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Lecture 25

Thursday: 15 April 2004

A Similar Application --Mass Spectrometer

Definition from chemistry:

“Mass spectrometers use the difference in mass-to-charge ratio (m/e) ofionized atoms or molecules to separate them from each other. Massspectrometry is therefore useful for quantitation of atoms or molecules andalso for determining chemical and structural information about molecules.Molecules have distinctive fragmentation patterns that provide structuralinformation to identify structural components.”

Mass Spectrometer Diagram

Adjusting the acceleratingpotential (V) and/or themagnetic field (B) “tunes”the spectrometer to detectonly ions with a specificratio of charge to mass.

Basic Operation of a Magnetic Sector Mass Spectrometer

Stage 1: IonizationThe atom is ionized by knocking one or more electrons off to give a positiveion. This is true even for things which you would normally expect to formnegative ions (chlorine, for example) or never form ions at all (argon, forexample). Mass spectrometers always work with positive ions.

Stage 2: AccelerationThe ions are accelerated so that they all have the same kinetic energy.

Stage 3: DeflectionThe ions are then deflected by a magnetic field according to their masses. Thelighter they are, the more they are deflected.The amount of deflection also depends on the number of positive charges onthe ion – in other words, on how many electrons were knocked off in the firststage. The more the ion is charged, the more it gets deflected.

Stage 4: DetectionThe beam of ions passing through the machine is detected electrically.

Class #25Take-Away Concepts

1. The ratio of e/m is determined by accelerating a streamof electrons through an electric potential difference andobserving their path in a magnetic field.

2. The formula for e/m (know how to derive it):

22 Br

V2

m

e

3. Mass spectrometers work by the same principle.

Optional Material for Class #25

How do we know the mass of an electron?

This is a great question!

We just measured e/m for an electron using table-top instruments thatwould have been available (in some form) 100 years ago.

The first accurate measurement of the mass of the electron was made(indirectly) by Robert Andrews Millikan in 1910. How did he do it?

Robert Andrews Millikan

R.A. Millikan1868-1953

Oil DropExperiment

(1910)

At the University of Chicago in 1910, Millikan developed his famous oil dropexperiment to determine the charge on an electron. An atomizer sprayed small oildroplets into the top chamber. Some of them fell through a small hole into a secondchamber. X-rays caused the air in the second chamber to become ionized. Thedrops in the second chamber picked up a small (variable) number of electrons.They were acted upon by both the force of gravity and an opposing electrical forcecreated by an adjustable electrical potential difference between the top and bottom.

Analysis of Oil Drop Experiment

Oil Drop

Q E

M g

1 . W i t h E = 0 , t h e t e r m i n a l v e l o c i t y o f t h e d r o p f a l l i n g t h r o u g ha i r a l l o w s c a l c u l a t i o n o f i t s m a s s ( M ) v i a a k n o w nm a t h e m a t i c a l r e l a t i o n s h i p .

2 . O n c e M i s k n o w n , E i s a d j u s t e d s o t h a t t h e d r o p i s i ne q u i l i b r i u m ( d r o p s t o p p e d ) . T h e n Q i s d e t e r m i n e d :

E

gMQ

3 . S t e p s 1 a n d 2 a r e r e p e a t e d m a n y t i m e s . E a c h d r o p h a s ad i f f e r e n t M a n d Q , b u t w h e n e n o u g h d r o p s a r e e x a m i n e d , t h es m a l l e s t d i f f e r e n c e b e t w e e n d i f f e r e n t Q v a l u e s i s f o u n d t o b ee , t h e c h a r g e o n o n e e l e c t r o n ( i g n o r i n g t h e – s i g n ) .

4 . T h e m a s s o f t h e e l e c t r o n i s

kg101.9)106.1()1076.1(em

em 3 11 9111

1

Physical Principles of DesignActivity for Class 24 Monday: 12

April 2004

“e/m Ratio for the Electron” J.J.Thomson-Experiment

Joseph John (“J.J.”) Thomson

J.J. Thomson1856-1940

J.J. Thomson was appointed in 1884 asthe third Cavendish Professor (head ofthe Cavendish Laboratory) at Cambridge,after James Clerk Maxwell and LordRayleigh. In 1899, his experiments withcathode ray tubes led him to postulate theexistence of a new particle with a ratio ofcharge to mass (e/m) far larger than thesame ratio for a positive hydrogen ion.

The word “electron” was coined in 1891 by G. Johnstone Stoney.

Today we will measure e/m for the electron.

Calculating Change in K.E.from Electric Potential (Review)

V = 50

V = 0

V = 100

initial

final

e

e

0UK o r UK V)e(VqU o r V)e(U

J106.1

)100()106.1()V)(e(K17

19

I f t h e e l e c t r o n s t a r t s a t r e s t ( o r v e r y c l o s e t o i t ) ,t h e n

Vevm 22

1

Magnetic Force on aMoving Charge (Review)

BvqF

q: charge of the particle (C; + or –)v:velocity of the particle (m/s)B:magnetic field (T) Force is at a right angle to velocity. Force is at a right angle to magnetic field.

Important: If q is negative, that reverses the direction of force.

The Radius of the Circle (Review)

v

r

F

A l t h o u g h t h e d i r e c t i o n s o f t h e v e c t o r s a r ec h a n g i n g , t h e m a g n i t u d e s s t a y t h e s a m e .

rv

mamF2

BvqF

rv

mBvq2

Bqvm

Bvqv

mr2

Apparatus for Measuring e/m

We will set Potential in tube (V). Current in coils (I).

We will observe Radius of circular

electron path (r).

We will calculate e/m.

The Cathode Ray Tube

Electrons

Electrons are randomly kickedout of the metallic cathode bythermal energy.

Once free of the metal, the electrons are accelerated througha potential difference of V from cathode to anode.

Analysis of Electron Acceleration

Electron Stream

pot = -V pot = 0

cathode anode UK V)e(U

Ve)]V(0[e

]V)[e(K

E l e c t r o n s h a v e v e r y l o w k i n e t i ce n e r g y w h e n t h e y l e a v e t h ec a t h o d e – e s s e n t i a l l y z e r o .

Vevm 22

1 o r

mVe2

v

Helmholtz Coils

MagneticField

H e l m h o l t z C o i l s a r e d e s i g n e d t o h a v e an e a r l y u n i f o r m ( c o n s t a n t ) m a g n e t i cf i e l d i n t h e c e n t e r . T h e f i e l d d i r e c t i o n i sa l o n g t h e a x i s o f t h e c o i l s . T h em a g n i t u d e i s p r o p o r t i o n a l t o I , t h ec u r r e n t . T h e f o r m u l a t o c a l c u l a t e t h i s i sa P h y s i c s 2 t o p i c , b u t f o r o u r c o i l s ,

I108.7B 4w h e r e B i s i n t e s l a a n d I i s i n a m p e r e s .

Derivation of e/m Formula

Be

vmr

Br

v

m

e

m

Ve2v

Br

V2

m

e

Br

V2m

e

Brm

Ve2

m

e

Br

V2

m

e o r22 Br

V2

m

e We set or observe all of the variableson the right side of the equation.

Experimental Procedure

1. Turn up V to get an electronbeam. Record V.

2. Turn up I (to make B) until theelectrons make a complete circle.Record I.

3. Observe r – use the mirroredscale in the rear.

3a. Or (easier): Adjust I until theelectrons just hit the far side ofthe tube. This is a known radius(5.5 cm). Record I.

4. Repeat three times with differentvalues of V.

Viewing the Electron Path

Activity #25Measuring e/m for the Electron

Objective of the Activity:

1. Work through the analysis steps to get the e/m formula.

2. Take your own measurements and compare your value of e/mfor an electron with the known value. (1.76 x 10+11 C/kg)