cape physics module 3

8/16/2019 CAPE PHYSICS MODULE 3

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photoelectric effect

In the photoelectric effect, electrons are emitted from matter (metals and non-metallic

solids, liquids or gases) as a consequence of their absorption of energy

from electromagnetic radiation of very short wavelength, such

as visible or ultraviolet radiation. Electrons emitted in this manner may be referred to asphotoelectrons.

The energy supplied by the photon will be, E =hf. Where h is planck’s

constant and f is the frequency of the light (radiation). t therefore !eans

that the !a" #.E. gained by the liberated electrons will be equi$alent to hf.

%o #.E.!a" = hf.

The photons of a light beam have a characteristic energy proportional to the frequency

of the light. In the photoemission process, if an electron within some material absorbs

the energy of one photon and acquires more energy than the wor function (the electron

binding energy) of the material, it is e!ected. If the photon energy is too low, the electron

is unable to escape the material. Increasing the intensity of the light beam increases the

number of photons in the light beam, and thus increases the number of electrons

e"cited, but does not increase the energy that each electron possesses. The energy of

the emitted electrons does not depend on the intensity of the incoming light, but only on

http://en.wikipedia.org/wiki/Electronhttp://en.wikipedia.org/wiki/Liquidshttp://en.wikipedia.org/wiki/Gaseshttp://en.wikipedia.org/wiki/Electromagnetic_wavehttp://en.wikipedia.org/wiki/Wavelengthhttp://en.wikipedia.org/wiki/Visible_lighthttp://en.wikipedia.org/wiki/Ultraviolet_lighthttp://en.wikipedia.org/wiki/Radiationhttp://en.wikipedia.org/wiki/Photonhttp://en.wikipedia.org/wiki/Work_functionhttp://en.wikipedia.org/wiki/Liquidshttp://en.wikipedia.org/wiki/Gaseshttp://en.wikipedia.org/wiki/Electromagnetic_wavehttp://en.wikipedia.org/wiki/Wavelengthhttp://en.wikipedia.org/wiki/Visible_lighthttp://en.wikipedia.org/wiki/Ultraviolet_lighthttp://en.wikipedia.org/wiki/Radiationhttp://en.wikipedia.org/wiki/Photonhttp://en.wikipedia.org/wiki/Work_functionhttp://en.wikipedia.org/wiki/Electron


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the energy or frequency of the individual photons. It is an interaction between the

incident photon and the outermost electron.

Experimental observations of photoelectric emission

The theory of the photoelectric effect must e"plain the e"perimental observations of the

emission of electrons from an illuminated metal surface.

#or a given metal, there e"ists a certain minimum frequency of incident radiation below

which no photoelectrons are emitted. This frequency is called the threshold frequency.

Increasing the frequency of the incident beam, eeping the number of incident photons

fi"ed (this would result in a proportionate increase in energy) increases the ma"imum

inetic energy of the photoelectrons emitted. Thus the stopping voltage increases. The

number of electrons also changes because the probability that each photon results in an

emitted electron is a function of photon energy.

$bove the threshold frequency, the ma"imum inetic energy of the emitted

photoelectron depends on the frequency of the incident light, but is independent of theintensity of the incident light so long as the latter is not too high %&'

#or a given metal and frequency of incident radiation, the rate at which photoelectrons

are e!ected is directly proportional to the intensity of the incident light. Increase in

intensity of incident beam (eeping the frequency fi"ed) increases the magnitude of the

photoelectric current, though stopping voltage remains the same.

The time lag between the incidence of radiation and the emission of a photoelectron is

very small, less than *& second.

+athematical equation

+a". .E. hf / 0

1or function, 0 / is the minimum energy required to liberate an electron from the

surface of a metal. If no electrons are emitted the .E. , then

hf / 0

hf 0

f 02h , where f is the threshold frequency. Threshold frequency is the

minimum frequency required for photoemission.

&ro! the wa$e equation c = f' , where c is the speed of light , ' is the

wa$elnght.

%o c' = 02h

3 02hc , where 3 is the cut-off wavelength.

http://en.wikipedia.org/wiki/Photoelectric_effect#cite_note-Zhang1996-8http://en.wikipedia.org/wiki/Photoelectric_effect#cite_note-Zhang1996-8


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STOPPING POTENTIAL

The electrons with the !a"i!u! #E can be stopped fro! co!pleting their ourney across the photoelectric tube if there is a stopping potential set*upto i!pede their progress. The for!ula that relates the #E of these

photoelectrons to this stopping potential is Ema" e4stopping

where

4stopping is the stopping potential, and


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e is the magnitude of the charge of an electron, .5 " -& coulombs.

This formula is based on the fact that wor is done on charged particles when they

cross through an electric field. The wor done (q∆4) equals the change in each

electron6s E.

f all the electrons are stpped it !eans the !a". k.e. = +

%o +=hf - * e4stopping

es = hf -

s = hfe * -e

/y plotting a graph of stopping potential $s frequency then

• he represents the gradient

• -e represent the y*intercept

http://online.cctt.org/physicslab/content/phyapb/lessonnotes/electrostatics/lessonelectricpotential.asphttp://online.cctt.org/physicslab/content/phyapb/lessonnotes/electrostatics/lessonelectricpotential.asphttp://online.cctt.org/physicslab/content/phyapb/lessonnotes/electrostatics/lessonelectricpotential.asphttp://online.cctt.org/physicslab/content/phyapb/lessonnotes/electrostatics/lessonelectricpotential.asphttp://online.cctt.org/physicslab/content/phyapb/lessonnotes/electrostatics/lessonelectricpotential.asphttp://online.cctt.org/physicslab/content/phyapb/lessonnotes/electrostatics/lessonelectricpotential.asp


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&ro! the equation 0 +a". .E. hf / 0, the equation can be written in another

way

7 mv8 hf / 0 , where v is the velocity of the liberated electrons.

This graph indicates

The photoelectric e1ect has so!e curious properties that cannot be

e"plained by classical physics. t was found that the nu!ber of electrons


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released by a !etal was proportional to the a!ount of ultra$iolet light, while

the energy of the electrons depended on the frequency of the light. /elow a

threshold frequency, there are no electrons released at all, no !atter how

bright the light is, while abo$e the threshold frequency, there are always

electrons released, no !atter how di! the light is. This contradicted classical

physics because classical wa$e theory stated that either increased intensity

or increased frequency should pro$ide !ore energy in the sa!e way, but the

obser$ed e1ect showed that only increased frequency pro$ided the needed

energy to eect an electron fro! the !etal.

t was proposed that light could not only be wa$es, but could also co!e in

packets of energy, as photons. 2s a photon hit an electron, it would pro$ide it

with a certain a!ount of energy. f it was enough, the electron would be

kicked to the surface of the !etal and be obser$ed, but if it wasn3t enough,

the electron would fall back to its ato!. Therefore, photons with energy

below the threshold had no discernible e1ect and the nu!ber of photons

could only deter!ine how !any electrons were released, as only one photon

at a ti!e was likely to hit an electron.

X-RAY

4*rays are produced when rapidly !o$ing electrons that ha$e been

accelerated through a potential di1erence of order 5 k to 5 6 strikes

a !etal target.

Electrons fro! a hot ele!ent are accelerated onto a target anode.

When the electrons are suddenly decelerated on i!pact, so!e of the

kinetic energy is con$erted into E6 energy, as 4*rays.


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7ess than 5 8 of the energy supplied is con$erted into 4*radiation during this

process. The rest is con$erted into the internal energy of the target

Properties of X-rays

4*rays tra$el in straight lines.

4*rays cannot be de9ected by electric :eld or !agnetic :eld.

4*rays ha$e a high penetrating power.

;hotographic :l! is blackened by 4*rays.

&luorescent !aterials glow when 4*rays are directed at the!.

;hotoelectric e!ission can be produced by 4*rays.

oni


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The graph shows the following features.

2 continuous background of 4*radiation in which the intensity

$aries s!oothly with wa$elength. The background intensity

reaches a !a"i!u! $alue as the wa$elength increases, then the

intensity falls at greater wa$elengths.

6ini!u! wa$elength which depends on the tube $oltage. The

higher the $oltage the s!aller the $alue of the !ini!u!

wa$elength.

%harp peaks of intensity occur at wa$elengths una1ected by

change of tube $oltage.

Minimm !a"elengt# in t#e X-ray Spectra

When an electron hits the target its entire kinetic energy is con$erted

into a photon.

The work done on each electron when it is accelerated onto the anode

is eV.

>ence hf = eV and the !a"i!u! frequency

h

eV f =max

eV

hc=

minλ

$#aracteristic X-ray Spectra

?i1erent target !aterials gi$e di1erent wa$elengths for the peaks in

the 4*ray spectra.


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The peaks are due to electrons knock out inner*shell electrons fro!

target ato!s.

When these inner*shell $acancies are re:lled by free electrons, 4*ray

photons are e!itted.

The peaks for any target ele!ent de:ne its characteristic 4*ray

spectru!

%ses of X-rays

n !edicine

To diagnose illness and for treat!ent.

n industry

To locate cracks in !etals.

4*ray crystallography

To e"plore the structure of !aterials.

Attenuation of X-Rays By Matter


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9-rays are attenuated as they pass through matter. That is, the intensity of an 9-raybeam decreases the farther it penetrates into matter. :asically, each interaction of an 9-ray photon with an atom of the material removes an 9-ray from the beam, decreasing itsintensity.

The amount of decrease in intensity of the 9-ray beam depends upon two factors

• The depth of penetration ( x ) or thicness

• $ characteristic of the material called its ;absorption coefficient; ( A).

The intensity decreases e"ponentially with the distance traveled, or

I I e"p (/ Ax )

where I is the initial 9-ray beam intensity.


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Atomic spectral line

In physics, one thins of atomic spectral lines from two viewpoints.

$n emission line is formed when an electron maes a transition from a

particular discrete energy level E@ of an atom, to a lower energy level E5, emitting a

photon of a particular energy and wavelength. $ spectrum of many such photons will

show an emission spie at the wavelength associated with these photons.

$n absorption line is formed when an electron maes a transition from a

lower, E5, to a higher discrete energy state, E@, with a photon being absorbed in the

process. These absorbed photons generally come from bacground continuum

radiation and a spectrum will show a drop in the continuum radiation at thewavelength associated with the absorbed photons.

The two states must be bound states in which the electron is bound to the atom, so the

transition is sometimes referred to as a ;bound/bound; transition, as opposed to a

transition in which the electron is e!ected out of the atom completely (;bound/free;

transition) into acontinuum state, leaving an ioni@ed atom, and generating continuum

radiation.

$ photon with an energy equal to the difference E 2 − E 1 between the energy levels is

released or absorbed in the process. The frequency ν at which the spectral line occursis related to the photon energy by :ohr6s frequency

condition E 2 - E 1 = hf where h denotes Alanc6s constant.

Energy levels of Hydrogen

http://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Energy_levelhttp://en.wikipedia.org/wiki/Bound_statehttp://en.wikipedia.org/wiki/Continuous_spectrumhttp://en.wikipedia.org/wiki/Ionizationhttp://en.wikipedia.org/wiki/Photonhttp://en.wikipedia.org/wiki/Planck's_constanthttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Energy_levelhttp://en.wikipedia.org/wiki/Bound_statehttp://en.wikipedia.org/wiki/Continuous_spectrumhttp://en.wikipedia.org/wiki/Ionizationhttp://en.wikipedia.org/wiki/Photonhttp://en.wikipedia.org/wiki/Planck's_constant


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ave ! particle nature of matter

The theory was proposed by =ouis de :roglie in &8B in his AhC thesis.%'. The de

Broglie relations show that the wavelength is inversely proportional to

themomentum of a particle and is also called de Broglie "avelength. $lso

the frequency of matter waves, as deduced by de :roglie, is directly proportional to the

particle6s total energy, i.e. the sum of particle6s inetic energy and rest energy.

$t the end of the &th century, light was thought to consist of waves of electromagnetic

fields which propagated according to +a"wellDs equations, while matter was thought to

consist of locali@ed particles (ee history of wave and particle viewpoints ). This division

was challenged when, in his &F paper on the photoelectric effect, $lbert

Einstein postulated that light was emitted and absorbed as locali@ed pacets, or

GquantaH (now calledphotons). These quanta would have an energy

Ehf

$s a wave light shows interference and diffractive properties.

$s a particle it can be e"plained using the photoelectric effect.

Cerivation for Ce :roglie Equation

?e /roglie, in his research, decided to look at Einstein’s research on

photons or particles of light and how it was possible for light to be

considered both a wa$e and a particle. 7et us look at how there is a

relationship between the!.

We get fro! Einstein (and ;lanck) two equations for energyA

E = h f (photoelectric e1ect) B E = !c@ (Einstein’s %pecial

Celati$ity)

Dow let us oin the two equationsA

E = h f = ! c@

http://en.wikipedia.org/wiki/Louis_de_Brogliehttp://en.wikipedia.org/wiki/Matter_wave#cite_note-0http://en.wikipedia.org/wiki/Wavelengthhttp://en.wikipedia.org/wiki/Inversely_proportionalhttp://en.wikipedia.org/wiki/Momentumhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Total_energyhttp://en.wikipedia.org/wiki/Kinetic_energyhttp://en.wikipedia.org/wiki/Rest_energyhttp://en.wikipedia.org/wiki/Maxwell%E2%80%99s_equationshttp://en.wikipedia.org/wiki/Wave-particle_duality#Brief_history_of_wave_and_particle_viewpointshttp://en.wikipedia.org/wiki/Photoelectric_effecthttp://en.wikipedia.org/wiki/Albert_Einsteinhttp://en.wikipedia.org/wiki/Albert_Einsteinhttp://en.wikipedia.org/wiki/Photonshttp://en.wikipedia.org/wiki/Louis_de_Brogliehttp://en.wikipedia.org/wiki/Matter_wave#cite_note-0http://en.wikipedia.org/wiki/Wavelengthhttp://en.wikipedia.org/wiki/Inversely_proportionalhttp://en.wikipedia.org/wiki/Momentumhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Total_energyhttp://en.wikipedia.org/wiki/Kinetic_energyhttp://en.wikipedia.org/wiki/Rest_energyhttp://en.wikipedia.org/wiki/Maxwell%E2%80%99s_equationshttp://en.wikipedia.org/wiki/Wave-particle_duality#Brief_history_of_wave_and_particle_viewpointshttp://en.wikipedia.org/wiki/Photoelectric_effecthttp://en.wikipedia.org/wiki/Albert_Einsteinhttp://en.wikipedia.org/wiki/Albert_Einsteinhttp://en.wikipedia.org/wiki/Photons


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&ro! there we getA

h f = p c (where p = !c, for the !o!entu! of a photon)

h p = c f

%ubstituting what we know for wa$elengths (' = $ f, or in this

case c f )A

h !c = '

hp ='

?e /roglie saw that this works perfectly for light wa$es, but does

it work for particles other than photons

ELE$TRON &I''RA$TION

• &e (roglie)s !a"es are not EM !a"es

– *e calle+ t#em ,pilot or ,material !a"es

– λB +epen+s on t#e momentm an+ not on p#ysical si.e of

t#e particle

• 'or a non-relati"istic free particle/

– Momentum is p = mv 0 #ere v is t#e spee+ of t#e particle

–

Em

h

mv

h

p

h B

2===λ

'or free particle total energy0 E0 is 1inetic

energy

22

22 mv

m

p K E ===


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ATOMI$ STR%$T%RE

T#omson Mo+el

>e proposed a !odel of the ato! that is so!eti!es called the F;lu!

;uddingG !odel.

2to!s were !ade fro! a positi$ely charged substance with negati$ely

charged electrons scattered about, like raisins in a pudding.

Rt#erfor+)s Gol+ 'oil E2periment

Cutherford’s e"peri!ent n$ol$ed :ring a strea! of tiny positi$ely

charged particles at a thin sheet of gold foil (@+++ ato!s thick)

6ost of the positi$ely charged FbulletsG passed right through the

gold ato!s in the sheet of gold foil without changing course at

all.

%o!e of the positi$ely charged Fbullets,G howe$er, did bounce

away fro! the gold sheet as if they had hit so!ething solid. >e

knew that positi$e charges repel positi$e charges.


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This could only !ean that the gold ato!s in the sheet were !ostlyopen space. 2to!s were not a pudding :lled with a positi$ely charged

!aterial.

Cutherford concluded that an ato! had a s!all, dense, positi$ely

charged center that repelled his positi$ely charged Fbullets.G

>e called the center of the ato! the FnucleusG

The nucleus is tiny co!pared to the ato! as a whole.

Cutherford reasoned that all of an ato!’s positi$ely charged particles

were contained in the nucleus. The negati$ely charged particles were

scattered outside the nucleus around the ato!’s edge


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(o#r Mo+el

2ccording to /ohr’s ato!ic !odel, electrons !o$e in de:nite orbits

around the nucleus, !uch like planets circle the sun. These orbits, or energy

le$els, are located at certain distances fro! the nucleus

&isproof of t#e P++ing

• Cutherford calculated fro! the results **5H55

• To re9ect alpha the I$e charge (and !ost of the !ass) has to be in a

$ery s!all dia!eter

• 2bout 5+*5J ! co!pared to 5+*5+ ! for the dia!eter of the ato!


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Solar System Mo+el

• Positi"ely c#arge+ ncles at centre

• Negati"ely c#arge+ electrons in or3it

• Pro3lem 4

– Or3iting electrons are accelerating 4

– 5ill gi"e o6 energy 4

– 5ill spiral in to centre

• Mo+el not sta3le

S3atomic Particles

Particle Sym3ol $#arge Relati"e

Mass

Electron e- 7- 8

Proton p9 9 7

Netron n 8 7

Atomic Sym3ols

Show the mass nm3er an+ atomic nm3er

Gi"e t#e sym3ol of t#e element

mass nm3er

:; Na so+im-:;

atomic nm3er 77


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Nm3er of Electrons

An atom is netral

T#e net c#arge is .ero

Nm3er of protons < Nm3er of electrons

Atomic nm3er < Nm3er of electrons

Mass Nm3er * Counts the number of protons and neutrons in

an atom

Isotopes Atoms !it# t#e same nm3er of protons0 3t +i6erent

nm3ers of netrons= Atoms of t#e same element >same atomic nm3er? !it#

+i6erent mass nm3ers Isotopes of c#lorine

;@$l ;$l7 7

c#lorine - ;@ c#lorine 4 ;

E2ample of an A"erage Atomic Mass

$l-;@ is a3ot @=@ B an+ $l-; a3ot :C=@B of natral

c#lorine=;@ 2 @=@ < :D=C

788;@=@

; 2 :C=@ < =8788

Milli1an)s oil +rop e2periment=


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6illikan deter!ined the sie showed that there was a s!allest Kunit’ of charge or that charge

is Kquantised’.

>e did this by !easuring the charge on nu!erous !icroscopic

charged oil drops.

2ll the charges were found to co!e in !ultiples of the basic Kunit’A

@e, Le or De where D is any whole nu!ber.

The charge of the electron e= 5.MN5+*5H is the s!allest a!ount

of charge detected.


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Nclear P#ysics

Ra+iationsA

5) a, b*, g are all e!itted0

@) protons and neutrons are DOT e!itted, e"cept in the case of !ass

nu!bers J and H0

L) alphas are e!itted only for !ass nu!bers greater than @+H, e"cept in the

case of !ass nu!ber P.

Alp#a > ? +ecay

e2ample/ :%:;F 8T#:;C 9 :aC 9

(eta mins >3-? +ecay

e2ample/ D$7C N7C 9 -738

$#arge an+ mass nm3ers are conser"e+

General RlesA

5) a e!itted to reduce !ass, only e!itted if !ass nu!ber is abo$e @+H


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@) b* e!itted to change neutron into proton, happens when there are too

!any neutrons

L) g e!itted to conser$e energy in reaction, !ay acco!pany a or b.

Alp#a &ecay

(eta &ecay

Gamma &ecay

Qa!!a rays are not charged particles like a and b particles.

Qa!!a rays are electro!agnetic radiation with high frequency.

When ato!s decay by e!itting a or b particles to for! a new ato!, the

nuclei of the new ato! for!ed !ay still ha$e too !uch energy to be

co!pletely stable.

This e"cess energy is e!itted as ga!!a rays (ga!!a ray photons ha$e

energies of R 5 " 5+*5@ S).

Mass &efect H (in+ing Energy


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/y +enition, !ass of M5@ is 5@.+++++ a!u.

The !ass of a proton (plus electron) is 7=88F: a!u. (The !ass of a

proton by itself is 5.++U@P a!u, and the !ass of an electron is +.+++JJ

a!u.)

The !ass of a netron is 7=88FDD@ am.

Dote that DJmproton9e 9 DJmnetron K m$-7:

T#e missing mass !as con"erte+ into energy >E7=88F: am? 9 D>7=88FDD@ am? - 7:=88888 am

< =8 am

(E < mJc: <

>8=8 am?J>7=DD278-:1gam?J>;278Fms?:

< 7=CF278-77 J>7 e7=D278-7 ? < :=; Me

'or $ar3on-7: !e #a"e/

(E < &mJc:

< :=; Me

If !e consi+er t#e 3in+ing energy per ncleon0 !e #a"e for car3on-

7:/

(Encleon < :=; Me 7: < =8 Mencleon

T#e largest (Encleon #appens for t#e sta3le isotopes of iron

>a3ot F=F Mencleon?=


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'ission an+ fsion


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Rate of +ecay

&ro! e"peri!ent, we :nd that the a!ount of decay of a radioacti$e !aterial

depends only on two thingsA the a!ount of radioacti$e !aterial and the

type of radioacti$e !aterial (the particular isotope).

The rate of decay does DOT depend on te!perature, pressure, che!ical

co!position, etc.

6athe!atically, then, we ha$eA

dDdt = *'ND

where ' is a constant that depends on the particular isotope, D is the

nu!ber of radioacti$e isotopes present, and the !inus sign co!es fro! the

fact that dDdt is ?ECE2%DQ rather than growing.

We can sol$e this di1erential equation for D(t)A dDdt = *'D , or dDD =

*'dt , or log (DDo) = *' t , or N>t? < No e-Qt .

&urther, if we de:ne acti$ity, 2, as

A < -+N+t then A < QD = 'Doe*lt = Aoe

-Qt 0

which !eans that t#e acti"ity +ecreases e2ponentially !it# time also.

*alf Life

N>t? < No e-lt The nu!ber of radioacti$e ato!s does decrease with ti!e.

/ut is there a +enite time in !#ic# t#e nm3er +ecreases 3y #alf ,

regardless of what the beginning nu!ber is VE%A

D(T=half life) = Do@ = Doe*'T , or 5@ = e*'T

or *'T = ln(5@) = ln(5) ln(@) = + * ln(@), or T>#alf life? < ln>:? Q .

Ce$iewA N>t? < No e-Qt

A < lD = Aoe-Qt

T>#alf life? < ln>:? Q .

We can n+ T(half life) if we can wait for D (or 2) to decrease by half.

We can n+ l by !easuring D and 2.

f we know either l or T(half life), we can :nd the other.


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Log grap#

E2ample of carbon datingA


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The present day ratio of *5 to *5@ in the at!osphere is 7=;278-7: . The

half*life of *5 is @0;8 years. What is the acti$ity of a 5 g! sa!ple of

carbon fro! a li$ing plant

A = 'D = Xln(@)JUL+ yearsYNXM"5+@L ato!s!ole N 5!ole5@ gra!s N 5

gra!YNX5.L"5+*5@ Y = U.PM"5+Myr = .@Hsec = 7@=8min

Thus, for one gra! of carbon, 2o = 5J.+!in .

f a 5 gra! carbon sa!ple fro! a dead plant has an acti$ity of H.+!in, then

usingA

A < Aoe-Qt ,

we ha$e H.+!in = 5J.+!in N e*(ln@JUL+yrs)t , or *(ln@JUL+ yrs)Nt = ln(H5J) ,

or

t = JUL+ years N ln(5JH) ln(@) = C0:88 years

cape physics module 3

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