MODERN PHYSICS

MODERN PHYSICS

1. ASTROPHYSICS & COSMOLOGY

   • Measuring distance
     • AU: d sun earth
       • astronomical unit (AU)  1AU: distance between Sun and Earth= 1.50×10^11m
     • ly: d c t=1 year
       • light year: distance travelled by light in vacuum through one year. = (c)(t)=9.46×10^15m.
     • pc: d r=1AU 1arcsecond
       • parsec is the distance at which a radius of 1 AU substends an angle of 1 arcsecond. => it derived by 1pc=1AU/(tan(1arcsecond)). for small angel: tanθ≈θ. while θ must be in radius. it becomes to  1pc=1AU/(1arcsecond in rad). approximately=2.06×10^5AUOR 3.26ly
       • 1 arcsecond: (1/3600)° 1 arcminute: (1/60)°
     • d= 1/p, angle of parallax p
       • Parallax: apparent shift NS -> B
         • apparent shift of nearby stars against the background of distant stars.
         • use parallax to measure distance: recording the positions of a stat twice at two different time. parallax angle:???
   • Stars Luminosity and surface temperature
     • Blackbody: perfect absorber of EM
       • refer to Kichoff's law: it can emit all ranges of EM
     • relationship with T
       • conventionally a hotter object  radiated more energy per second
       • Stefan law:L=(4πr^2)(σ)(T^4)
         • σ: stefan's constant is  5.67×10^-8 [Wm^-2K^-4]
       • Wien's law: λmax=(Wien's constant)/T
         • peak wavelength (at which radiation has highest intensity) is inversely proportional to absolute temperature. Wien's constant is 3×10^-3[mK].
         • graph of intensity-peak wavelength
     • L=P radiated
       • Louminosity is defined as power radiated. [Js-1] OR [watt]
   • Cosmology
     • is a general study of Universe, its origins and evolutions. Uni contains billions of galaxies surrounded by massive amounts of tiny spread, invisible material called dark matter.
     • Emission spectra: c discreteL f elements emit
       • consists of discrete lines of frequency characteristic of the elements emitting the radiation.
       • not continuous like a rainbow(blackbody radiation).
       • f=△E/h
         • △E transition energy. it is determined like that as elements emitting light of diff f by absorbing different photon energy given by transition of electron.
     • Absorption spectra: c WB crossed DL f elements absorbe
       • consists of white light background crossed with dark lines of frequency characteristic of elements absorbing the radiation.
       • white background: consists of radiation of all frequencies
         • e.g. hot WB go through cooler gas, gas absorbe radiation of certain f.
       • Doppler effect[shift] of dark lines
         • red shift for recession: wave be stretched λ↑ f↓(v unchanged)
           • -> support Bigbang theory
             • distance galaxies are receding(red shift). Bigbang theory refers to Uni begins as a concentrated point and then exploded.
         • blue shift for approachment: wave be compressed λ↓ f↑
         • appli: use spectrum to find out relative speed
           • 1. from spectrum obtain △λ for a spectral line. 2. using λo measured on Earth. 3. (△λ)/(λo)=v/c.
         • appli: use to find out rotational speed
           • (facts: galaxies is receding and rotating) 1.each side of rotating galaxy has diff relative speed(if V1=VG+v, V2=VG-v), hence diff red shift. Edge rotating away from us has relatively higher speed than edge towards us . 2.appli (△λ)/(λo)=v/c to obtain V1,V2. △λ:comparing diff in spectrum of a spectral line.  λo: recorded on Earth before. 4. differences between two relative speed be used to determine rotational speed ((V1-V2)/2 ).
     • Cosmological principle: (assumption on Uni) viewed at vLS: H&I, laws bold
       • assumption on University viewed at large enough scale: 1. uni is Homogenous(uniform matter distribution). 2. uni is Isotropical(no differences of view in all directions). 3. Laws of physics is universal(bold).
       • (补充) 1.=> density of uni/galaxies are constant which means structure of galaxies are the same.? 2. => no centre, edge of Uni.
   • Doppler effect: △λ/ f relative motion
     • change in wavelength OR frequency of observed wave due to relative motion between observer and source.
     • v/c= △λ/λo= △f/fo
   • Lives of stars
     • Hertzsprung-Russell diagram: absolute magnitudes ∝ spectral class [O->M], scale ↓ from origin
       • absolute magnitudes of star size verse spectral class. dwarft, giant refer to magnitude.
     • Classification: depends on star I & T
       • classification of stars by Brightness(intensity) and Temperature.
     • Magnitude: measure of I
       • magnitude of star is a measure of brightness(intensity) of it.
       • describe as bright, dim.
       • Apparent magnitude: I appears from Earth
         • is the intensity of stars appears from Earth.
       • Absolute magnitude: apparent magnitude of stars 10 parsecs from Earth [-10, +15]
         • 1.it ranges from -10 up to +15: stars intensity falls(less bright). 2.log scale relationship??
     • Temperature: be determined by CL by CST [2500, 40000]
       • the surface temperature of star can be determined by color of loight it emits by Classification of spectral type.
       • describe as cold, hot.
       • juicing CST
         • 1.Hot bodies?? emit a range of EM radiation of a range of f,λ, there is always a peak Intensity(->P/A=E/(At)=hf/(At)) at one particular f,λ. 2. as T↑ I↑ f↑,λ↓. 3. hottest star, minimum λ, emits blue end of visible spectrum. refer to O Type. coolest star, maximum λ, emits red end. refer to M Type.
   • The Bigbang Model of Universe: m ISS -> exploded & creation -> NIE
     • 1. at some time, all mass in the Universe was located in a infinitly small singlarity. 2. then, it exploded, then cooled, made Hydrogen, made stars, made us. 3. the universe is non-infinite expanding. (non-infinite size, perhaps non-infinite small size)
     • Evidence
       • Red-shift of spectral lines
         • 1.take the spectum of galaxy at two points. 2.spectral lines are red shift.  3.[???????]. 4.all move away from us. universe is expanding. 5.balloon expanding model. space itself expanded, carrying the galaxies with it.
       • CMB radiation
         • cosmic microwave background. 1.in theory, if the universe has a bigbang with hot T, it must be cooling now. so somehow scientist perdicted T≈2.725K. 2.experiment by Penzias Twilson. all light in μm have T≈2.725K continuous and completed in λ. strongly supports the theory.
       • Olbern's Paradox: expanding non-infinite Universe
     • [recession speed related to distance] Hubble's law: v∝d. v=(Ho)(d)
       • relative recession speed = (constant)(relative distance from Earth). in kms-1, Mpc. Ho: Hubble's constant.
       • t=v/d=1/Ho=Age of Uni
         • t:Hubble's time. this is the time taken for any galaxy to reach its present position, starting at Bigbang. it is the age of Universe. [so awaresome: if we know Ho we can guess the age of universe. Age≈13.7Gyears]
       • [observed correlation supports dark energy]
         • the energy supports the Universe to expand in an increasing rate. it acts opposite to gravity/mass.
   • LIfe cycle of stars

2. MEDICAL IMAGING TECHNIQUES

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