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A pie chart shows 26.8 percent dark matter, 4.9 percent atoms and 68.3 percent dark energy.
Estimated distribution of matter and energy in the universe. (credit: NASA/WMAP Science Team)


  • The early universe was hot and dense.
  • The universe is isotropic and expanding.
  • Cosmic background radiation is evidence for the Big Bang.
  • The vast portion of the mass and energy of the universe is not well understood.

Key equations

Momentum of a charged particle in a cyclotron p = 0.3 B r
Center-of-mass energy of a colliding beam machine W 2 = 2 [ E 1 E 2 + ( p 1 c ) ( p 2 c ) ] + ( m 1 c 2 ) 2 + ( m 2 c 2 ) 2
Approximate time for exchange of a virtual particle between two other particles Δ t = h E
Hubble’s law v = H 0 d
Cosmological space-time metric d s 2 = c 2 d t 2 a ( t ) 2 d Σ 2

Conceptual questions

What is meant by a “cosmological model of the early universe?” Briefly describe this model in terms of the four fundamental forces.

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Describe two pieces of evidence that support the Big Bang model.

The observed expansion of the universe and the cosmic background radiation spectrum.

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In what sense are we, as Newton once said, “a boy playing on the sea-shore”? Express your answer in terms of the concepts of dark matter and dark energy.

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If some unknown cause of redshift—such as light becoming “tired” from traveling long distances through empty space—is discovered, what effect would that have on cosmology?

If light slow down, it takes long to reach Earth than expected. We conclude that the object is much closer than it really is. Thus, for every recessional velocity (based on the frequency of light, which we assume is not disturbed by the slowing), the distance is smaller than the “true” value, Hubble’s constant is larger than the “true” value, and the age of the universe is smaller than the “true” value.

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In the past, many scientists believed the universe to be infinite. However, if the universe is infinite, then any line of sight should eventually fall on a star’s surface and the night sky should be very bright. How is this paradox resolved in modern cosmology?

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Additional problems

Experimental results suggest that a muon decays to an electron and photon. How is this possible?

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Each of the following reactions is missing a single particle. Identify the missing particle for each reaction.

(a) p + p n + ? (b) p + p p + Λ 0 + ? (c) π + p Σ + ? (d) K + n Λ 0 + ? (e) τ + e + + υ e + ? (f) υ e + p n + ?

a. n ; b. K + ; c. K + ; d. π ; e. ν τ ; f. e +

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Because of energy loss due to synchrotron radiation in the LHC at CERN, only 5.00 MeV is added to the energy of each proton during each revolution around the main ring. How many revolutions are needed to produce 7.00-TeV (7000 GeV) protons, if they are injected with an initial energy of 8.00 GeV?

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A proton and an antiproton collide head-on, with each having a kinetic energy of 7.00 TeV (such as in the LHC at CERN). How much collision energy is available, taking into account the annihilation of the two masses? (Note that this is not significantly greater than the extremely relativistic kinetic energy.)

14.002 TeV 14.0 TeV

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When an electron and positron collide at the SLAC facility, they each have 50.0-GeV kinetic energies. What is the total collision energy available, taking into account the annihilation energy? Note that the annihilation energy is insignificant, because the electrons are highly relativistic.

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Questions & Answers

A 10kg mass lift to a height of 24m and release. what is the total energy of the system
mechanics is that branch of physical and mathatics that
what is the difference between a molecule and atom
Natanim Reply
Atoms are single neutral particles. Molecules are neutral particles made of two or more atoms bonded together.
what I'd dynamic propulsion
Elias Reply
A body quadruples its momentum when its speed doubles.What was the initial speed in units of c.i.e..what was u/c ?
Lekshmi Reply
what is enthalpy?
prabir Reply
a thermodynamic quantity equivalent to the total heat content of a system
proparty of tharmo dainamic
What is the meaning of Nuclear Fission?
Benita Reply
what do you mean by dynamics single particles
Peacekamei Reply
عند قذف جسم إلى أعلى بسرعة إبتدائية فإنه سيصل إلى ارتفاع معين (أقصى ارتفاع) ثم يعود هابطاً نحو سطح الأرض .   إذا قُذِفَ جسم إلى أعلى ووجد أن سرعته 18 م / ث عندما قطع 1/4 المسافة التي تمثل أقصى ارتفاع سيصله فالمطلوب إيجاد السرعة التي قُذِف بها بالمتر / ث . إن هذه السرعة هي واحدة من الإجابات التالية
Aml Reply
what is light
Ayebanifesunday Reply
light is a kind of radiation That stimulates sight brightness a source of illumination.
Electromagnet radiation creates space 7th, 8th, and 9th dimensions at the rate of c.
That is the reason that the speed of light is constant.
This creation of new space is "Dark Energy".
The first two sets of three dimensions, 1 through 6, are "Dark Matter".
As matter decays into luminous matter, a proton, a neutron, and an electron creat deuterium.
There are three sets of three protons, 9.
There are three sets of three neutrons, 9.
A free neutron decays into a proton, an electron, and a neutrino.
There are three sets of five neutrinoes, 15.
Neutrinoes are two dimensional.
A positron is composed of the first three dimensions.
An electron is composed of the second three dimensions.
What is photoelectric
Hsssan Reply
light energy (photons) through semiconduction of N-P junction into electrical via excitation of silicon purified and cristalized into wafers with partially contaminated silicon to allow this N-P function to operate.
i.e. Solar pannel.
Photoelectric emission is the emission of electrons on a metal surface due to incident rays reflected on it
If you lie on a beach looking at the water with your head tipped slightly sideways, your polarized sunglasses do not work very well.Why not?
Rakhi Reply
it has everything to do with the angle the UV sunlight strikes your sunglasses.
this is known as optical physics. it describes how visible light, ultraviolet light and infrared light interact when they come into contact with physical matter. usually the photons or light upon interaction result in either reflection refraction diffraction or interference of the light.
I hope I'm clear if I'm not please tell me to clarify further or rephrase
what is bohrs model for hydrogen atom
Swagatika Reply
what is the value of speed of light
Propessor Reply
1.79×10_¹⁹ km per hour
what r dwarf planet
Sivalakshmi Reply
what is energy
Isiguzo Reply
কাজের একক কী
কাজের একক কী
Energy is ability so capacity to do work.
Practice Key Terms 4

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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