B-fieldpoints

into page

1900-01 Studying the deflection of these rays in magnetic fields, Becquerel and the Curies establish rays to be charged particles

1900-01 Using the procedure developed by J.J. Thomson in 1887 Becquerel determined the ratio of charge q to mass m for

: q/m = 1.76×1011 coulombs/kilogram identical to the electron!

: q/m = 4.8×107 coulombs/kilogram 4000 times smaller!

Discharge Tube

Thin-walled(0.01 mm)glass tube

to vacuumpump &Mercurysupply

Radium or Radon gas

Noting helium gas often found trapped in samples of radioactive minerals, Rutherford speculated that particles might be doubly ionized Helium atoms (He++)

1906-1909 Rutherford and T.D.Royds develop their “alpha mousetrap” to collect alpha particles and show this yields a gas with the spectral emission lines of helium!

Mercury

Status of particle physics early 20th century

Electron J.J.Thomson 1898

nucleus ( proton) Ernest Rutherford 1908-09

Henri Becquerel 1896 Ernest Rutherford 1899

P. Villard 1900

X-rays Wilhelm Roentgen 1895

Periodic Table of the Elements

Fe 26

55.86

Co 27

58.93

Ni 28

58.71

Atomic “weight” values averaged over all isotopes in the proportion they naturally occur.

6

Isotopes are chemically identical (not separable by any chemical means)

but are physically different (mass)

Through lead, ~1/4 of the elements come in “single species”

The “last” 11 naturally occurring elements (Lead Uranium)

recur in 3 principal “radioactive series.”

Z=82 92

92U238 90Th234 91Pa234 92U234

92U234 90Th230 88Ra226 86Rn222 84Po218 82Pb214

82Pb214 83Bi214 84Po214 82Pb210

82Pb210 83Bi210 84Po210 82Pb206

“Uranium I” 4.5109 years U238

“Uranium II” 2.5105 years U234

“Radium B” radioactive Pb214

“Radium G” stable Pb206

Chemically separating the lead from various minerals (which suggested their origin) and comparing their masses:

Thorite (thorium with traces if uranium and lead)

208 amu

Pitchblende (containing uranium mineral and lead)

206 amu

“ordinary” lead deposits are chiefly 207 amu

Masses are given in atomic mass units (amu) based on 6C12 = 12.000000

Mass of bare hydrogen nucleus: 1.00727 amuMass of electron: 0.000549 amu

number of neutrons

number of

protons

dxexfkF ikx)(2

1)(

f(x) g'(x) g(x)= e+ikxi

k

dxxgx'fxgxf )()()()(

2

1

dxek

ix'fe

k

xif ikxikx )()(

2

1

f(x) is

boundedoscillates in thecomplex plane

over-all amplitude is damped at ±

we can integrate this “by parts”

Starting from the defining relation of a Fourier transform:

dxex'fk

ikF ikx)(

2

1)(

)()(2

1kikFdxex'f ikx

Similarly, starting from:

dkekFxf ikx)(2

1)(

)()(2

1xixfdkek'F ikx

And so, specifically for a normal distribution: f(x)=ex2/22

differentiating: )()(2

xfx

xfdx

d

from the relation just derived: kdekF

ixf

dx

d xki ~)

~(

2

1)(

~

2 '

Let’s Fourier transform THIS statement

i.e., apply: dxeikx

2

1on both sides!

dxei

kikF ikx 2

1)( 2 1

2 F'(k)e-ikxdk~ ~~

kdkFi ~

)~

(2 '

ei(k-k)xdx~ 1

2

(k – k)~

kdkFi

kikF~

)~

()( 2 '

ei(k-k)xdx~ 1

2

(k – k)~

)()( 2 kFi

kikF '

selecting out k=k~

rewriting as: 2

)(

/)( kkF

dkkdF

0

k

0

k

dk''

''dk'

22

2

1)0(ln)(ln kFkF

2221

)0(

)( ke

F

kF 22

21

)0()(k

eFkF

2221

)0()(k

eFkF

22 2/)( xexf Fourier transforms

of one anotherGaussian distribution

about the origin

dxexfkF ikx)(2

1)(

Now, since:

dxxfF )(2

1)0(

we expect:

10 xie

22

1)0(

22 2/

dxeF x

2221

2)(k

ekF

22 2/)( xexf Both are of the form

of a Gaussian!

x k 1/

x k 1

orgiving physical interpretation to the new variable

x px h