1. Atomic Nuclear and Particle Physics
1.1. Atomic models
1.1.1. Models in history
1.1.1.1. Thomson's atomic model
1.1.1.1.1. Atom is a sphere of positive charge.
1.1.1.1.2. Negatively charged electrons are embedded in the sphere.
1.1.1.1.3. so-called "plum pudding" model
1.1.1.2. Rutherford's model
1.1.1.2.1. A planetary model of an atom which consists of a tiny but massive positively charged nucleus surrounded by electrons.
1.1.1.2.2. limitation: could not explain why matter is stable
1.1.1.3. Rutherford's conclusions from experimenting
1.1.1.3.1. Most of the alpha particles did pass straight through the foil.
1.1.1.3.2. A small number of alpha particles were deflected by large angles (> 4°) as they passed through the foil.
1.1.1.3.3. A very small number of alpha particles came straight back off the foil.
1.1.1.4. the Bohr model
1.1.1.4.1. Structure: electrons could exist in certain specific states of definite energy, without radiating away energy.
1.1.1.4.2. Evidence: emission and absorption spectra
1.1.2. Discrete energy
1.1.2.1. Electrons occupy difference energy levels from n = 0, n = 1 ... to n = ∞.
1.1.2.2. Bohr suggested that an atom can make a transition from a state of higher energy to a state of lower energy by emitting a photon, the particle of light.
1.1.2.2.1. In a stable orbit the electron does not emit radiation.
1.1.2.2.2. Radiation(photon) is only emitted when the electron makes transition from a higher to lower energy state.
1.1.2.3. Discrete energy differences between the levels cause that the energy of an atom was discrete, i.e. it could have one out of a specific set of values.
1.1.2.4. ∆E = h × f = h × c / λ
1.1.2.4.1. h is the Planck constant: 6.62607015 × 10^-34 m^2 kg / s
1.1.2.4.2. ∆E is usually expresses using eV, which is equal to 1.602 × 10^-19 J.
2. Oscillations and Waves
2.1. Oscillations
2.1.1. Simple Harmonic Motion
2.1.1.1. Concept: repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side.
2.1.1.2. Related concepts
2.1.1.2.1. Cycle: one complete 'there and back' swing, from A to B and back to A.
2.1.1.2.2. Amplitude (x0): the maximum displacement from equilibrium position.
2.1.1.2.3. Time period (T): time taken for one complete cycle.
2.1.1.2.4. Frequency (f): the number of complete cycles per second. f = 1/T
2.1.1.3. Approximations
2.1.1.3.1. The displacement is horizontal (in reality the bob moves slightly up).
2.1.1.3.2. The force acting towards the equilibrium position is the horizontal component of the tension.
2.1.1.3.3. The weight is approximately the same as the tension.
2.1.1.4. Examples
2.1.1.4.1. Mass hanging on a string
2.1.1.4.2. Simple pendulum
2.1.1.5. Graphs (taking mass on a string for example)
2.1.1.5.1. displacement-time
2.1.1.5.2. velocity-time
2.1.1.5.3. acceleration-time
2.1.1.6. Relation to energy
2.1.1.6.1. relation to kinetic energy
2.1.1.6.2. relation to potential energy
2.1.1.6.3. relation between kinetic energy and potential energy
2.1.1.7. Phase
2.1.1.7.1. In phase: the phase difference is zero. (Two motions or waves are of identical pattern.)
2.1.1.7.2. Out of phase: the phase difference is not zero.
2.1.1.7.3. How to calculate phase difference
2.2. Travelling Waves
2.2.1. Related concepts
2.2.1.1. Wavelength (λ): the distance between successive crests of a wave, especially points in a sound wave or electromagnetic wave.
2.2.1.2. Frequency (f): frequency refers to the number of waves that pass a fixed point in unit time.
2.2.1.3. Period (T): The time it takes for two successive crests (one wavelength) to pass a specified point.
2.2.1.4. Relation between period and frequency: f = 1 / T
2.2.1.5. velocity of wave = distance travelled / time taken = λ / T = λ × f
2.2.1.5.1. Therefore, for light waves, c = λ × f
2.2.2. Transverse waves and londitudinal waves
2.2.2.1. Transverse waves: motion in which all points on a wave oscillate along paths at right angles to the direction of the wave's advance.
2.2.2.1.1. examples: ripples on the surface of water & vibrations in a guitar ring
2.2.2.1.2. graph representation
2.2.2.2. Longitudinal waves: wave consisting of a periodic disturbance or vibration that takes place in the same direction as the advance of the wave.
2.2.2.2.1. examples: sound waves & ultrasound waves
2.2.2.2.2. graph representation
2.2.3. Common types of waves (according to different magnitudes of wavelengths)
2.3. Wave Characteristics
2.3.1. Amplitude and Intensity
2.3.1.1. Relationship: the intensity of the wave is directly proportional to the square of its amplitude
2.3.1.2. I ∝ A²
2.3.2. Superposition
2.3.2.1. Displacements of portions of waves superpose when they overlap.
2.3.3. Polarization
2.3.3.1. Polarization, property of certain electromagnetic radiations in which the direction and magnitude of the vibrating electric field are related in a specified way.
2.4. Wave Behavior
2.4.1. huygen's principle (The natural state wave propagates)
2.4.1.1. Infinite disturbances on a single wave, it interferes with each other and propagates holding the shape of the wave.
2.4.2. Wave
2.4.2.1. Wave fronts
2.4.2.1.1. The pattern of wave that occur periodically according to its wavelength
2.4.2.2. Wavelength
2.4.2.2.1. The distance between two adjacent
2.4.3. Reflection
2.4.3.1. Incident wave
2.4.3.1.1. The wave enters a medium. It forms a incident angle with the surface of the line between media
2.4.3.2. Refractive wave
2.4.3.2.1. The wave reflected from a medium. It forms a reflective angle with the surface of the line between media
2.4.3.3. Reflection of traveling wave
2.4.3.3.1. The refractive point fixed
2.4.3.3.2. The Refractive point freed
2.4.4. Refraction
2.4.4.1. Refractive wave
2.4.4.1.1. The wave emitted from a medium. It forms a refractive angle with the surface of the line between media
2.4.4.2. Incident wave
2.4.4.2.1. The wave enters a medium. It forms a incident angle with the surface of the line between media
2.4.4.3. Formula (Snell's law)
2.4.4.3.1. sin(incident angle)/sin(refractive angle)=incident wave speed/refractive wave speed
2.4.4.4. Mechanism
2.4.4.4.1. When wave gets across the media, the velocity changes due to the media it travels in. Sooner the wave enters the media, sooner the change of velocity happens. It bends the path of the wave travelling.
2.4.5. Interference of wave
2.4.5.1. The individual displacements of waves will be added vertically, called superposition
2.4.5.1.1. Constructive wave
2.4.5.1.2. Destructive wave
2.4.5.2. Path difference
2.4.5.2.1. The difference on distance between two waves
2.4.5.3. Phase difference
2.4.5.3.1. The difference on periodicity between two waves
2.4.6. Diffraction
2.4.6.1. 1. Diffraction takes place when a wave passes through a small opening. Wave propagates expandingly after it travels through the small opening
2.4.6.2. 2. Diffraction also takes place when an obstacle lied in front.
2.4.6.3. The phenomenon does not happen if the width of slit is too short
2.4.6.4. The diagram of diffraction:
2.4.6.4.1. Equal distance between fringes
2.4.6.4.2. Intensity is greatest in the center, decreasing intensity when it gets broader
2.4.7. Double-slit intervention
2.4.7.1. Definition: Parallel waves pass through two slits and diffract individually. Two diffracted wave interfere with each other and form ordered shape of spectrum to a screen opposed to the slits
2.4.7.2. Formula: s = D * λ / d
2.4.7.3. Spectrum
2.4.7.3.1. Similar Intensity
2.4.7.3.2. Similar slit difference
2.5. Standing Waves
2.5.1. Mechanism: Two coherent wave with opposing directions and same amplitude. It ensures that certain points of resulting wave stay still, which means there is no displacement in the wave.
2.5.2. Feature
2.5.2.1. No energy transfer, but associated
2.5.2.2. Varying amplitude to a specific location
2.5.2.3. Either in phase or out of phase
2.5.2.4. frequency stays the same, except for nodes
2.5.2.4.1. Nodes: the unchanging location in standing wave
2.5.3. Wave behavior
2.5.3.1. nth harmonic
2.5.3.1.1. nth nodes appear in the standing wave
2.5.3.2. Two ends fixed
2.5.3.2.1. General rule
2.5.3.3. One end fixed, one end freed
2.5.3.3.1. General rule
2.5.3.4. Two ends freed
2.5.3.4.1. general rule