Waves and Cosmology - AQA GCE Physics Revision Notes

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Matter waves

  • As waves can behave as a stream of particles, particles can also behave as a wave

De Broglie wavelength:         λ =         where mv is the momentum of the particle

  • Diffraction rings are where electron waves interfere constructively to produce a maximum - energy gained by electron is equal to the kinetic energy of the electron.

Here, electrons are accelerated by a voltage of 2000 V;

2000 x (1.6 x 10-19) = x (9.11 x 10-31) x v2                    Mass of electron = 9.11 x 10-31

3.2 x 10-16 =  x (9.11 x 10-31) x v2

v2 = 7.025247 x 1014

v = 2.65 x 107 ms-1

So the momentum of electron: (9.11 x 10-31) x (2.7 x 107) = 2.5 x 10-23 kgm/s

The de Broglie wavelength:  λ = = = 2.6 x 10-11 m

  • If the accelerating voltage increases, energy and momentum of the electron would decrease the wavelength. Shorter wavelength blue light falling on diffraction grating produced fringes that are closer together than longer wavelengths (red light).
  • Resolving power is the wavelength of radiation used to determine the smallest object we are able to detect with it. The smaller the wavelength, the better the resolution. I.e. Resolution of visible object is limited by its wavelength of 5 x 10-7 m.

In electron microscope, electrons are accelerated through 30000 V have wavelength         of about 10-12 m, and so can produce images of object as small as a nanometre.

When probing matters, the accelerated particle has to have a wavelength about the         same size as the particle it is colliding with. So for electrons to probe the proton, its         de Broglie wavelength should be about the same as the proton diameter 2.4 x 10-15

Momentum of electron:        λ =   =>  mv = = = 2.75 x 10-19 kgm/s

Kinetic energy required: mv2   =>  = = 4.15 x 10-8 J

This would be around: = 2.59 x 1011 eV

  • Bohr mode of the atom suggested that electron accelerated around the nucleus in its orbit. Accelerating electron radiates energy and as its energy is lost; the electron will spiral towards the nucleus (due to electrostatic attraction) and collide into the nucleus, as it doesn’t have enough energy to remain in orbit.

So it is suggested that electrons can only have certain discrete values/ quantized                 energies so there is a stationary wave with whole number of loops in the        orbit.

When n=1, there’s one loop (half a wavelength)

When n=2, there’d be two loops (one whole wavelength)

Fundamental particles

  • The standard model suggests that there are 2 types of fundamental particles – leptons and quarks. They each have a n equivalent antiparticle.

  • Leptons are small point like particles and electron is a lepton with a charge of -1e and its antiparticle, the positron, has a charge of +1e

  • There’re 3 leptons families the electron (e), muon (μ) and tau (τ) each with their associate neutrino (and antineutrinos) that are electrically neutral. Electron and muon are very light particles whereas tau is heavier (around 1800 x that of an electron)

  •  Each lepton is given a lepton number, particles (neutrinos) have a lepton number of +1 and the antiparticles (antineutrino) have a lepton number of -1.

  • Neutrinos are every hard to detect but come in vast numbers from all directions in space. They can pass through earth without its intensity decreasing and they rarely interact with other particles.

  • The beta particles emitted in beta decay have a range of energies from virtually 0 to maximum energy. In beta decay, Etotal of recoil nucleus and β particle are not always constant – leading to a suggestion that a β particle is not the only particle emitted during beta decay, as the Ebefore = Eafter due to the laws of conservation of energy.

  • It is predicted that there exist a particle that would carry away the energy and momentum and evidence is found for the existence of neutrinos. In beta decay, antineutrino is emitted to conserve lepton number; they have a very small mass.

  • The quark family consist of 6 particles and 6 corresponding antiparticles. Quarks are never found on their own but exist in hadrons – which are formed from different combinations of quarks.

  • Quarks are assigned baryon numbers to explain which particle can exist and outcome of interactions. All quarks have a baryon number of 1 / 3, whereas all anti quarks has a baryon number of -1 / 3.

  • Strangeness explains the behaviour of massive particles such as kaons, they are created in pairs in collisions and have a longer lasting lifetime (10-10 s not 10-23 s)

The property of strangeness sis conserved during their creation but not when they decay. A strange antiquark has a strangeness of +1 (K0 – ds or sd/ K+ - us) whereas a strange quark has a strangeness of -1 (K- - su)

A particle that contains a strange quark automatically has a strangeness of -1, and if there are 3 strange quarks present, the particle would have strangeness of -3.

  • A Feynman diagram demonstrates the interaction between particles.

Particle and their interaction

  • When new particles are produced in accelerators, pair production occurs, where a particle is produced along with a corresponding particle.

  • When a particle collides with its antiparticles, they annihilate each other (disappear/ destroyed) i.e. when an electron meets a positron a Z0 particle. It has a short lifetime. At low energy, it decays to produce photons of EM radiation (used in PET scanners)

At high energy, Z0 decays to produce another electron – positron pair or a quark – antiquark pair, resulting in streams of new particle.

  • Particles consisting of quarks makes up a class of particle makes up a class called hadrons, they experience the strong force and has 2 sub classes – baryons (3 quarks) and mesons (consists of 2 quarks)

The only stable baryon is the proton, all other baryons eventually decays to form a proton and something else. Quarks have baryon number of +1 / 3, whereas anti- quarks have baryon number of -1 / 3

  • Baryons have 3 quarks and have a baryon number of -1 or +1, whereas mesons consist of 2 quarks and have a baryon number of 0.

  • When particle interact / decay, the event must follow the conservation rules. Energy and mass are equivalent, so energy could be converted into mass and vice verse.

  • In particle physics, the total charge, baryon and lepton numbers must also be the same after the event as it is before.

  • Particle containing a strange quark have a strangeness of -1, the K0 meson contains an anti-strange quark so has a strangeness of 1. Particles with 3 strange quarks have strangeness of -3.

  • When a strange particle decays through weak interaction, strangeness is not conserved (i.e. when strange quark turns into an up quark). But strangeness is conserved when there is a strong interaction – involving strong force.

Hence, strange particles always occur in pairs, if 2 particles interact to produce a strange particle, than a strange antiparticle must also appear.

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π-  +  p  ->  K0  +  λ0

ud  +  uud  ->   ds   +   sud

π-  +  p  ->  π-  +  π+  +  π-  +  p

The K meson and the hyperon (lambda particle) doesn’t produce any tracks in a bubble chamber.

The K0 meson decays into a π- pion and a π+ pion, which annihilates each other, whereas the λ0 decays into a π- pion and a proton. However, in each of these two decays, the strangeness is not conserved.


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