Transcript L1_008 - Particle Physics and Particle Astrophysics

to Atomic and Nuclear
Physics
Purpose of the course:
To provide basic knowledge of the atom, its
constituents and nuclear processes
Phil Lightfoot, E47, (24533) [email protected]
to Atomic and Nuclear
Physics
In 1897 few would have imagined that the probing of materials at the atomic
level would reveal so much.
These early discoveries of atomic constituents and their structure would pave
the way for semi-conductor electronics, develop key concepts in physical
laws, and offer a replacement energy source for fossil fuels in the form of
nuclear power.
This course summarises key discoveries in early particle physics and
combines historical background with the detailed physics understanding
needed to fully appreciate the subject.
Phil Lightfoot, E47, (24533) [email protected]
Most Important Thing !!!!!!
I’m always available to help with
any aspect of the course
My contact details are on the top of
your lecture notes
Assessment for A&N Physics
Contribution from this course towards final
course grade in PHY008 will be:
Final Examination
2 assessed homeworks
Books and Course Pack
Everything you need to know is given to you
in the notes. However …..
Any A level textbook would be useful in
addition to the recommended textbooks
What you should now have
1. Full copy of the lecture notes (34 pages
including formula sheets).
2. All problem class questions including
worked examples.
3. Homework 1 and 2 attached to the problem
class questions.
Problem Class Questions
The only way to really understand a topic and ensure very high
performance in the final exam is to do loads of questions.
In every lecture we’ll go through questions together in order to
apply what we’ve learned to real examples.
I’ve also supplied you with questions to try during the problem
class sessions. In addition I’ve included loads of questions with
full model answers already supplied to help with the course.
If you understand the lectures, and can do these questions, you
will do very well in the final examination.
Outline of the Course
Chapter 1: The electron and the photon
Chapter 2: The Atom
Chapter 3: The nucleus
Chapter 4: Radioactivity
How much do you know already ???
Questions:
Can you calculate the electric field if you know voltage and separation ?
What is the charge in coulombs on an electron ?
What is the equation for the force on an electron in an electric field E ?
What is the equation for the force on an electron in a magnetic field B ?
What is the force due to gravity on a body of mass M ?
What is the equation relating acceleration with initial and final velocity ?
What is Fleming’s left hand rule ?
The electron (cathode rays)
The story of atomic and nuclear physics begins in the 1850s.
Science lecturers who travelled from town to town delighted audiences by
showing them the ancestor of the neon sign.
Fill a glass tube with low pressure gas….put
wires in opposite ends.. put a high voltage
across.... and the interior of the tube glows!!!
Around 1897 J.J. Thomson was investigating a long-standing puzzle known
as "cathode rays."
If the low pressure gas in the glass tube was replaced by a total vacuum then
the glow disappeared.
However, where the positive high voltage electrode passed through the glass
a fluorescent glow was seen.
The electron (cathode rays)
Thomson proposed that these mysterious rays are streams of particles
called electrons: very small, negatively charged particles that are repelled by
the cathode and attracted by the anode
The electron gun fires electrons towards
the metallic Maltese cross which has a
high positive potential. The electrons that
hit the cross are stopped by the metal,
Gun but those that get past it hit a fluorescent
screen on the tube which glows white.
Thomson also noted that they could be
deflected by electric and magnetic fields.
Anode
Cathode
Here we have deflection by an
electric field between D and E
The electron (cathode rays)
Thomson wanted to know more about electrons.
Two of the most important features of any particle are its mass and charge
and Thomson was the first to obtain a ratio for these constants
In order to understand what he did we need to know a little physics first….
Electric field : If we have two parallel plates a distance d apart
and the voltage difference between them is V, we can say that the
electric field is E where V is in volts, d in metres and E in Vm-1.
V
E
d
Charge on an electron : The charge on an electron is 1.6 × 10-19 C where C
is coulombs (a unit of charge). The mass of the electron is 9.11 × 10-31 kg.
Force on a charged particle in an E field : If the particle has a F
electric  qE
charge of q, then the force on it is qE in newtons when q is given
in coulombs and E is given in Vm-1.
Newton’s 2nd law : Force in newtons is equal to the mass of an
object in kg multiplied by its acceleration in ms-2.
F  ma
The electron (cathode rays)
Example: Thomson didn’t know the charge and mass of an electron but to
help show how he designed an experiment to find them, let’s do this example
in which we can use their actual values.
What is the electric field?
E
V 400

 20000 Volts per metre
d 0.02
What is the force on the electron?
Felectric  qE  (1.6 10 19 )  20000  3.2 10 15 newtons
Neglecting gravity, in which direction does the electron move and what is its
acceleration?
15
UP
F 3.2 10
15
2
F  ma and so a  

3.51

10
ms
m 9.1110 31
If it starts at the ground plate, what is its velocity when it hits the top plate?
v 2  u 2  2as and so v 2  2  3.511015  0.02  1.4 1014
v  1.4 1014  1.2 107 ms 1 But Thomson didn’t know either charge or mass!!!
The electron (cathode rays)
In the last slide we saw the effect of an electric field on a charged particle.
Here we look at the effect of a magnetic field on an electron.
Magnetic field : When the field lines B and the particles velocity v are at right
angles, the force on a charged particle q is also at right angles to both and is
defined as : Fmagnetic  B q v
B is in teslas, v in ms-1, and q in coulombs.
Current is defined
as the flow of
positive charge
The direction of the force
on the particle is
determined by Fleming’s
Left Hand Rule.
The particle travels in a
circle as force is always at
right angles to motion.
The direction of the
field is either an ×
to indicate it is
passing into the
paper or a • to
show it is coming
out of the paper.
The electron (cathode rays)
Example of magnetic fields
An electron travelling at a velocity of 3×107 ms-1 enters a magnetic field B of
strength 1.1 teslas as shown in the diagram.
v
In which initial direction will it experience a
force due to the magnetic field?
Force is directed up the page by Fleming
B
What is the force on the electron?
Fmagnetic  Bqv  1.1 (1.6 1019 )  3 107  5.3 1012 newtons
How is the effect of this force different to that produced by an electric field?
In electric fields the electron is attracted to the positive
potential and so the force always points towards this.
In magnetic fields the force is always directed at right
angles to the motion of the electron and the magnetic
field lines and so the electron spins in a circle.
The electron (cathode rays)
Let’s see how Thomson did it….
An electron, moving from left to right, passes between two parallel plates, and
feels a force towards the positive plate.
The force due to the E field is :
Felectric  qE
So the vertical acceleration is :
a
qE
m
This force acts only while the electron
is between the plates, a time of :
t
L
v x So the vertical velocity of the electron as it exits the
parallel plate is :
vvertical  at 
qE L
m vx
After this point, electron carries on to screen with constant vx vy .
The electron (cathode rays)
If the distance to the screen D>>L, then the time T taken for the electron to
travel to the screen is given by :
D
T
vx
In this time the electron will have
also had a vertical velocity vy
deduced on the previous page as :
vy 
qE L
m vx
So we can say that when the electron hits the screen it has a vertical
displacement y given by :-
y  Tvvertical 
D qEL qDEL

v x mvx
mvx2
This is very interesting but although we can measure y, D, and L, we cannot
even state a ratio for the charge q to mass m for the electron because we
don’t know vx the horizontal velocity of the electron.
The electron (cathode rays)
But Thomson had an idea. He left the electric field switched on so that the
electrons were still being deflected.
Then he applied a magnetic field positioning it in such a way that the force due
to the magnetic field was in opposition to the force due to the electric field.
He then increased B until the deflection y = 0 and the forces therefore balanced.
E
At this point he was able to say that : Bqv x  qE and so v x 
B
After substituting back into the expression for y we find :
qDEL qDELB 2 qDLB 2
q
yE
y



and therefore that
mvx2
mE 2
mE
m DLB 2
The electron (cathode rays)
Thomson had for the first time measured two fundamental properties of the
electron. Of course the best he could do was to measure the charge and mass
as a ratio of one another but it was better than nothing!!!!
He knew that the overall charge of elements is zero, and it was
obvious that the charge on an electron was negative. Since he
couldn’t find a corresponding positive particle, in 1904 he
created the plum pudding model of the atom.
q
yE

m DLB 2
In this model the atom is composed of
electrons, surrounded by a soup of
positive charge to balance the
electron's negative charge, like
negatively-charged "plums" surrounded
by positively-charged "pudding".
This concept existed until 1911, when
Rutherford built his own model of the
atom - the "planetary" one.
http://www-outreach.phy.cam.ac.uk/camphy/electron/electron4_1.htm