7. Breaking Matter Down

Question 1

I) Define an electric field.

Answer 1

A region in which a charged particle experiences a force due to its charge.

Question 2

I) Define electric field strength (E) at a point in an electric field.

Answer 2

The force per unit charge on a small positively charged object at that point in the field.

Question 3

I) In coulombs law, which sign is assigned to a repulsive and attractive force.

Answer 3

A repulsive force is considered positive and an attractive force is considered negative.

Question 4

I) How would you calculate the electric field strength (E) in a uniform magnetic field?

Answer 4

E = V/d where V is the pd across the two plates and d is their separation.

Question 5

I) What is the unit for electric field strength?

Answer 5

Vm^-1 or NC^-1

Question 6

I) What are the two heating methods used in thermionic emission?

Answer 6

Direct heating - where the filament itself is heated by passing a current through it.

Indirect heating - where a cathode is heated by a separate filament close to it.

Question 7

I) Define the term thermionic emission.

Answer 7

The emission of electrons, produced by raising a surface to a high temperature.

Question 8

I) What is the work function of a metal?

Answer 8

The minimum energy required for an electron to leave a metals surface.

Question 9

I) How would you decrease the work function of a metal?

Answer 9

By coating metals with different metallic oxides.

Question 10

I) What is a diode valve?

Answer 10

A diode valve consists of 2 electrodes (an anode and a cathode) and a filament located near the cathode all stored in a vacuum. The filament heats the cathode and, through indirect heating, causes thermionic emission to occur. The anode is included to set up an electric field which accelerates the emitted electrons through the vacuum in the tube.

Question 11

I) What is an electron gun?

Answer 11

An electron gun has a similar set up to a diode valve with the anode, cathode and filament, but the anode is in the shape of a hollow cylinder.

This allows the accelerated electrons to travel straight through the anode and out the other side, creating a beam of electrons.

Question 12

I) What is the specific charge of an electron?

Answer 12

e/m or 1.76 x 10^11 CKg^-1

The ‘specific’ indicates that it is the charge per unit mass.

Question 13

I) What is the value of the electric field strength inside a hollow conductor such as the anode in an electron gun and what does it mean about the motion of the electrons as they pass through?

Answer 13

Zero

It means that the are not accelerated as they pass through.

Question 14

I) How are a particles horizontal and vertical components of velocity affected if it passes through a uniform electric field that is applied perpendicular to its direction of motion and has a charge of Q?

Answer 14

Its horizontal component of velocity remains unchanged.

Its vertical component changes due to the face that there is a force of magnitude EQ acting in the vertical direction. Therefore it accelerates toward the oppositely charged electrode at a rate of EQ/m since F = ma.

Side note: You can use SUVAT equations to work out the different components of the particles motion.

Question 15

I) In flemings left hand rule, what does each finger represent?

Answer 15

Thumb - Direction of the force acting on conductor or the resultant Motion of the particle.

First Finger - Direction of the magnetic Field.

Second Finger - Direction of CONVENTIONAL current which is the direction in which positive charge moves.

Question 16

I) How would you calculate the force acting on a charged particle with charge Q travelling with velocity v in a magnetic field of strength B?

Answer 16

F = BQv

Question 17

I) Describe how charged particles moving in a magnetic field undergo circular motion.

Answer 17

Since the force acting of the particle is always perpendicular to its motion, the particle will be constantly accelerated at right angles to its motion, leading to circular motion.

Thus, the magnetic force is providing the centripetal force needed to keep the particle in circular motion.

Equating the magnetic force with the centripetal force give the equation: BQv = mv^2/r
Cancelling off the v gives the equation r = mv/BQ

Question 18

I) Describe how you would demonstrate the magnetic for on an electron and how it would allow you to calculate the specific charge of an electron.

Answer 18

You would fire electrons into a semi-evacuated tube, containing neon or nitrogen, using an electron gun.

A magnetic field acting parallel to the electrons motion is created by 2 helmholtz coils on either side of the tube. This forces the electron into circular motion.

By measuring the accelerating voltage, radius of the circle and the magnetic field strength, a value for the specific charge of an electron can be calculated.

The gas atoms in the tube get excited due to collisions with the beam electrons which causes the gas to emit light and make the circle visible.

Question 19

I) In 1897, how did J.J.Thompson use crossed fields to calculate the specific charge of an electron?

Answer 19

He used an election gun to fire a beam of electrons between two oppositely charged parallel plates, generating a uniform electric field.

In addition, he applied a magnetic field parallel to both the electric field and the electrons motion.

He designed the experiment so that the Forces due to the electric and magnetic fields acted in opposing directions.

Therefore by making the electron travel in a straight line, he was equating the electric and magnetic forces which allowed him to calculate the specific charge on an electron by rearranging the equations.

Question 20

I) What is a mass spectrometer?

Answer 20

A device used to measure the mass-to-charge ratio of charged particles by deflecting them using a magnetic field.

Question 21

I) What does the ion chamber do in a mass spectrometer?

Answer 21

Before the mass of the particles are measured, the samples must be converted into gas. This can be done using using lasers or heating coils.

An inert gas carries the gaseous particles into the mass spectrometer.

On entering the ion chamber, the atoms are ionised by bombardment with high energy electrons. This collision causes the atoms to loose an electron, converting them into positive ions (cations).

Because all of the ions have a charge of +1 and mass spectrometers separate ions based on their charge and mass, it can be said that the mass spectrometer separates ions with different masses.

Question 22

I) What does the velocity selector do in a mass spectrometer?

Answer 22

From the ion chamber, the ions are accelerated through a hole in the cathode onto the velocity selector.

The purpose of this chamber is to select particles with a certain velocity.

In order to do this both electric and magnetic fields are applied to produce forces in opposite directions so that they exactly cancel out only for particles with a certain velocity.

Particles with the correct velocity will then pass through two slits which ensure that the beam is in a straight line.

Since BQv = EQ it can be said that these particles have a velocity of v = E/B

Question 23

I) What does the momentum selector do in a mass spectrometer?

Answer 23

From the velocity selector, the ions enter the momentum selector, all with the same velocity.

In this chamber there is only a uniform magnetic field that bends the beam of ions into a circular path with radius r.

The radius is given as r = mv/BQ

The ion beam consists of singly ionised particles (each of constant charge Q) of constant velocity (v) travelling in a uniform magnetic field (of constant magnetic field strength B).

Thus r is proportional to m and particles of different masses therefore have different radii when put through a mass spectrometer.

Question 24

I) What does the ion detector do in a mass spectrometer?

Answer 24

Originally the ion detector was a photographic plate in which the degree of exposure was proportional to the intensity of the ions.

Modern mass spectrometers have detectors which monitor and amplify the ion current (into electrical current) transmitting it to a data system where it is recorded in the form of a mass spectra ready for analysis.

Question 25

How does the length of a linear accelerator affect its use?

Answer 25

The longer the accelerator, the higher the energies of the accelerated particles.

e.g. when accelerating electrons for the production of x-rays for medical use, they may be around a meter long. However, in nuclear research they can be much longer such as the Stanford Linear Accelerator in California which is 3.2km long.

Question 26

I) What are drift tubes, what do they do and why do they get longer as the particle travels down the linac?

Answer 26

Drift tubes are hollow metallic cylindrical electrodes which are connected to a radio-frequency supply.

The ions are accelerated by the electric field that exists between watch pair of drift tubes.

In order to use a constant frequency supply, each drift tube needs to be longer then the previous one due to the fact that as the particles move faster, they will travel a further distance in the time for which the alternating supply has the ‘wrong polarity’.

Question 27

I) How are the particles accelerated before they enter the full linac?

Answer 27

They are first accelerated using an accelerator based on a van der graph generator.

Question 28

I) List the steps that a proton goes through when it is accelerated in a linac.

Answer 28

A few slow moving protons enter the first drift tube from the van der graph generator.

Whilst in the first drift tube, the protons move at a constant speed.

The proton beam accelerates through the gap between the first and the second tubes as the second drift tube is negative with respect to the first drift tube.

The protons move with constant speed inside the second drift tube for nearly half a period of the alternating voltage. The polarity of the even drift tube reverse whilst the proton is in the second drift tube.

The protons then emerge from the second drift tube and accelerate across the gap between the second and third tube since the second tube is now positive with respect to the third tube.

Question 29

I) The special theory of relativity was developed from which two fundamental ideas?

Answer 29

The speed of light is the same for all observers irrespective of their reference frame.

The laws of physics are the same in any inertial frame of reference.

Question 30

I) What 3 quantities are affected when an object approaches the speed of light?

Answer 30

Their mass increases.
Their length contracts.
Their time runs much slower.

All relative to a stationary observer!

Question 31

I) How are Mass, Time and Length affected when a particle approaches the speed of light using gamma to show the change?

Answer 31

m = gamma x mo
t = gamma x to
l = lo / gamma

Where gamma is the lorentz factor and the ‘o’ notates the dimension measured when the object is stationary.

Question 32

I) List some of the advantages and disadvantages to Linacs.

Answer 32

Advantages

• They are simple.
• They are cheaper to build than circular accelerators because no high power deflecting magnets need to be installed.
• They can accelerate ions to greater energies than other circular accelerators which tend to loose energy due to synchrotron radiation.
• They can potentially work continuously whereas other accelerators tend to work in bursts.

Disadvantages

• They are very long which means that they take up a lot of space.
• They are expensive to maintain.
• The large amount of internal energy generated in the accelerator tends to mean that lilacs are not operated continuously like they could potentially be.

Question 33

I) Describe how a cyclotron works.

Answer 33

Charged particles enter the accelerator with a small velocity at the centre of a pair of D-shaped electrodes called ‘dees’ because of their shape. The dees are enclosed in an evacuated chamber.

A magnetic field is applied at right angles to the dees which accelerates the charge particles in a semicircular path until they reach the gap.

An alternating voltage is applied to the dees. This produces an electric field which reverses every half cycle and always accelerates the charged particles across the gap.

The particles gain energy as they travel round.

As the particles travel faster, they trace a larger arc meaning that the always take the SAME TIME to travel each semi circle. This allows the voltage applied to the dees to be at a constant frequency.

Question 34

I) What are some of the problems with cyclotrons?

Answer 34

The problem with cyclotrons is that in order to obtain the maximum kinetic energy possible, the cyclotron should have as large a radius as possible and as large a magnetic field as possible.

However, it is very difficult to produce strong uniform magnetic fields which act over large areas.

As particles approach the speed of light, relativistic factors mean that their masses increase. This makes accelerating them more difficult.

Since all particles orbit at the same frequency, regardless of their speed, they begin to lag behind the applied electric field.

Question 35

I) Why are protons preferred ‘atom smashers’ over electrons.

Answer 35

Because protons have a much greater mass and therefore they can reach much higher kinetic energies.

Question 36

I) Why is it better to fire 2 protons towards each other rather than at a stationary proton?

Answer 36

Because then the annihilation of the pair of colliding protons will have twice the initial kinetic energy and therefore release much more energy when the pair annihilate.

Question 37

I) What happens to the magnetic field strength as the particle gets faster in a synchrotron?

Answer 37

The magnetic field strength must increase in order to keep the particle orbiting with the same radius. since r =mv/BQ

Question 38

I) Where are the deflecting magnets situated in a synchrotron and how does it impact the size of the chamber?

Answer 38

The magnets are situated along the beam path rather than over the whole area of the orbit.

This means that the chamber can be much larger than is practicable with a cyclotron.

Question 39

I) How are particles accelerated around the ring in a synchrotron?

Answer 39

A high frequency alternating voltage is applied between electrodes positioned around the ring like a linac which accelerates the charged particles to high energies.

Question 40

I) How are the particles accelerated before they enter the main synchrotron?

Answer 40

Using a smaller synchrotron, cyclotron or linac which lead directly to the main synchrotron.

Question 41

I) What is synchrotron radiation and how does it arise?

Answer 41

A property of an accelerated charged particle is that it emits electromagnetic radiation.

The charged particles in a synchrotron are accelerating and therefore emit EM radiation.

Synchrotron radiation is the EM radiation emitted when charged particles, moving at velocities close to the speed of light, are forced to change direction under the action of a magnetic field.

The synchrotron radiation is emitted at a tangent to the particle’s orbit.

Question 42

I) How can synchrotron radiation be used?

Answer 42

Synchrotron radiation is of very high intensity an can be generated across the electromagnetic spectrum, from infrared to x-rays.

The intense beams of radiation enable scientists to investigate fields of biotechnology, medicine, environmental studies and material science.

Synchrotrons are very popular and sought after by scientists due to the fact that the produce extremely intense radiation.
e.g. the Diamond Light synchrotron in the UK produces X-rays that are a million times more intense than a hospital X-ray machine.

Question 43

I) What is the world’s largest particle accelerator?

Answer 43

The Large Hadron Collide (LHC)

Question 44

I) Why does the LHC fire bunches of Protons and no a continuous beam?

Answer 44

It is not possible to accelerate a continuous beam using accelerating electrodes.

Question 45

I) Why isn’t the LHC completely circular?

Answer 45

There are straight sections where radio-frequency (rf) cavities provide an electric field in order to accelerate the protons and where the 4 particle detectors (ATLAS, ALICE, CMS and LHC experiments) are located.

Question 46

I) How cold are the magnets in the LHC?

Answer 46

-271 degrees

Question 47

I) What is the strength of the electric field in each cavity in the LHC?

Answer 47

6MVm^-1

Question 48

(1 mark)
Suggest the purpose of the two slits in a mass spectrometer- one slit as the particles leave the ion chamber and one slit as they leave the velocity sector.

Answer 48

-Defines beam owtte/ ensures beam parallel/ ions predictable path/ fine beam/ linear (NOT focuses)

Question 49

(4 marks)
Using appropriate equations explain why POSITIVE ions in a mass spectrometer passing through the slit at the end of the velocity selector into the momentum selector have to be travelling at a critical velocity regardless of their mass.

Answer 49

-Fe and Fb (electric force and magnetic force) are opposites (in opposite directions)
-Electric force=EQ
-Magnetic force= BQv
-EQ=BQv
therefore v=E/B
-Comment that mass is not included in relation

Question 50

Explain what happens to the (positive) ions passing through the velocity sector if they are going more slowly than the ones passing through a second slit at the end of the velocity selector in a mass spectrometer.

Answer 50

• Hit below slit or attracted to bottom (negative) plate

- Because EQ>BQV now

Question 51

(7 marks)
Scenario: Positive particle travelling through an electric field, positive particle travelling through a magnetic field.

Explain why the speed of the particle changes in one of the above situations but remains constant in the other

Answer 51

In electric field:
-Force is always perpendicular to the plates
-There is an acceleration in the direction of the force/ perpendicular to the plates
or work is done on the charge
-Increases speed vertically
-Horizontal speed constant

In magnetic field:
-Force/acceleration always perpendicular to the direction of motion
-No component of force/ acceleration in the direction of motion
or no work done so no change in ke
-Motion is in a circular path

Question 52

(3 marks)
Explain what the electron stationary wave in an atom represents and state what you can infer about the location of the electron

Answer 52

-Electron likely where the amplitude is maximum
or impossible where amplitude is zero
-Probability is proportional to amplitude squared

Question 53

(2 marks)

Explain why ions do not accelerate when inside the cylindrical electrodes in a linac

Answer 53

• No electric field/ no pd within electrode

- Hollow cylinder/ conductor at constant potential