Higher Physics Particles and Waves.

Higher Physics Particles and Waves

Particles and Waves: Contents The Standard Model of Fundamental Particles Forces on charged particles Nuclear Reactions Wave Particle Duality Interference and diffraction Refraction of light Spectra

Particles and Waves: The Standard Model
Atoms The fundamental building blocks of matter were first thought to be atoms. Atom comes from the Greek atomos meaning indivisible.

The Rutherford Atom gold foil alpha particles (positive charge) When alpha particles are fired at thin gold foil most pass straight through. A few particles are deflected through large angles. This suggests that an atom must be mostly empty space with a small positive nucleus that contains most of the mass of the atom.

Protons (+) Neutrons Electrons (-)

Mass and Atomic number The number of protons in the nucleus of an atom is called the atomic number. Each element has a different atomic number. The number of protons and neutrons is called the mass number.

Example C 12 6 This is the element carbon. It contains 6 protons and 6 neutrons in its nucleus. mass number atomic number C 14 6 This is also carbon but it has 6 protons and 8 neutrons in its nucleus.

Orders of Magnitude Object/particle Order of magnitude / m Proton Hydrogen atom Human Earth Sun Galaxy

Factor Name Symbol 1024 yotta Y 1021 zetta Z 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k Factor Name Symbol 10-3 milli m 10-6 micro 10-9 nano n 10-12 pico p 10-15 femto f 10-18 atto a 10-21 zepto z 10-24 yocto y

The development of new particle accelerators and detectors in the 1950s led to the discovery of many sub-atomic particles. The Standard Model of Fundamental Particles and Interactions was developed in the 1970s in an attempt to tidy up the number of particles being discovered.

} } Particles and Waves: The Standard Model
Physicists believe that there are 12 fundamental particles. fermions charm quark top quark up quark } quarks down quark bottom quark strange quark electron neutrino tau neutrino muon neutrino } leptons tau electron muon

Hadrons are composite particles made of quarks. Baryons proton (uud) neutron (udd) (particles made of 3 quarks) Hadrons Mesons (particles made of 1 quark and 1 antiquark)

Antimatter Every particle has an antimatter equivalent that has the same mass but the opposite charge. A positron has the same mass as an electron, but a positive charge. electron e positron e or e+ Some (not all) electrically neutral particles, like the photon, are their own antiparticle. . A particle and its antimatter particle annihilate when they meet

Beta decay During beta decay a neutron changes to a proton and a beta particle is emitted from the nucleus. Beta particles are electrons (or their antimatter equivalent, positrons). By applying the law of conservation of momentum to Beta decay a new particle with no charge and a very small mass was discovered – the neutrino.

The Fundamental Forces
Particles and Waves: The Standard Model The Fundamental Forces All interactions between matter are governed by forces. There are four fundamental forces. Gravity and electromagnetism are the most familiar of the four. The other two are the strong and weak nuclear forces. The strong and weak forces act only on extremely short distance scales – so short that these forces can only be felt within atomic nuclei. These forces fall off to zero outside the nucleus.

Except for hydrogen, nuclei contain more than one proton, all of which are positively charged. Thus the electromagnetic force pushes protons apart inside the nucleus. With just the electromagnetic force all atomic nuclei would fly apart! The strong force, so-called because it is strong enough to overcome electromagnetic repulsion, is the force holding nuclei together. All particles made from quarks feel the strong force.

The weak force is important in nuclear reactions and radioactive decay. Neutrinos feel the weak force only. Both the electromagnetic and gravitational forces act over an infinite range. The strength of the force is proportional to 1/r2.

The Force-Mediating Particles The force-mediating particles are called bosons. The photon is associated with the electromagnetic force. The photon has zero mass. Gauge bosons W+, W– and Z0 are responsible for the transfer of the weak nuclear force. Gluons are associated with the strong nuclear force that acts between quarks. Gravitons are thought to carry the gravitational force through the universe. Gravitons have not yet been detected but are thought to have zero mass.

Force Relative strength within nucleus Relative strength beyond nucleus Exchange particle (all bosons) Major role Strong 100 Gluons Nucleon binding Electromagnetic 1 Photon Chemistry and biology Weak 10-5 Weak bosons W+, W- and Z0 Nuclear reactions Radioactive decay Gravity 10–43 Graviton Large-scale structure

Particles and Waves: Forces on charged particles
Electric Fields In physics, a field means a region where an object experiences a force without being touched. In a gravitational field a mass will experience a force. In an electric field a charged particle will experience a force.

Field lines can show the strength and direction of the force. + Field lines around a positive charge The closer the lines the stronger the force. The direction shows how a positive charge would move.

+ +

+

+ -

The Definition of the Volt If 1 joule of work is done in moving 1 coulomb of charge between two points, there is a potential difference of 1 volt between the points. Ew = QV p.d. (V) work done (J) charge (C)

Example An electron is accelerated through a potential difference of 200 V. Calculate a) the kinetic energy gained b) the final speed of the electron. a) Ek gained = work done by field Ew = QV = 1·6 x x 200 = 3·2 x J b) Ek = ½ mv2 3·2 x = ½ x 9·11 x x v2 v = 8·38 x 106 ms-1

Magnetic Fields When a current flows through a wire a magnetic field is produced. Moving charge produces a magnetic field.

A moving charge entering a magnetic field experiences a force. N S

The direction of the force can be determined if you know the sign on the charge and the direction of the magnetic field. Magnetic field direction runs from north to south. If you use your right hand the diagram above shows the direction of the force on a negatively charged particle. The force will be in the opposite direction for a positively charged particle.

Particle Accelerators Particle accelerators accelerate charged particles to high speeds using electric and magnetic fields. Linear Accelerator A linear accelerator uses electric fields to accelerate charged particles in a straight line to collide with a stationary target.

Cyclotron A cyclotron uses a magnetic field to bend charged particles into a semicircular path between accelerations by an applied electric field.

Synchrotron Synchrotrons use electric and magnetic fields to accelerate particles around a ring. As the particles increase in energy the strength of the magnetic field that is used to steer them must be changed with each turn to keep the particles moving in the same ring. The change in magnetic field must be carefully synchronized to the change in energy or the beam will be lost. Hence the name "synchrotron".

Large Hadron Collider The LHC re-uses a 27 km circumference tunnel built for a previous accelerator.

The tunnel contains two adjacent beam pipes, each containing a particle beam (lead ions or protons) travelling in opposite directions.

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Uses of Accelerators Medical therapy. Accelerator-produced x-rays and particle beams of electrons, protons, neutrons, or heavy ions can be directed at tumours not reachable by other treatment techniques; Research and materials analysis. X-rays or accelerated particles can be directed at a target to analyze its structure by measuring the resulting scattering of particles; Non-invasive security assessment. Accelerators produce x-rays that can quickly identify the contents of containers located in trucks, shipping containers, or luggage to detect hidden explosives, chemicals, or contraband; Radionuclide production. High-energy protons or charged particles can be directed at targets to create radionuclide's (radioactive atoms) for medical, research, and industrial uses. .

Particles and Waves: Nuclear Reactions
Radioactive Decay Some atoms are unstable. To achieve stability they can emit nuclear radiation, alpha, beta or gamma. An alpha particle (a) is like a helium nucleus, it has 2 protons and 2 neutrons, He 4 2 Beta particles (b) are fast moving electrons, they are emitted when a neutron decays into a proton and an electron, e -1 Gamma radiation (g) has no mass or charge, it is a high energy electromagnetic wave.

Examples Alpha decay The atomic number falls by 2 and the mass number falls by 4 Ac Fr + He 223 89 219 87 4 2 Beta decay Po At e 215 84 85 -1 The atomic number increases by 1 and the mass number is unchanged Gamma decay Only energy is released.

Nuclear Fission Fission is when a large nucleus splits into two. Fission can happen spontaneously, but can be induced by neutron bombardment. energy neutron

Nuclear Fusion Fusion occurs when two small nuclei join. energy + In fission and fusion reactions energy is released.

E = mc2 In fission and fusion reactions the total mass before the reaction is greater than the total mass after the reaction. Einstein suggested that the ‘lost’ mass is changed into energy. E = mc2 energy (J) mass (kg) speed of light (ms-1)

Example The following statement represents a nuclear reaction. 239 1 137 100 1 Pu n Te Mo n + energy 94 52 42 What type of reaction is shown above? The total mass of the particles before the reaction is 3·9842 x kg and the total mass after the reaction is 3·9825 x kg. Calculate the energy released by this reaction.

Particles and Waves: Wave Particle Duality
Photoelectric Effect Electromagnetic radiation above a certain frequency can eject electrons from the surface of some metals. zinc leaf falls ultraviolet light Electrons are ejected from the negatively-charged electroscope when the uv light strikes the zinc plate.

Explaining the Photoelectric Effect A beam of radiation can be regarded as a stream of individual energy bundles called photons. The energy of a photon is given by: E =hf energy (J) Planck’s constant = 6.63 x Js frequency (Hz) Radiation with a high frequency (energy) can eject electrons from the surface of some materials.

Questions 1. Calculate the energy of a photon of light of frequency 6·8 x 1014 Hz. 2. Calculate the energy of a photon of light of frequency 3∙7 x 1014 Hz. 3. Calculate the energy of a photon of light of wavelength 5·4 x 10-7m. 4. Calculate the energy of a photon of light of wavelength 640 nm. 5. A photon has an energy of 3∙6 x 10-19J. Calculate the wavelength of the photon.

Photoelectric Effect Experiment light zinc evacuated tube mA - + Light strikes the zinc plate and causes photoelectrons to be emitted. The electrons move across the tube producing a current that is measured by the milliammeter.

current f0 frequency Below a certain frequency f0 , called the threshold frequency, there is no photoelectric emission. For a frequency greater than the threshold frequency an increase in the irradiance will produce an increase in photoelectric emission.

Work Function The minimum energy required to release an electron from a surface is called the work function. E0 = hf0 work function (J) threshold frequency (Hz) Example The work function for a metal is 5 x J. Calculate the minimum frequency that will eject electrons from the metal. E0 = hf0 5 x = 6·63 x x f0 f0 = 7·54 x 1014 Hz

If a photon of energy greater than the work function strikes the surface of a metal then the extra energy will appear as kinetic energy of the ejected electron. photon E =hf electron Ek metal (work function = hf0) Ek = hf – hf0

Interference Particles and Waves: Interference
Interference is the test for wave motion. Interference occurs when waves meet.

+ = Particles and Waves: Interference
When two sets of waves meet in phase they add to make a larger wave. This is called constructive interference.

+ = Particles and Waves: Interference
When two sets of waves meet completely out of phase they cancel each other out. This is called destructive interference.

Particles and Waves: Interference

Coherent Sources Two sources are coherent if they have the same frequency, amplitude and are exactly in phase. By passing waves through two small gaps ( about a wavelength) it is possible to produce two coherent sources.

Path Difference Constructive interference S1 S2 Destructive interference Path difference = S2P – S1P Maximum (constructive) path difference = ml m=0,1,2,3… Minimum (destructive) path difference = (m + ½)l

Example 520 mm 550 mm S1 S2 The point P is the third order maximum. S1P is 520 mm and S2P is 550 mm. Find the wavelength of the source. path difference = ml 550 – 520 = 3l l = 10 mm

Interference of Light double slits screen laser (monochromatic light)

grating screen laser A diffraction grating has lots of narrow slits. The interference pattern is brighter than the pattern produced using only two slits.

grating screen monochromatic light q For constructive interference: d sinq = ml m = 0,1,2,3,4…… distance between slits angle from centre wavelength

Example Light from a monochromatic source strikes a diffraction grating of 400 lines per mm. The first order maximum is produced at an angle of 140. Find a) the slit separation b) the wavelength of the source. 1 x 10-3 b) ml = dsinq a) d = 400 1l = 2·5 x 10-6 sin140 = 2·5 x 10-6 m l = 6 x 10-7 m

Interference with red, green and blue light using the same grating.
Particles and Waves: Interference White Light Spectra Colour Wavelength/nm Red to 700 Green to 580 Blue to 490 Interference with red, green and blue light using the same grating. d sinq = ml q  l

screen grating white light source white white light prism

Particles and Waves: Refraction of light
Refraction occurs when light passes from one medium into another. When light travels from air into glass it slows down and bends (refracts) towards the normal. When light travels from glass into air it speeds up and bends away from the normal. air glass ray of red light

Refractive index ray of red light Experiment q1 q2 q1 sinq1 q2 sinq2

sinq1 sinq2 sinq2 sinq1 The experiment shows that = constant. The constant is called the refractive index ( n ).

Particles and Waves: Refraction
Higher exam data sheet

Example A ray of red light passes from air into water. 200 air water The refractive index is 1·33 for this light in water. Calculate the angle of refraction in water. sinq2 sinq1 n = 1·33 = sin 700 sin θ2 sin θ2 = 0·7065 θ2 = 450

Refractive index, Speed and Wavelength When light passes from air into glass the speed decreases and the wavelength decreases. The frequency of the light always stays the same. Speed and wavelength can be calculated using: l1 v1 n = n = v2 l2

Example Light of frequency 6 x 1014 Hz passes from air into water. The refractive index for water for this light is 1·33 Calculate the wavelength of the light in air. Calculate the wavelength of the light in water. Calculate the speed of the light in water. l1 v1 v a) l = b) n = c) n = v2 F l2 = 6 x 1014 3 x 108 5 x 10-7 3 x 108 1·33 = 1·33 = l v v = 2·26 x 108 ms-1 l = 3·76 x 10-7 m = 5 x 10-7 m

Critical Angle refracted ray reflected ray 90º critical angle glass incident ray If the angle of incidence in the glass is larger than the critical angle all the light is internally reflected.

Critical Angle and Refractive Index air 900 glass qc At the critical angle the angle of refraction in air is 900. sin 900 n = sin qc but sin 90o = 1 1 sin qc = n

Example A ray of red light passes from air into glass. X 630 The refractive index is 1·5 for this light in the glass. Show by calculation whether the ray is totally internally reflected at point X. 1 sin qc = 630 is greater than the critical angle therefore the light will totally internally reflect. n 1 sin qc = 1·5 θc = 420

Particles and Waves: Irradiance
The irradiance of radiation (light) at a surface is the power per unit area incident on the surface. power (W) P I = A area (m2) irradiance (Wm-2)

Example A lamp shines onto a surface of area 4 m2. The irradiance at the surface is 0·02 Wm-2. Calculate the power of the incident light.

Irradiance and Distance point source light meter metre stick irradiance distance

1 distance2 The graph is a straight line through the origin therefore: 2 2 1 I  or I1d1 = I2d2 d2

Example The irradiance from a lamp at a distance of 3 m is 0·2 Wm-2. Calculate the irradiance at a distance of 1 m.

Particles and Waves: Spectra
Emission Spectra 400 nm 500 nm 600 nm 700 nm Continuous spectrum of light e.g. light from a filament lamp Line spectrum e.g. light from a spectral lamp

Explanation of Emission Spectra electron increasing energy Bohr model of the atom. In the Bohr model of the atom electrons are confined to certain orbits (shells). Electrons can move between energy levels. Light is emitted when an electron falls from a high energy orbit to a low energy orbit.

An energy level diagram shows the electron orbits. W3 Ionisation level electron W2 increasing energy W1 W0 Ground state Energy of photon = W2 – W1 W2 – W1 = hf

Example The diagram shows some of the energy levels for a particular atom. E4 -1·4 x J E3 -2·4 x J E2 -5·6 x J E1 -21·8 x J Which transition produces radiation with the longest wavelength? Calculate the frequency of the photon produced when an electron falls from E3 to E2.

Absorption Spectrum Experiment sodium gas prism white light absorption spectrum torch

Absorption Spectra When light is passed through a gas then some photons are absorbed. The photons that are absorbed have the same frequency as the photons emitted to produce the emission spectrum of the gas. During absorption electrons move from low energy orbits to high energy orbits W2 hf = W2 – W1 W1

Continuous spectrum e.g. light from a filament lamp Line spectrum e.g. light from a spectral lamp Absorption spectrum e.g. white light passes through a gas

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