Fields, Capacitance, Nuclear, Option Flashcards
Motor Effect
motor effect: when a current-carrying wire placed in a magnetic field experiences a force.
the force on a wire is:
- greatest when the wire is perpendicular to the magnetic field ( T = BIlndcos (0) )
- zero when the wire is parallel to the magnetic field ( T = BIlndcos (90) )
direction of force,current and field are related which we can find via fleming’s left-hand rule ( ie. if current is reversed or field is reversed then the direction of force is reversed)
Electron beams undergoing a magnetic field
- beam is deflected downwards when a magnetic field is directed towards the vacuum tube
- each electron in the beam experiences a force due to the magnetic field
- the beam follows a circular path
- ## this is because the direction of the force on each electron is perpendicular to the direction of motionof the electron (and to the field direction)
Why do current-carrying wires in a magnetic field experience a force?
The electronics moving along the wire are pushed to one side by the force of the field.
How does the direction of motion of a charged particle in a magnetic field affect the force on the particle?
- force on a charged particle in a magnetic field = BQv
-The direction of motion of a charged particle in a magnetic field is at angle θ to the lines of the field
- the component of the field perpendicular to the direction of motion of the charged particle is given by Bsin θ
- if the velocity of the charged particle is perpendicular to the direction of the magnetic field, θ = 90°, so the equation is F=BQv
- if the velocity of a charged particle is parallel to the direction of the magnetic field, θ = 0, F= 0 so no force is experienced.
Hall Probes
- hall probes are used to measure magnetic flux density
- they contain a slice of semiconducting material
how it works:
- a constant current passes through
- the charge carriers are deflected by the magnetic field
- a potential difference (hall voltage) is created between the top and bottom edges of the slice ( this is the hall effect )
- once the hall effect occurs charge carriers passing through the probe no longer are deflected because the forced caused by the magnetic field is opposed by the force of the electric field.
- the voltage produced is proportional to the magnetic flux density (provided a constant current)
Force of the magnetic fields on a MOVING charged particle is…
The force of the magnetic field on a moving charged particle is at
right angles to the direction of motion of the particle
Why is the kinetic energy of a charged particle unaffected by the magnetic field?
- NO work is done by the magnetic field on the particle as the force ALWAYS acts at RIGHT ANGLES to the velocity of the particle.
- The direction of motion is changed by the force but not its speed
- The kinetic energy of the particle is unchanged by the magnetic field
Circular Path of a particle in a magnetic field
- the magnetic force is always perpendicular to the velocity at and point along its path
- the particle thus moves on a circular path with the force ALWAYS acting towards the CENTRE of curvature of the circular path
- the force causes a centripetal acceleration
- the path is a complete circle due to the magnetic field being uniform and the particle remaining in the field
- the radius r of the circular orbit is dependent on the speed and magnetic flux density
- r = mv/BQ
The cyclotron (incomplete)
The mass spectrometer (incomplete)
Present the Universal Law of Gravitation in a sketch graph
Also known as the inverse square Law
*insert
test
test
Carbon Dating
- plants and trees contain a small percentage of radioactive isotope, carbon-14
- due to carbon being taken in by living plants due to photosynthesis a small percentage of the carbon content of any plant is carbon-14.
- the isotope has a half-life of 5570 years ( thus there is negligible decay during the lifetime of a plant)
- after a tree is dead the proportion of carbon-14 decreases due to nuclei decay.
- by measuring the activity of the dead sample its age can be calculated
( carbon-14 is formed in the atmosphere as a result of comics rays knocking out neutrons from nuclei )
Argon dating FINISH THIS
- ancient rocks have argon gas trapped within them as a result of the radioactive decay
What is a Capacitor?
- Capacitors are electrical components which can be used to store electrical charge in a circuit
Battery vs Capacitor
Capacitor -
- Stores potential energy in the electric field
- Stores relatively little charge
- Charges and Discharges quickly
Battery -
- Stored potential energy as a chemical store
- Stores relatively large amounts of charge
- Charges and discharges slowly
What is Capacitance?
The Capacitance of an object is a measure of the amount of charge stored in the object per potential difference used to store it
Assumptions made with capacitors
- the capacitance of a capacitor is constant throughout it’s use
( for alevel only the minimum capacitance of a capacitor, which occurs when the potential difference is a maximum, is considered)
Remember when using the capacitance equation
- the charge calculated for a capacitor will also be the charge of the circuit as the capacitor is discharging or charging because charge must always be conserved
- the potential difference calculated for a capacitor is ONLY for the capacitor so if there are other components in a circuit that will not be the emf/total V of the circuit.
Dangers of Capacitors
Due to capacitors being able to discharge and thus deposit charge very quickly, they can be lethal
How does a Capacitor work?
- A capacitor consists of two conducting parallel plates separated by a gap.
- capacitor is placed in a direct current source, charge builds up on its plates
- the plate connected to the negative terminal of the power supply gains electrons, making it negatively charged
- the plate connected to the positive terminal of the power supply loses electrons, making it positively charged
- this is due to the repulsion caused by the negatively charged electrons on the opposite plate and their attraction to the positive terminal
- A potential difference forms between the plates
- electrons can not travel between plates as the air gap is a poor conductor
- the better the insulator between the plates, the greater the charge imbalance that can form
- thus the gap creates a charge imbalance over the two plates
Dielectrics
- A solid insulating material ( typically a poorer conductor than air) placed between the two plates of a capacitor in order to increase the amount of charge it can store.
- the insulated gap of capacitor creates a charge imbalance, the better the insulator between the plates the greater the charge stored.
Are Capacitors charged?
- no extra charge is stored in a capacitor when it is charged compared to when it is uncharged
- when a capacitor is charged the positive plate has lost electrons and the negative plate as gained them
- therefore the no. of electrons leaving the plate is the same as the no. of electrons gained by the negative plate.
- thus overall the capacitors when charged will not gain charge, rather they remain electrically neutral
What happens to the potential difference and current of a capacitor when a capacitor is discharged?
- when a capacitor is discharged the current in the circuit goes up as there are more electrons flowing ( with greater energy)
- but the potential difference across the capacitor decreases as there is less potential energy stored in the dielectric material between the capacitor.
Relative premativity
The ratio of the charge stored with the dielectric between the plates to the charge stored when the dielectric is not present.
( this relates to The increase in capacitance of a capacitor after the addition of a dielectric material or the increase in charge after the addition of a dielectric material.)
Polar Dielectrics
- a dielectric being polarised increases the effect of the dielectric
- ∴ a polarised material can increase the dielectric constant
- when a capacitor is uncharged the polar molecules of the dielectric are distributed randomly
- when a capacitor is charged the polar molecules rotate according to the electric field
-the delta-negative end goes to the positively charged plate, the delta-positive end goes to the negatively charged plate - the molecules themselves also produce an electric field as charged particles which are opposite in direction to the electric field produced by the capacitor
- this reduces the overall electric field
- at each plates the polar molecules force further electron movement during the charging process, due to the further repulsion from one end and further attraction from another on the electrons at each plate by the molecules (see diagram)
When a capacitor is charged will all the electrons at the positive terminal be attracted off the plate?
- the positive terminal attracts the electrons off the plate initially
- this occurs quickly due to the number of electrons occupying the plate being a lot
- over time positive charge builds up on the plate
- this build up of positive charge makes it more difficult to remove more charge off the plate as the electrons are now attracted to the now more positive plate.
How does too high of a potential difference impact a capacitor?
- risk of breaking capacitor
- too much charge is forced onto the plates causing charge to leak across them and destroy the dielectric between them
When Discharging a capacitor in a circuit why does the change in current replicate exponential decay?
- there is initially a large current as the electrons leave the negative plate
- the current flows in the opposite direction from the charging current
- as the number of electrons on the negative plate falls so does the size of the repulsive force making current fall at a slower rate
- when no more electrons move in the circuit the current drops to zero
When discharging a capacitor why does the change in voltage over time form exponential decay?
- the discharging process happens the fastest with the greatest potential difference across the plates
- as the capacitor is discharged the rate of change of the voltage decreases with time
What is the charging process of a capacitor dependent on?
- the capacitance of the capacitor
- the resistance of the circuit
What is the time constant?
- The time taken for the value measured to fall by 63% when a capacitor is charged or discharged
(x0.37)
after one time constant a value should have fallen to be only 37% of what it was originally
this means that Q=Q(0)0.37 - the gradient of a linearised graph of a measure value (ie voltage, charge etc) will = 1/-RC
- T1/2 = 0.69RC
How is power effected by the rate of discharge of slow discharging capacitor?
- if a capacitor is discharged slowly through a high resistance circuit, it produces a low current over a longer time
- the energy is therefore released slowly, (the rate at which energy is released js dependent on the time constant of a discharged circuit)
- thus less power
- ( this can be useful for temporary power supplies)
How is power effected by the rate of discharge of a fast discharge capacitor?
- If a capacitor is discharged quickly through a low resistance circuit, it produces a short burst of large current
- the energy is thus released quickly from the capacitor
- thus greater power
(e.g how a camera flash is powered)
Energy stored in a capacitor
- when a charge builds up on the plates of a capacitor, electrical energy is stored by the capacitor, it becomes a store of potential electrical energy
The electrical potential energy stored is the work done to move the extra charge onto the plates
- this is work done against the potential difference across the plates
- on a graph the total energy stored in a capacitor is E = 1/2QV, the energy supplied is E=QV
( other iterations: E=1/2CV^2, E=1/2Q^2/C)
Electrostatic forces vs gravitational forces
Gravitational forces
- ALWAYS attractive
ELECTROSTATIC
- attractive and repulsive
what is a field?
A force field is a region where an object within it can experience a non-contact force due to it’s position in the field
( an object must contain a property of that field to experience the non-contact force, e.g gravitation field - mass)
Assumptions made when suing Newton’s Law of Gravitation
- the masses are point masses
- the objects have a uniform density
- there is a vacuum between objects
Gravitational Field Strength
The force per unit mass experienced by an object inside a gravitational field (Nkg^-1)
- before radius R of earth where the distance between an object and the earth’s core decreases, the gravitational field strength would decrease linearly, until it reaches zero at the centre
Properties of a Field
- Force law
- Field strength
- Potential
- Potential difference
Why are there areas of denser gravitational field lines on a planet’s surface?
- A variation in gravitational field strength on a surface of a planet is caused by the material varying in density
- the greater the density of material (for the same volume), the greater the mass, the greater the gravitational field produced.
Describe two causes of the energy losses in a transformer and discuss how these energy losses may be reduced by choice of design and materials
- AC currents in the primary and secondary coils.
- Coils will have residence and the currents cause heating of the coils, causing some energy to be lost
- loss reduced by using low resistance wire/ low resitivity material for coils
- the magnetic flux passing through the core is changing continuously.
- the metallic core is being cut by this flux and the continuous change in flux induces emfs in the core itself.
- A continuous core with induced emfs will cause eddy currents
- these heat the core causing energy to be wasted.
- to reduce eddy currents layer and laminate the core because currents cannot flow in a conductor which is discontinuous.
Gravitational Potential Definition
- The work done in moving a unit test mass from infinity to a point in the field
Gravitational Potential Differencd
The work done in moving a unit mass from one point to another in a gravitational field. (J/kg)
What are the requirements for an element of Large nuclei of small nuclei to be stable?
- large stable nuclei: no. of protons < no. of neutrons
- ∵ the range of the strong force does not cover the entire nucleus so to compensate more neutrons are needed to ensure the strong force is much larger than the electromagnetic force
- small stable nuclei: no. of protons = no. of neutrons
- ∵ the range of both the strong and electromagnetic force is around the same and the no. of nucleons present make the strong force large
What causes a Nucleus to be stable or unstable?
- This is due to the forces occurring within the nucleus
- the attraction of the strong force and repulsion of the electromagnetic force
- If the electromagnetic and strong forces are very closely balanced, a nucleus will be unstable
- this will make the nucleus susceptible to radioactive decay
- If the Strong force is much larger than the electromagnetic force, a nucleus will be very stable
- thus the nucleus will not decay.
Alpha Radiation
- weakly penetrating
- to protect against irradiation: mask/clothing, 1/2 m of distance
- highly ionising
- alpha particles produce 10^4 ions in every mm it travels
- deflected in a magnetic field
Beta Radiation
- occurs due to the exchange of a W- boson
- moderately penetrating
- blocked by aluminium but not paper
- ionising
- produced 10^2 ions in every mm it travels
Gamma radiation
- electromagnetic wave released when a nucleus is still within an excited state
- highly penetrative
- multiple layers of lead and greater distance away needed to protect against it
- weakly ionising
- produces 10^1 ions in every mm it travels
Why is Gamma radiation more dangerous than visible light?
- gamma radiation has a greater frequency so there is more energy per second that it transfers making it more likely to ionise particles than visible light.
- E = hf
Handling radiation/radioactive material
- always handle with tongs
- prevents your hands from becoming contaminated (unstable nuclei coat the object)
- keeping as far away as possible from radiation source
- spending as little possible time in the presence of the source
- shielding using concrete barriers or lead plates
- warning signs when in use
Why is one unable to detect the type of radiation a source emits when using a geiger-muller tube?
- geiger muller tubes are unable to distinguish between the different forms of radiation
When recording the activity via a geiger-muller tube can there be anomalous results?
- no anomalous results because radioactive decay is a random process
What happens to the binding energy per nucleon during fission and fusion
- the binding energy per nucleon increases in both scenarios
- During nuclear fission ( large unstable nucleus splits into two fragments which are more stable than the original nucleus), the binding energy per nucleon increases in this process
- During nuclear fusion (making small nuclei fuse together to form a larger nucleus), the product nucleus has more binding energy per nucleon than the smaller nuclei ∴ the binding energy per nucleon increases (provided the nucleon no. of product is no greater than 50)
- an increase in binding energy/nucleon shows and increase in stability
Examples of Fissile Material
- Urnaium
- Plutonium
Nuclear Fission
Nuclear Fission is the splitting of a large unstable nucleus into two daughter nuclei
- It can be induced by colliding a neutron with an unstable nucleus (i.e. uranium)
- it is a chain reaction when uncontrolled
- this is due to the (typically 3) neutrons produced in the reaction which can cause further fission
- Each fission event releases a huge amount of energy within a very short time ( 1/n of a second)
- thus in comparison to burning a fossil fuel within an equal amount of time, the nuclear fission reaction releases significantly more energy - The energy released during fission is equal to the change in binding energy
How is energy released during a fission reaction?
- energy is released when a fission event occurs due to the repelling of the fragments (both positively charged) with sufficient force to overcome the strong nuclear force
- this causes the fragment nuclei and neutrons to have a gain in KE
- the two fragments will have a greater binding energy per nucleon
- the energy released is equal to the change in binding energy
How is Nuclear Fission Controlled in a Thermonuclear Reactor?
Moderators: Slows fast (High KE) neutrons produced from the intimate fission event to slow thermal neutrons
- the fission neutrons need to be slowed down significantly to cause further fission of the fissile material, else they’ll be too fast to cause further fission (pass right through nucleus instead)
- the moderator slows them by collisions with moderator atoms
Control Rods: used to absorb the neutrons emitted. The depth of the control rods within the reactor core can be adjusted to keep the no. of neutrons in the core constants so that exactly one fission neutron per fission event is exchanged. (typically made of boron or cadmium)
- this keeps the rate of release of energy constant
- can be adjusted further to reduce fission entirely too
How can the energy released in a fission reaction be calculated?
- the energy released (Q) is equivalent to E=mc^2
where m -> Δm ( the difference between the total mass before and after the event)
Q = Δmc^2
What conditions are required for Nuclear Fusion to occur?
- Nuclear fusion only occurs if the two nuclei that are to be combined collide at high speed
- ∵ it needs energy to overcome the electrostatic repulsion between the two nuclei so they can be close enough to interact through the strong nuclear interaction.
During Nuclear Fusion, how is energy released?
- when the two individual nuclei combine the individual nucleons become more tightly bound together
- causing the binding energy per nucleon of the product nucleus to be greater than the initial nuclei
- Due to the nucleons being held tightly within the nucleus, there is a release of energy equal to the binding energy
How does the Sun produce energy?
- Solar energy is produced as a result of fusion reactions in the sun
- at high temperatures the nuclei and there electrons are separated (plasma)
- the nuclei of the plasma move at very high speeds which provides them sufficient energy to overcome the electromagnetic force when two nuclei collide and become close enough to establish interaction through the strong nuclear force.
What does CRESS stand for? Wha
C - Concrete building
R - Remote Handling
E - Emergency shut down system
S - Steel vessel for reactor core
S - Spent Fuel Rods (much more radioactive when spent)
What is the Critical Mass?
- The minimum mass of a fissile material ( U/Po) needed before a chain reaction can occur
- for uranium around its 134kg
- this is also the minimum mass needed to maintain the rate of fission
Moderators
- Moderators reduce the speed of fission neutrons down to thermal
- The Moderators slow down the neutrons via repeated collisions with the moderator atoms
- fission neutrons are slowed to kinetic energies comparable to the moderator molecules ( hence why we refer to it as a thermal nuclear reactor)
- in a typical thermal nuclear reactor water acts as both the moderator and coolant ( + the mode of energy transfer to move turbines for generators)
Safety Features of a Thermal Nuclear Reactor
- the reactor core is a thick steel vessel which absorbs beta, some gamma radiation and neutrons
- the core is in a building built with very thick concrete walls which absorbs the neutrons and gamma radiation escaping from the reactor
- emergency shut down system designed to insert the control rods fully to complete end the reaction
- sealed fuel rods are insured and removed from the reactor by remote controlled devices
- spent fuel rods are lot more radioactive due to the emission of a radiation from fuel cans and b/y due to the neutron rich fission products
Radioactive Waste
- radioactive waste is categorised according to its activity: high, intermediate, low - level
- High-level radioactive waste
- highly dangerous
- e.g spent fuel rods
- must be stored underwater in cooling ponds for a year
- remaining material must be stored away in large trenches away from food and water supplies
- Intermediate-Level waste
- low activity material
- material sealed in drums that are encased in concrete
- Low-Level waste
- e.g laboratory equipment and protective clothing is sealed in metal drums and buried in large trenches
Estimation via Closest Approach of the nuclear radius
Nuclear Radius Estimation via nucleon number
Nuclear Excited States
inverse-square law for Gamma Radiation
Nuclear Used (26.4)
Simulators and Differences between Gravitational Fields and Electric Fields
Explain Why Alpha Particles Gain Kinetic Energy during Alpha Decay
Alpha Decay
- the nucleus recoils when alpha particle is emitted
- energy released from recoil is shared between the alpha particle and the nucleus
- momentum must be conserved during the recoil
- therefore the emitted nucleus and alpha particle will gain KE,
- the KE will be shared and inversely proportional to their masses
Explain why the kinetic energy of beta particles varies when energy is released during Beta Decay
Beta Decay
- the energy released during beta decay is shared in variable proportions
- between the emitted nucleus, neutrino/anti-neutirno and beta particle
- the maximum KE a beta particle can have will always be slightly less than the total energy released
- this is due to energy being used in the recoil of the nucleus (conserving momentum)
What happens to the energy released during electron capture within the nucleus?
- electron capture
- the nucleus emits a neutrino which carries away the energy released in the decay
- the atom also emits an X-ray photon when the innershell electron used in the capture is replaced (another electron replaces it)
Shuttling Ball Experiment
- shuttling ball experiment shows electric current is a flow of charge
- a conducting ball is suspended between two plates
- when a high voltage is applied across them the ball bounces back and forth between the plates
- touched -ve plate - gains electrons
- touches +ve plate - loses electrons
- ∴ transferring charge - this can be detected using an ammeter
- bringing the plates closer together results in the ball moving back and forth more rapidly
- causing the ammeter reading to increase because charge is ferried across at a faster rate
∴ I = Qf or Q/(time for 1 cycle)
What did Rutherford find from his alpha-scattering experiment?
- most of the atom’s mass is concentrated in a small region, the nucleus, at the atoms centre
- the nucleus is positively charged (because it repels alpha particles, which a +ve, that approach to closely)
What happens to alpha particles that interact with the nucleus of the gold atoms in the alpha-scattering experiment?
- α particles that collide head-on rebound (reflect at 180°)
- α particles close to the nucleus are deflected at different angles, the closer it is to being head on
- the greater the deflection is because the electrostatic forces of repulsion increase with decreased separation between nucleus and α particle
Closest-Approach Method and understanding behind it
- foil just be very thin otherwise α particles are scattered more than once (must be a few atoms thick)
- the probability of an α being deflected is 1 in 10,000n
- it’s also dependent on cross-sectional area
- d^2 = D^2/(10,000n)
where d is nucleus diameter, n is the layers of atoms, and D is atom diameter
How does an ionisation chamber show the properties of the different radioactive decays?
- the ionising effect of each type of radiation can be investigated using an ionisation chamber
- α radiation causes strong ionisation but when moved from chamber by a few centimetres ionisation ceases
- β radiation has a much weaker ionsiation effect than alpha, its range in air varies up to around a metre
- β radiation produces fewer ions per millimetre along its path than an alpha particle does
- γ radiation much weaker ionising effect than both other radiation, because photons do not carry charge so they have a lower effect, can travel for many miles
Absorption tests
- the no. of counts in a given time is the count rate
- the count rate is measured from a source at a fixed distance from the geiger tube
- the count rate is then measured with the absorber in place
- the corrected (taken in to account bg radiation) count rate with and without the absorber can be compared
- by using absorbers of different thicknesses the effect of an absorber can be investigated
count rate scale against thickness is a logarithmic scale
Range in Air of Radiation
- alpha - only a few centimetres in air, count rate decreases sharply, all particles from a given source have the same initial KE
- beta - range in air up to about a metre, count rate gradually decreases until same as background, beta particles from a given source have a range of initial KE, faster beta particles travel further in air than slower ones
- gamma - unlimited range in air, count rate gradually decreases with increasing distance because radiation spreads out in all directions
Ionising Effect Values
- gamma - 10^4 ions per mm
- beta - 100 ions per m
- gamma - very weak
Inverse Square Law for γ radiation
- the intensity I of the radiation is the radiation energy per second passing normally through unit area
- for a source that emits n γ photons per second the radiation energy per second = nhf
- intensity = (radiation/s)/total area
- nhf/(4πr^2)
- inverse square relationship between intensity and r^2
Hazards of Ionising Radiation
- ionising radiation damages living cells
- it destroys cell membranes which causes cells to die
- it can damage vital molecules such as DNA directly or indirectly (through free radicals) causing cell mutation
- this can lead to cancerous growth
How can radiation exposure be monitored?
- when using ionising radiation you must wear a film badge
- this monitors exposure to ionising radiation
- badge contains a strip of photographic film, different areas of the film are covered by absorbers
- the amount of exposure to ionising radiation can be estimated from the blackening of the film
- max recommended exposure per year is 15mSv
Background Radiation
- occurs naturally due to cosmic radiation and from radioactive materials in rocks, soil and the air
- varies with location due to the local geological features
Storage and Use of radioactive materials
- should be stored in lead-lined boxes/containers then ensure the gamma radiation produced falls to background level
- a record of the sources should be kept
- no source should be contact with the skin
- solid sources should be transferred using handling tools such as tongs < ensures intensity of radiation is as low as possible for sure
- liquid, gas and solids in powdered form must be in sealed containers
(to prevent inhalation and thus contamination) - radioactive sources should not be used for longer than necessary
Argon Dating
- Ancient rocks contain trapped argon gas as a result of the decay of radioactive isotope of potassium in to Argon, through electron capture
- or via the potassium decaying via Beta - emission to form calcium (x8 more likely then electron capture)
- half life of the decay of potassium is 1250 million years
- age of rocks can be determined by measuring the proportion of argon-40 to potassium-40
Industrial Used of Radioactivity
Engine Wear
- rate of wear of a piston ring in an engine can be measured by fitting a radioactive ring
- as the ring slides along piston the radioactive atoms transfer from ring engine oil
- the mass of radioactive metal transferred can be determined and thus the rate of wear via measuring the radioactivity of the oil
Thickness Monitoring
- a detector measures the amount of radiation passing through foil
- if too thick detector will drop in readings
- the source used is a beta emitter with a long half life ( alpha too weakly penetrative, gamma passes straight through)
Power source for remote devices
- Satellites, weather sensors and remote devices are powered using radioactive isotopes
- the isotope is within a thermally insulated sealed container which absorbs all the radiation emitted by the isotope
- the energy transferred per second from the source = λNE where E is nucleus release energy, N is no. of radioactive isotopes present
- source needs a reasonably long half life
Radioactive Tracers
- A radioactive tracer is used to follow the path of a substance through a system
the radioactive isotope in a tracer should:
- have a half-life which is stable enough for the necessary measurements to be made and short enough to decay quickly after use
- emit beta or gamma radiation so it can be detected outside the flow path
Define Half-life
- The Half-life of a radioactive isotope is the time taken for the same mass of the isotope to decrease to half the initial mass
/
time taken for the number of nuclei of the isotope to half the initial number
What is Activity?
- The activity A of a radioactive isotope is the number of nuclei of the isotope that disintegrate/decay per second
- the activity of a radioactive isotope is proportional to the mass of the isotope
How can you calculate the energy transferred per second from a radioactive source?
energy transfer per second from a radioactive source = AE
where A is the activity, E energy of the particle/photon
Describe the type of decays likely to occur for an element according to the stability curve
- for light isotopes N = Z from 0-20
- as Z increases beyond 20 the neutron proton ratio increases, the extra neutrons helps to bind the nucleons together without introducing repulsive forces
- alpha emitters occur beyond Z=60, they have more neutrons than neutrons but they are too large to be stable
- because the strong nuclear force begeeen the nucleons cannot overcome the electrostatic forces of repulsion between protons - beta- emitters occur to the left of the stability belt where isotopes are neutron-rich which is not very stable, the n->p to regain stability
- beta+ emitters occur to the right of the stability belt where isotopes are proton-rich, to regain stability p->n and emit a beta+ particle ( + neutrino)
- electron capture also takes place in this region
Nuclear Energy Levels
- emission of a γ photon does not change the nucleon no. but does allow nucleus to lose energy
- occurs if daughter nucleus is formed in an excited state (after going under other decays)
- the excited state is short-lived and the nucleus moved to its lowest energy state = the ground state
- can be represented by an energy level diagram
Technetium Generator
- a source that emits purely γ radiation
- used in hospitals for medical diagnosis
- technetium exists in an excited state long enough to be separated from parent isotope
- thus exists in a metastable state
- forms from the beta decay if molybdenum
What is a Metastable state?
- A nucleus can exist in an excited state for a long period due to it being stable
Estimating the diameter of the nucleus using high-energy electron diffraction
- when a beam of high energy electrons is directed at a thin solid sample the electrons incident diffract due to the nucleus
- the electrons diffract due to their de Broglie wavelength (around 10^-15)
- detector is used to measure no. of electrons per second diffracted through different angles
- the diffraction of the beam causes maxima and minima
- the angle of the first minimum is measured and used to calculate the diameter of the nucleus (provided wavelength of the incident electrons is known)
How can one find the radius of nucleus using its mass number?
- The radius R is dependent on mass number A according to R=R(o)A^1/3
where R(o) = 1.05fm
Nuclear Density
- assuming a spherical nucleus
- V = 4/3 π R^3 = 4/3 π R(o)^3A
- The volume is proportional to the mass of the nucleus, so the density of the nucleus is constant
- This means the density is independent of the nuclear radius
- shows that nucleons are separated by the same distance regardless of size, so distributed evenly inside nucleus
- if mass = Au
then density = Au/(4/3 πR(o)^3A) - this shows us how dense neutron stars are in comparison to other solar bodies
