radioactivity

Radioactivity

The discovery of nucleus- Rutherford scattering

Polonium: α emitter

The vast majority of α passed straight through either undeflected or deflected by a small angle: the atom must be mostly empty space

A small proportion of α were deflected through angles bigger than 90◦ and an even small proportion were deflected through 180◦: there must be a very small point in the atom that has all of the positive charge and most of the mass

Could chamber

When α particles pass through the cool air saturated with ethanol vapour, they leave a trial. The air is ionised and the vapour condense around the ions forming the trial. Each trial is the same length, proving the source is emitting α particles.

The intensity of gamma radiation is the energy per second emitted from a source passing normally through a unit area (W/m2)

Activity: the number of decays per second on average (Bq)

The decay constant is the probability of a nucleus decaying per second (s-1)

Random nature of radioactive decay:

There is equal probability of any nucleus decaying, it cannot be known which particular nucleus will decay next, it cannot be known at what time a particular nucleus will decay, it is only possible to estimate the proportion of nuclei decaying in the next time interval.

Millikan's setup for the oil drop experiment

Plot of the Bethe-Weizsäcker-formula for the bind...

Thomas Young's sketch of two-slit diffraction, whi...

The half-life is the time it takes for the number of active nuclei in a sample (activity) to drop to half of its original value

Why the isotope technetium-99 is often chosen as a suitable source of radiation for use in many medical diagnoses: it only emits gamma rays, and can be detected outside the body, it has a short enough half-life and will not remain active in the body after use, it has a long enough half-life to remain active during diagnosis

Nuclear energy

Mass difference: mass of nucleus is less than the total mass of the constituent nucleons

Binding energy: energy required to break up a nucleus into its separate nucleons/energy released when a nucleus is formed from separate nucleons

Binding energy per nucleon: the average energy that must be supplied to release a single nucleon from the nucleus

Nuclear fusion: two light nuclei combine to form a more massive one nucleus, as both nuclei are positively charged, electrostatic repulsion has to be overcome, nuclei have to be given kinetic energy for them to meet

Nuclear fission: a heavy nucleus splits into two smaller nuclei, neutrons are released

Induced fission: splitting of large nucleus into two smaller nuclei brought about by bombardment

Thermal neutrons: have low energies or speed e.g. 0.03eV

Self-sustaining chain reaction: fission reaction gives out neutrons from fission cause further fission, self-sustaining when one fission leads to at least one further fission

Critical mass of a fissile material is the minimum mass of it that will support a self-sustaining chain reaction

Why spent fuel rods present a greater radiation hazard: it is easy to stay out of range, most fission fragments are more radioactive and are initially most likely to be beta emitters, ionising radiation damage body tissue

Thermal physics

The internal energy of a substance is the sum of the potential and kinetic energies of all its particles.

The specific heat capacity of a material is the energy needed to cause a temperature rise of 1K in a mass of 1 kg

The specific latent heat of fusion of a substance is the energy required to change 1kg of a solid into 1kg of liquid with no change in temperature

The specific latent heat of vaporisation of a substance is the energy required to change 1kg of a liquid into 1kg gas with no change in temperature

The discovery of the electron

Discharge tube:

Why light was emitted: ions present are accelerated by electric field , excitation of gas atoms occur, photon emitted on return to lower energy to ground state

Why the glow was not observed until the pressure of the air in the tube was low enough: ions do not gain enough kinetic energy as they collide with air particles, also because too many atoms present

Electron gun:

Unit A: 6V, supply current to the filament and heats up the filament

Unit B: 2kV, to make the anode positive, so that the electrons are attracted to the anode

Reduce A: Beam current is reduced, because fewer electrons are emitted per sec from the filament as it become less hot; Increase B: electrons travel faster/ gain more kinetic energy, because the electrons are attracted toward the anode with greater acceleration

Thermionic emission: this is the emission of conduction electrons when they gain sufficient kinetic energy to overcome the work function of a heated wire

Why it is essential that the container is evacuated: electrons from wire can collide with gas atoms and lose kinetic energy/speed

Determining e/m:

Why the beam curves up at an increasing angle to the horizontal as an electron enter an electric field:

each electron experiences an electrostatic for vertically upwards,

this force does not change as the electron moves across the field,

therefore each electron has a constant acceleration vertically upward,

velocity of each electron has a constant horizontal component of velocity and has an increasing vertical component of velocity,

so the direction of motion become closer and closer to a vertical line

Why electrons move in a circular path at a constant speed in the magnetic field:

Magnetic force on each electron in the beam is perpendicular to velocity

No work is done on each electron by magnetic force so ke/speed is constant

Magnitude of magnetic force is constant because speed is constant

Magnetic force is always perpendicular to velocity so is centripetal

Value of specific charge of the electron compared with the specific charge of H+ ion:

Specific charge for the electron=2000 x specific charge of H+

Which was the largest known specific charge before the specific charge of the electron was determined

This is due to a much smaller mass of the electron

Millikan's oil drop experiment:

Why the droplet stopped moving when the potential difference between the plates was adjusted to Vc: force due to electric field is vertically upwards and is proportional to the potential difference between the plates, at V=Vc, force due to field is equal and opposite to the weight of the droplet, no resultant force at Vc

Why the initial acceleration of the droplet is equal to g: the viscous force is initially zero, resultant force = ma, a=g

Why a charged oil droplet reaches a constant speed:

Weight pulls droplet down, no electric fore to counteract weight, viscous force increases with speed, weight=viscous force at terminal speed

Millikan had discovered that the charge is quantised, the charge on each droplet is a whole number times 1.6 × 10-19 C, the least amount of charge (or the quantum of charge) is the charge of electron

Wave particle duality

Young's double slit experiment:

Wave are emitted by each slit, each slit diffracts light

There are two coherent lights sources with constant phase difference and same frequency

They diffract through the gap and overlap with one another

Bright fringes formed where constructive interference happens, the path difference is whole number (n) of wavelengths

Dark fringes formed where destructive interference happens, the path difference is whole number + half wavelengths

Interference is a wave property

Since n is any whole number, more than two bright fringes are observed

Explain what Newton theory of light would predicts for the same experimental arrangement: light consists of corpuscles, corpuscles would not be diffracted, and only two bright fringes would be seen, dark fringes cannot happen with corpuscles

Use Newton's theory to explain refraction:

Light consists of corpuscles

They are attracted towards glass surface

Velocity normal to surface increase

Velocity parallel to surface unchanged

Huygens' theory considered light waves as longitudinal and hence could not explain polarisation and Newton's scientific reputation was more influential

Electromagnetic waves:

The electric and magnetic fields are in phase with one another, at right angles to each other, and at right angles to the direction of propagation of the wave

Explain why an alternating emf is induced in the loop:

Magnetic wave vibrate perpendicular to loop, causing alternating magnetic flux cutting through the loop, alternating magnetic flux induce an alternating emf

Photoelectric effect

There is a minimum frequency, called the threshold frequency below which it could not occur

The threshold frequency varies for different metal

The effect is instantaneous when the UV light hits the metal

The kinetic energy of the photoelectrons vary from zero up to a maximum

The maximum kinetic energy is dependent on the frequency of the light but not on the intensity

Light consists of photons, energy of a photon=hf

Minimum energy required for an electron to escape the metal surface is called the work function ϕ, an electron will be emitted if hf ≥ϕ

Maximum kinetic energy=hf-ϕ

During the photoelectric effect, one photon interacts with one electron and transfers all its energy to it

Wave theory could not explain the observation:

Energy should be spread across the whole wavefront, meaning the electrons would each share a small proportion of the wave's energy, thus the effect would not instantaneous

All frequency of light should cause electrons to be emitted

Hence cannot explain why light below threshold frequency could not cause photoelectric emission

Electromagnetic radiation

Wave like nature-interference, young's double slit experiment

Particle like nature- photoelectric effect

Matter particles

Wave like nature-electron diffraction of a beam of electron by a thin metal sample

Particle like nature- electrons can be deflected by E and B fields

Transmission electron microscope

Condenser lens: produce a wide uniform parallel beam of electros

Objective lens: produce an intermediate, magnified image

Projector lens: further magifies the image and projects it onto the screen

The object needs to be very thin, so that the electrons do not slow down

Lens aberrations caused by electrons having a range of speed , lower resolution

Anode voltage decrease: If the speed decrease, the wave length of electron increase, larger wavelength produce more diffraction, so the resolution is decreased

Why it is important that the eletrons in the beam have the same speed: force on an electron in a magnetic field depends on speed, electrons at different speed would be focussed differently, image would blurred

Scanning tunnelling microscope

With a p.d., electrons transfer from - to + only, with zero p.d., equal transfer in either direction

Explain, interms of wave particle duality, why an electron can cross this small gap: electrons have wave-like nature, a wave can penetrate thin barriers/ tunnel across gap, probability of transfer of an electron negligible if gap is too wide

Constant height mode:

Tip height constant

Gap width varies as tis scams across at constant height

Current due to electron transfer is measured

Current decreases at gao with increases or vise versa

As tip moves across surface, variation of current with time is used to map surface

Constant current mode:

Height of probe tip changed to keep gap width constant

Tip height altered to keep current constant

Current due to electron transfer is measured

As tip moves across surface, variation of height of tio with time maps the surface

Special relativity

The Michelson-Morley experiment

Why interference fringes shift their position if the distance from either of the two mirrors to the smei-silvered glass block is changed: (Two beams reach the observer, inteference takes placebetween two beams) birght fringe is seen where the two beams are in phase, changing the distance to either mirror changes the path difference, so fringes shift

Rotate 90◦:

Why is it predicted that a shift of the fringes would be observed:

Speed of light was through to depend on the speed of the light source

Distance travelled by each beam unchanged by rotation

Time difference between the two beams would change

Phase difference would therefore change (so fringes would shift)

Conclusion drawn:

Speed of light is independent of the speed of the light source

Ether hypothesis incorrect

Absolute motion does not exist

1st postulate: An inertial frame of reference is one which Newton's 1st law is valid

2nd postulate: the speed of light in free space is invariant: the speed of light in free space is constant and does not depend on the motion of the source or the observer