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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)

Summary

  • 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

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
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Eliyee
devaluation
Eliyee
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WARKISA
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Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
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Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
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Shukri
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Lilia Reply
what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
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Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
types of unemployment
Yomi Reply
What is the difference between perfect competition and monopolistic competition?
Mohammed
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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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