Transcript no electric field - the SASPhysics.com

Unit 5D
Turning Points in Physics
Chapter 1 – The electron
Part 1 – The discovery of the electron
• Allesandro Volta invented the first
battery in 1800, but the nature of
electricity wasn’t really understood
• It was found that, by making and
breaking a circuit and using coil of
wire, high voltages could be
generated, producing sparks (1850s)
• But could electricity flow even
without air?
Gas Discharge Tubes
• Developments in glass blowing and vacuum
pump technology were key to making progress
• Around 1857 Heinrich Geissler produced the
first working gas discharge tube
Gas Discharge Tubes
• It was found that, for low pressure gas,
electricity was conducted and glowing regions
appeared in the tube.
• This was attributed to “rays” coming from the
electrodes, but there was much debate about
their source and nature.
• Different gases in the tube produced different
colours of light.
Gas Discharge Tubes
• Soon
decorative
Geissler
tubes were
being sold as
amusements,
like today’s
plasma balls.
Gas Discharge Tubes
• The details of the glowing regions also
depended on the applied voltage and the
pressure of the gas
FF: What causes the glow?
• Near the cathode:
– The strong electric field ionizes some gas atoms.
– Nearby positive ions hit the cathode and release more
of the free electrons
– Electron-ion pairs recombining release energy as
emitted photons (negative glow)
• Near the anode:
– Some electrons get further and collide with atoms to
excite them, then the atoms emit photons when they
drop back to their ground states.
Crooke’s Tube
• At lower gas pressures
the glass itself glowed
• Moving the anode
around the corner
suggested the cathode
was the source of the
rays
• Casting of shadows
suggested rays
travelled in straight
lines
• (Roentgen went on to discover
x-rays using the same
apparatus)
A flurry of activity...
• William Crookes, Johann Hittorf, Juliusz Plücker,
Eugen Goldstein, Heinrich Hertz, Philipp Lenard,
J.J. Thomson and others investigated the nature
of cathode rays
William Crookes
J. J. Thomson
Eugen Goldstein
Key Experimental Findings
• A paddle wheel is
pushed from – to + when
a voltage is applied.
Shining light on it
doesn’t move it.
• The rays are deflected by
magnetic and electric
fields.
Pulling it all together
• J .J. Thomson ended the debate in 1897.
• He demonstrated that cathode rays:
1.
2.
3.
4.
have energy, momentum and mass,
are not electromagnetic waves,
have a negative charge,
have the same properties even if you change the gas or
the material of the cathode,
5. have a specific charge much higher than that of hydrogen
atoms,
6. travel in straight lines.
•
The electron was “discovered”.
Thermionic Emission
• In discharge tubes electrons
are produced by ionising gas
atoms with an electric field
• A more efficient way of
producing them is to use
thermionic emission and
accelerate them with an
electric field in a vacuum.
• Used in Valves (Fleming,
1904) and enabled the birth
of electronics and computers
• Still used in some esoteric
applications (eg iTube
amplifier and dock)
Thermionic Emission
• Increasing temperature
increases the electron energy
• So at higher temperature
more electrons have enough
energy to leave the surface of
the metal
• Like a crowded fish pond!
• With some encouragement,
electrons can leave
permanently
The Electron Gun
The Electron Gun
The Electron Gun
• Electrons are released through thermionic emission are accelerated
towards the anode
• Some escape through a hole in the anode
• No field beyond the anode, so travel on with constant velocity
• Need a vacuum to avoid electrons colliding with other particles
• Filament current adjusts number of electrons (intensity of beam)
• Accelerating voltage adjusts speed of electrons (energy of beam)
• (usually inside of tube has a conductive coating to provide a return
path and keep the tube itself neutral)
Speed of Electrons
Work done by field  eVA
1
Kinetic energy gained  mv 2
2
1
eVA  mv 2 ,
2
2eVA ...provided we are well
away from the speed of
so v 
light!
m
Electron Deflection – E field
• The faster the electrons are travelling, the less they are
deflected
Electron Deflection – E field
Constant vertical force of
eV/d experienced by
electrons between plates
So maximum
deflection Y
is proprtional
to Vp
F eV p
a 
,
m md
1 2
y  at
2
Constant vertical
acceleration and x
velocity, so path
here is PARABOLIC
(remember SUVAT)
p
p
Y
p
p
Electron Deflection – B field
• Helmholtz coils give a
(calculable) uniform field over
most of the volume in
between the coils
• If we provide a magnetic field
perpendicular to the e-beam
we induce a circular path
Electron Deflection – B field
• Magnetic field produces a
force always perpendicular to
direction of electron travel
– Circular motion
Force due to magnetic field : F  Bev
mv2
For circular motion : Bev 
r
The faster the electrons are travelling,
the less they are deflected
Fine beam tube contains
a horizontally mounted egun and is filled with low
pressure gas to show
electron path
Specific Charge of the Electron (1)
• Balance opposite forces from E and B fields
• If e-beam is undeflected:
Bev 
eV p
d
, so v 
Vp
Bd
– This gives us the velocity.
• Now switch off B-field to get deflection y:
e ad
 F
a   
so 
m Vp
 m  md
eV p
All directly
measurable
quantities
2y
L
e 2 yv 2d 2 yV p
we know a  2 and t  , so  2
 2 2
t
v
m
L Vp
LB d
Specific Charge of the Electron (1)
• Alternatively: we still have
Bev 
eV p
d
, so v 
Vp
Bd
• Now switch off E-field to get circular motion,
measure radius r:
mv 2
 Bev
r
Vp
e
v
so 
 2
m Br B dr
All directly
measurable
quantities
You don’t need to
memorise this, but you do
need to know which
equations apply (on
formula sheet) and be able
to do similar calculations
Specific Charge of the Electron (2)
• Deflect with a B field, calculate centripetal
force (fine beam tube)
mv 2
Ber
 Bev , so v 
r
m
remember w e calculated velocity from e - gun :
2eVA
Ber
2eVA
v
, so

m
m
m
e
2V
or  2 A2
m B r
All directly
measurable
quantities
Specific Charge of the Electron (2)
• For a better value can
measure values of r and B.
e
2VA
2VA m 1 k
 2 2 , so r 

m Br
e B B
• Plotting r against 1/B gives a
straight line with gradient k
• e/m is then calculated:
2VA m
e 2VA
k
, so  2
e
m k
Again, you don’t need to
memorise this, but should
be prepared to answer
questions on the
experiment
Significance of e/m
• e/m=1.76x1011 Ckg-1
• This was 1860 times larger than the Hydrogen
ion, the largest known value so far.
– But is the charge much bigger, the mass much
smaller, or a bit of both?
• In 1895 Thomson could not draw any further
conclusions, as neither e or m were known
independently.
Millikan’s Oil Drop Experiment
• Very difficult to do! But allowed him to
determine the charge on the electron in 1913.
Robert Millikan
Millikan’s Oil Drop Experiment
• Drops of oil fall through
the hole in the top plate
• By measuring the size of
the drop and the speed at
which it falls you can
calculate its mass
• Some become ionised by
the radiation source
• By adjusting the pd
between the two plates
weight and electrostatic
force can be equalised:
the drop is stationary
• You can then calculate
the charge on the drop
Millikan’s Oil Drop Experiment
• For a stationary drop:
QV p
mgd
mg 
, so Q 
d
Vp
• So if we know m we can
calculate Q
• Note that the top plate must have the
opposite charge to the oil drop
Finding the mass of an oil drop
• With no electric field, the oil drops fall at their terminal speed.
• Millikan could measure the speed of the drop with his
microscope
h is viscosity of air
• Stoke’s Law gives the drag force: 6phrv
• At terminal velocity:
mg  6phrv
• We can measure the density of the oil r and write:
4 3
9hv
pr rg  6phrv, so r 2 
3
2 rg
• Now we know r we can turn on the field and write QV p  4 pr 3 rg
d
3
• The only unknown is Q...
Millikan’s Results
• After making many measurements on many charged oil
droplets, he found that the charge Q was always an
integer multiple of 1.6 × 10−19 C.
• In other words, he showed that electric charge is
quantised in whole number multiples of 1.6 × 10−19 C.
• He concluded that
– the charge of the electron is 1.6 × 10−19 C
– the whole number n corresponds to how many electrons
on the droplet are responsible for its charge.
– The mass of the electron was very small, so there must be
other things in the atom providing the mass
• He was within 2% of the currently accepted value
• What might have been the sources of experimental
error he had to deal with?
Something to note
• You might be asked about the motion of drops
with the field on, be careful:
– Tiny oil drops reach terminal velocity (up and down
forces equal) in a fraction of a second
– They then move at constant velocity
– The velocity depends on the drag force, weight and
electric force:
=0
d) Electric force equal to
weight, drop is stationary,
so no drag force
Checklist
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What are cathode rays and how were they discovered?
Why does the gas in a discharge tube emit light of a certain colour?
How is a beam of electrons produced in a vacuum tube?
How can electron beams be controlled and deflected?
What happens to the deflection of an electron beam if the speed of
the electrons is increased?
How can we determine the speed of the electrons in a beam?
How can e/m be measured?
What measurements are needed to determine e/m?
What was the significance of the first accurate determination of
e/m?
How can e be measured?
What measurements are needed to determine e?
Why was Millikan’s determination of e important?
• Do all the Chapter 1 summary questions!
• Let’s look at some exam questions
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