to Atomic and Nuclear to Atomic and Nuclear PhysicsPhysics

Phil Lightfoot, E47, (24533) p.k.lightfoot@shef.ac.uk

Purpose of the course:Purpose of the course:

To provide basic knowledge of the atom, its To provide basic knowledge of the atom, its constituents and nuclear processes constituents and nuclear processes

All these slide presentations are at: http://www.hep.shef.ac.uk/Phil/PHY008.htm

Most Important Thing !!!!!!Most Important Thing !!!!!!

I’m I’m alwaysalways available to help with any available to help with any aspect of the courseaspect of the course

Stop me if you’re confusedStop me if you’re confused

My contact details are on the top of My contact details are on the top of your lecture notesyour lecture notes

Review of last lecture

What is the force on an electron in the diagram bottom left ?

What is equation for force on electron moving with velocity v in magnetic field ?

In which direction does the force on the electron act due to the magnetic field ?

How do we define the direction in which current flows?What is Fleming’s left hand rule ?

What is the electric field in the diagram bottom left ?

Does an electron have positive or negative charge ?

Because of its charge, in which direction does the electron move in the diagram bottom left ?

In which direction does the force act ?

Negative

Opposite charges attract so moves towards positive 400V

Towards the positive voltage

kV/m 200.02

400

d

VE

BqvFmagnetic

newtons103.220000)10(1.6 1519 qEFelectric

Other way to electron flow

See diagram middle bottom

Always at 90 degrees to both the field and the flow of current and here down page

Cathode ray tubes (CRT)Before we go on we should mention a major use of ‘cathode rays’.

The screen of old fashioned TVs is coated on the inside surface with dots of chemicals called phosphors. When a beam of electrons hits a dot, it glows.

There are 3 signals that control the 3 electron beams, one for each RGB colour, each touching the dots that the signal tells it to light. This is then repeated for all the other pixels on the screen by scanning across the screen.

These phosphor dots are in groups of three: Red, Green, and Blue which then create all the other colours by combining which dots are illuminated.

Here we see a photo of a water droplet acting as a magnifying glass on a TV screen. See how the three colours of dots create the overall pink.

Reminder of stuff covered in last lecture

2DLB

yE

m

q

In 1897 Thomson had for the first time measured two fundamental properties of the electron using a combination of electric and magnetic fields. 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!!!!

Two of the most important features of any particle are its mass and charge.

Although this was a great measurement it’s clearly not very useful without knowing each value individually!!!!!

Millikan’s oil droplet experiment In 1909 Millikan had an idea how to find the charge on an electron

In order to understand what he did we need to remember 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. d

VE

Force on a charged particle in an E field : If the particle has a 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.

qEFelectric

Newton’s 1st law : An object at rest stays at rest and an object in motion stays in motion with the same speed and direction unless acted on by an unbalanced force.

Force due to gravity : Force in newtons is equal to the mass of an object in kg multiplied by ‘g’ which is 9.81 ms-2.

mgF

Millikan’s oil droplet experiment All that stuff should be pretty clear apart from the last bit maybe…

Newton’s 1st law : An object at rest stays at rest and an object in motion stays in motion with the same speed and direction unless acted on by an unbalanced force.

If you jump out of a plane what happens to your velocity as you fall to earth and why?

What are the forces acting on your body as you fall?

If you are at terminal velocity what can you say about these forces?

The net force is zero so the force of air resistance and weight are the same.

The drag force on the drop is where v1 is the terminal velocity of

the falling drop, η is the viscosity of the air, and r is the radius of the drop.

Millikan’s oil droplet experiment Let’s have a look at what Millikan did …. Instead of jumping out of a plane he squirted some oil vapour, watched it fall, and measured its terminal velocity by timing it between two points.

1vrFdrag 6

3rπV3

4

V

M

grMgW 3

3

4

WFdrag

grvrFdrag 31 3

46

g

vr

2

9 12

The volume of a sphere is :

When the droplet is at terminal velocity we can write:

and by rearranging we can say:

So :

and its weight is :

Density is :

Now as the oil droplets were slowly falling down, he decided to switch on an electric field with the positive voltage at the top.

Millikan’s oil droplet experiment

g

vr

2

9 12 Since we can find the weight of the oil droplet since

As he increased the strength of the field he noticed that some of the oil droplets slowed down and some actually started rising!!!!

The only way this could be explained was by saying those droplets had a negative charge on them.

What is the force due to the electric field on an oil droplet of charge q ?

What can we say about the forces on the droplet when the electric field is increased so that the droplet remains stationary?

grMgW 3

3

4

qEFelectric

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=357.0

Millikan’s oil droplet experiment What can we say about the forces on the droplet when the electric field is increased so that the droplet remains stationary?Since the droplet is stationary there is no drag force and so weight must be exactly equal to the force due to the electric field.

qEFelectric

g

vr

2

9 12

grmgW 3

3

4

Since we have already worked out that

we can say that gg

vmgW

2

3

1

2

9

3

4

Since when the droplet is stationary …

gg

vqE

2

3

1

2

9

3

4

WFelectric

and therefore … gg

vq

2

3

1

2

9

3E

4

We can measure all values on right hand side and so can get a value for q, the charge on the droplet.

Millikan’s oil droplet experiment

That’s really interesting and everything ….. But how does this help find the charge of an electron ? After all, what you’ve just found is the total net charge on an oil droplet !!!

gg

vq

2

3

1

2

9

3E

4We can measure all values on right hand side and so can get a value for q, the charge on the droplet.

What Millikan found when he looked at the values of q for many many oil droplets was that they were all integer multiples of 1.6 × 10-19 C.

http://physics.wku.edu/~womble/phys260/millikan.html

The fact is that when you spray oil droplets (he used his mother’s perfume atomiser) you don’t charge them much. You just add one or two electrons to the droplet (not more than 10 at most). So the charge represented integer multiples of the charge of a single electron which Millikan stated was 1.6 × 10-19 C

Remember that Thomson had calculated the charge to mass ratio? This was used to find the value for the mass of an electron as 9.1 × 10-31 kg

Electron-VoltsThis is such a tiny topic but it is also one of the most important ones. You will use electron-volts in two main ways; (i) as a convenient unit of energy, and (ii) to calculate the velocity of a charged particle passing through an electric field.

Definition: The change in energy of a charged particle q as it moves through a potential difference V is given by :

qVEnergy

1 electron-volt =1eV =1.610-191 = 1.610-19 J.

(i) In particle physics we often deal with very small energies and it is often therefore more convenient to refer to 3.210-19 J as 2 eV for example.

qVmv 2

2

1

m

qVv

2

(ii) Imagine a particle of mass m and charge q is accelerated from rest through a

voltage V. The energy given to the electron is therefore

If all this energy is converted into motion then this will be equal to the final kinetic

energy of the particle. So and the final velocity of electron is:

v is in metres per second, V is in volts, q is in coulombs, m in kilograms.

qVEnergy

Let’s try a couple of potential exam questions

Answer: The velocity of the electrons when they reach the anode is

Electrons are emitted from the cathode in an evacuated tube. The electrons start from rest and are accelerated through a potential difference of 1150V.

What is the speed of the electrons when then arrive at the anode?

(Charge on an electron is 1.6 × 10-19 C and mass of electron is 9.1 × 10-31 kg).

m

qVv

2

1731

19

ms 102109.1

1150101.622

m

qVv

Let’s try a couple of potential exam questions

a) metreper Volts 620000.005

310

d

VE

C 104.862000

9.81103 1915

E

mgq

b) Sphere is stationary so we know that so WFelectric mgqE

This is the charge of 3 electrons.

Let’s try a couple of potential exam questions

a) BqvFmagnetic qEFelectric

When the electron travels in a straight line then forces must balance.

qEBqv v

EB so teslas

v

EB 3

7

4

101.1101

101.1

so

Let’s try a couple of potential exam questions

b) If the electric field is switched off then the only force is BqvFmagnetic

The electron feels a centrifugal force as it starts to curve. Once the force due to the magnetic field has been balanced by the centrifugal force, the electron rotates in a perfect circle.

R

mvBqv

2

So so

This force always acts at 90 degrees to the magnetic field and direction of travel.

Forces balance and so :

Bq

mvR m0.051

101.6101.1

101109.1193

731

R