Solid State Physics (QMUL):
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Mechanics (QMUL):
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PHY108 Condensed Matter Physics (QMUL):
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Electromagnetic Fields (EMF):
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Thermodynamics and Kinetic Physics (TKP):
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MTH5112 Linear Algebra I (QMUL): incomplete notes
[ Intro + Weeks 6-11 ]
5112 Linear Algebra I - Exam 2011
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Dynamics (QMUL):
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Waves and Optics cont. (QMUL):
[ Lecture 6 ]
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Table 1 - Half-lives of various long-lived radioactive isotopes.
Isotope: t1/2 (years):
Samarium-146 103,000,000
Uranium-236 234,200,000
Uranium-235 703,800,000
Potassium-40 1,280,000,000
Uranium-238 4,468,000,000
Rubidium-87 4,750,000,000
Thorium-232 14,100,000,000
Lutetium-176 37,800,000,000
Rhenium-187 43,500,000,000
Lanthanium-138 105,000,000,000
Samarium-147 106,000,000,000
The Earth's age of 4.55 billion years is known with an error of less than one percent from the dating of meteorites using a variety of elements from the table above.
4.55 billion years (plus or minus about 1%)
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Table 2 - Ages derived from various recent studies of radioactive elements in old stars.
Authors Isotope Star Age:
Cowan et al. (1997) 232Th CS 22892-052 15.2 +/- 3.7 Gyr
Cowan et al. (1999) 232Th HD115444 15.6 +/- 4.6 Gyr
Cayrel et al. (2001) 238U CS 31082-001 12.5 +/- 3 Gyr
Wanajo et al. (2002) 238U CS 31082-001 14.1 +/- 2.5 Gyr
The Sun's main-sequence lifetime is about 10 billion years, so a star 10,000 times as luminous will live only 10 million years.
... an age of 9.5 +1.1/-0.8 Gyr for the disk of the Milky Way
Age estimate for the Milky Way galaxy obtaining 14.5 +2.8/-2.2 Gyr. (Comparable to the 13.7 billion yrs for the Universe)
A reasonable guesstimate of c. 13 Gyr for the MW galaxy, t0 ~ 13.7 Gyr for the age of the Universe, and H0 ~ 72 km/s/Mpc. (See WMAP, HST and SNe data).
An age estimate for the oldest globular clusters ~ 12 Gyr might be reasonable, as the ages have been revised downward from the earlier initial estimates.
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Radioactive Dating of an Old Star
A very interesting paper by Cowan et al. (1997, ApJ, 480, 246) discusses the thorium abundance in an old halo star. Normally it is not possible to measure the abundance of radioactive isotopes in other stars because the lines are too weak. But in CS 22892-052 the thorium lines can be seen because the iron lines are very weak. The Th/Eu (Europium) ratio in this star is 0.219 compared to 0.369 in the Solar System now. Thorium decays with a half-life of 14.05 Gyr, so the Solar System formed with Th/Eu = 2^4.6/14.05 * 0.369 = 0.463. If CS 22892-052 formed with the same Th/Eu ratio it is then 15.2 +/- 3.5 Gyr old. It is actually probably slightly older because some of the thorium that would have gone into the Solar System decayed before the Sun formed, and this correction depends on the nucleosynthesis history of the Milky Way. Nonetheless, this is still an interesting measure of the age of the oldest stars that is independent of the main-sequence lifetime method.
A later paper by Cowan et al. (1999, ApJ, 521, 194) gives 15.6 +/- 4.6 Gyr for the age based on two stars: CS 22892-052 and HD 115444.
A another star, CS 31082-001, shows an age of 12.5 +/- 3 Gyr based on the decay of U-238 [Cayrel, et al. 2001, Nature, 409, 691-692]. Wanajo et al. refine the predicted U/Th production ratio and get 14.1 +/- 2.5 Gyr for the age of this star.
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But recent Hipparcos results show that the globular clusters are further away than previously thought, so their stars are more luminous. Gratton et al. give ages between 8.5 and 13.3 Gyr with 12.1 being most likely, while Reid gives ages between 11 and 13 Gyr, and Chaboyer et al. give 11.5 +/- 1.3 Gyr for the mean age of the oldest globular clusters.
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Table 3 - Recent main-sequence turnoff measurements of the ages of several globular clusters.
Authors: Age:
Chaboyer et al. 1997 14.6 +/- 1.7 Gyr
Gratton et al. (1997) 11.8 +/- 2.3 Gyr
Reid et al. (1997) 12-13 Gyr
Chaboyer et al. (2001) 11.5 +/- 1.3 Gyr
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Table 4 - Summary of recent measurement of the age of the Universe.
Method: Authors Object Age:
Cosmological: Various Universe 13.7 +/- 0.2 Gyr
Radiometric: Cowan et al. (1999) HD 115444CS 14.5 +/- 3.0 Gyr
Wanajo et al. (2002) CS 31082-001 16 +/- 5 Gyr
Main-sequence turnoff: Gratton et al. (1999) Multiple GCs 12.3 +/- 2.5 Gyr
Chaboyer et al. (2001) Multiple GCs 12.0 +/- 1.5 Gyr
White dwarf cooling: Hansen et al. (2004) M 4 12.8 +/- 1.1 Gyr
Determination of the Universe's Age, to
Source:- Daniel Perley, (Berkeley)
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Age estimates
Method: Value [Gyr]: +Errorbar: -Errorbar:
Elements 14.5 +2.8 -2.5
Old Stars 14.4 +2.2 -2.2
GC MSTO 12.2 +1.3 -1.3
Disk WDs 11.5 +infinity -1
GC WDs 12.8 +1.1 -1.1
Weighted Mean 12.94 +0.75 -0.75
(Estimated age of the Universe, t0 ~ 13.7 Gyr as above)
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... the baryon acoustic scale at a redshift of z = 0.6, or 5.7 billion years before now ...
New observations using the Hubble Space Telescope yield a distance of 17.1 +/- 1.8 Mpc. to the Virgo cluster galaxy M100. This distance leads to a value of H0 = 80 +/- 17 km/s/Mpc
Ten+1 measurements of the Hubble Constant
Method Used: Citation: Value (km/second/Megaparsec):
Cepheid variables in distant galaxies W. Freedman et al (1999) 70 +/- 7
M101 group velocity and distance Sandage and Tammann (1974) 55.5 +/- 8.7
Virgo Cluster Peebles (1977) 42 - 77
Globular Clusters Hanes (1979) 80 +/- 11
Virgo Sc HII luminosities Kennicutt (1981) 55
Type I supernovae Branch (1979) 56 +/- 15
Type I supernovae Sandage and Tammann (1982) 50 +/- 7
Infrared Tully-Fisher relation Aaronson and Mould (1983) 82 +/- 10
SN-Ia and Cepheids Sandage, et al. (1994) 55 +/- 8
Cepheids in Virgo (M100) Freedman, et al. (1994) 80 +/- 17
Surface Brightness Fluctuation Tully (1993) 90 +/- 10
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EM Spectrum
Region Wavelength Wavelength Frequency Photon Energy:
(Angstroms) (centimeters) (Hz) (eV)
Radio > 10^9 > 10 (=0.1m) f < 3 x 10^9 E < 10^-5
Microwave 10^9 - 10^6 10 -0.01 (0.1-10^-4m) 3 x 10^9-3 x 10^12 10^-5-0.01
Infrared 10^6 - 7000 0.0 -7 x 10^-5 3 x 10^12 -4.3 x 10^14 0.01 - 2
Visible 7000 - 4000 7 x 10^-5 -4 x 10^-5 4.3 x 10^14 -7.5 x 10^14 2 - 3
Ultraviolet 4000 - 10 4 x 10^-5 -10^-7 7.5 x 10^14 -3 x 10^17 3 - 10^3
X-Rays 10 - 0.1 10^- -10^-9 3 x 10^17-3 x 10^19 10^3 - 10^5
Gamma Rays < 0.1 < 10^-9 (=10^-11m) > 3 x 10^19 > 10^5
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Visible region :
Color: Wavelength:
Violet 400-420 nm
Indigo 420-440 nm
Blue 440-490 nm
Green 490-570 nm
Yellow 570-585 nm
Orange 585-620 nm
Red 620-780 nm
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Region of the EM spectrum - Main interactions with matter :
Radio - Collective oscillation of charge carriers in bulk material (plasma oscillation). An example would be the oscillation of the electrons in an antenna.
Microwave through far infrared - Plasma oscillation, molecular rotation
Near infrared - Molecular vibration, plasma oscillation (in metals only)
Visible - Molecular electron excitation (including pigment molecules found in the human retina), plasma oscillations (in metals only)
Ultraviolet - Excitation of molecular and atomic valence electrons, including ejection of the electrons (photoelectric effect)
X-rays - Excitation and ejection of core atomic electrons, Compton scattering (for low atomic numbers)
Gamma rays - Energetic ejection of core electrons in heavy elements, Compton scattering (for all atomic numbers), excitation of atomic nuclei, including dissociation of nuclei.
High-energy gamma rays - Creation of particle-antiparticle pairs. At very high energies a single photon can create a shower of high-energy particles and antiparticles upon interaction with matter.
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Keywords: physics, astrophysics, astronomy, stellar structure, stellar evolution, quantum mechanics, general relativity, cosmology, lecture notes, MSc degree, MSci degree, university degree, physical sciences