radioactive dating

Dating the earth

Patterson: lead

Ionizing radiation

Thomas Midgley

• Midgley made another great contribution to industrial chemistry’simpact on the environment: he developed chloro-fluorocarbons(CFCs) as refrigerants, which we now know lead to ozone loss inthe upper atmosphere.

• From Wikipedia:At 51, he contracted polio, which left him severelydisabled. This led him to devise an elaborate system ofstrings and pulleys to lift him from bed. In what must beone of the most ironic deaths in the history of science,Midgley was accidentally entangled in the ropes of thisdevice and died of strangulation at the age of 55.

Wikipedia cites a book by Bill Bryson called A Short History ofNearly Everything. I’ve read the book; it’s wonderful, and tellsmore of the story of both Midgley and Patterson along with manyother stories covering a sweep through most sciences.

X rays

Röntgen

Use and abuse

Generating X rays

Radioactivity

Rutherford


Isotopes

Nucleus: properties

Radioactivity

Decay chains

Radiactive decay

Radioactive dating

Dating the earth

Patterson: lead

Ionizing radiation

Patterson: a responsible scientist

• Patterson wasn’t thrilled about spending time battling lead additivesto fuels. From a cover letter for a manuscript in 1965:

The enclosed manuscript does not constitute basicresearch and it lies within a field that is outside of myinterests. This is not a welcome activity to a physicalscientist whose interests are inclined to basic research.My efforts have been directed to this matter for thegreater part of a year with reluctance and to thedetriment of research in geochemistry. In the end theyhave been greeted with derisive and scornful insults fromtoxicologists, sanitary engineers and public healthofficials because their traditional views are challenged.

• Lead finally banned in U.S. gasoline in 1986, and lead levels in theblood of Americans have dropped by more than 80% since then(similar declines are observed in lead levels in the snow inGreenland).

http://www.nap.edu/html/biomems/cpatterson.html

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