ASTRO 101 CH.17 HMW
When a proton and an antiproton collide, they
convert into two photons
What was the approximate temperature of the universe when the universe was just 1 second old?
10^10 K Recall that, in scientific notation, 1s=100s. Along the horizontal axis, this point is the tick mark halfway between the tick marks labeled 10−5 and 105. From the height of the red line, this point corresponds to a temperature of about 1010K.
Based on observations of the expansion of the universe, the current age of the universe is about __________
14 billion years
Daytime at "Night." According to Olbers' paradox, the entire sky would be as bright as the surface of a typical star if the universe were infinite in space, unchanging in time, and the same everywhere. However, conditions would not need to be quite that extreme for the "nighttime" sky to be as bright as the daytime sky. The luminosity of the Sun 3.8×1026W and the distance between the Earth and the Sun is 1.496×1011m, 1ly=9.461×1015m. The inverse square law for light is: apparent brightness=(star luminosity)/(surface area of imaginary sphere)=L4πd2 Using the inverse square law for light, determine the apparent brightness of the Sun in our sky.
1400 W/m^2
The Big Bang theory is closely linked to Hubble's discovery that the universe is expanding, which seems to imply that there was a time in the past when the expansion first began. Nevertheless, the Big Bang theory did not gain widespread acceptance among scientists until the 1960s. Why wasn't expansion alone enough to convince scientists that the Big Bang really happened?
Although expansion seems to imply a Big Bang, no other specific predictions of the Big Bang theory were tested and confirmed until the 1960s.
During the history of the universe, what important event occurred about 0.001 seconds after the Big Bang?
Most matter was annihilated by antimatter.
During the history of the universe, what important event occurred about 380,000 years after the Big Bang?
Light began to travel freely through the universe. This time when light could first travel freely marks the release of the cosmic microwave background, which we can still observe today.
Suppose you were a microscopic being that had lived since the first instant after the Big Bang. With the passage of time, you would have noticed your observable universe __________.
becoming larger
Essentially all the hydrogen nuclei that will ever exist in our universe were created __________.
by the time the universe was about 3 minutes old
Suppose you have a compressed gas, like that in a piston in a car engine. As the piston moves so that the gas expands, what happens to the gas temperature?
it cools as it expands
The cosmic microwave background consists of __________.
microwave photons coming to Earth from all directions in space
The charge of an antiproton is
negative
Which of the following does not provide strong evidence for the Big Bang theory?
observations of the amount of hydrogen in the universe
Which of these pieces of evidence supports the idea that inflation really happened?
observations of the cosmic microwave background that indicate a flat geometry for the universe
The universe is expanding with time, which makes the observable universe grow larger in size as time passes.
(Note that the "observable universe" means the size of the universe as it would appear to any hypothetical observer located any place within it.)
Shown following are several times in the history of the universe. Imagine that you were able to watch a single photon that has been part of the cosmic microwave background since it first became present in the universe. Rank these times from left to right based on the wavelength this photon would have at each time, from shortest to longest.
-500,000 years after the Big Bang -1 million years after the Big Bang -100 million years after the Big Bang -1.5 billion years after the Big Bang -today
Shown following are several times in the history of the universe. Rank these times from left to right based on the peak wavelength in the spectrum of the cosmic microwave background, from shortest to longest.
-500,000 years after the Big Bang -1 million years after the Big Bang -100 million years after the Big Bang -1.5 billion years after the Big Bang -today
Today, most scientists accept the Big Bang theory because its predictions agree so well with observations. But a scientific theory can always be revised or discarded if future observations do not agree with its predictions. Consider the following hypothetical future observations. Which one(s) would be inconsistent with the Big Bang theory?
-Careful studies of quasar spectra show that, 12 billion years ago, the temperature of the cosmic microwave background was slightly lower than it is today. - Over the next 10 years, the temperature of the cosmic microwave background falls to 1 K. -Astronomers discover distant protogalactic clouds with a helium abundance below 20%.
Shown following are the same eras shown in Parts A and B. Rank the eras from left to right based on the size of the observable universe during each one, from smallest to largest.
-Planck era - all 4 forces operated as one -Gut era - strong, electroweak forces unite as GUT force -electroweak era - 3 forces operated: gravity, strong, electroweak -particle era - protons, neutrons both common -era of nucleosynthesis - fusion created helium nuclei -era of nuclei - H, He nuclei and electrons existed but no neutral atoms -era of atoms - neutral atoms existed, but not stars -era of galaxies - stars and galaxies common
To gain familiarity with the various eras in the history of the universe, as defined by prevailing physical conditions at different times.
-Planck era - all 4 forces operated as one -Gut era - strong, electroweak forces unite as GUT force -electroweak era - 3 forces operated: gravity, strong, electroweak -particle era - protons, neutrons both common -era of nucleosynthesis - fusion created helium nuclei -era of nuclei - H, He nuclei and electrons existed but no neutral atoms -era of atoms - neutral atoms existed, but not stars -era of galaxies - stars and galaxies common
Shown following are the same eras shown in Part A. Rank the eras from left to right based on the temperature of the universe during each one, from coolest to hottest.
-era of galaxies - stars and galaxies common -era of atoms - neutral atoms existed, but not stars -era of nuclei - H, He nuclei and electrons existed but no neutral atoms -era of nucleosynthesis - fusion created helium nuclei -particle era - protons, neutrons both common -electroweak era - 3 forces operated: gravity, strong, electroweak -Gut era - strong, electroweak forces unite as GUT force -Planck era - all 4 forces operated as one
Shown following are several times in the history of the universe. Rank these times from left to right based on the average temperature of the universe at each time, from coolest to hottest.
-today -1.5 billion years after the Big Bang -100 million years after the Big Bang -1 million years after the Big Bang -500,000 years after the Big Bang
Daytime at "Night." According to Olbers' paradox, the entire sky would be as bright as the surface of a typical star if the universe were infinite in space, unchanging in time, and the same everywhere. However, conditions would not need to be quite that extreme for the "nighttime" sky to be as bright as the daytime sky. The luminosity of the Sun 3.8×1026W and the distance between the Earth and the Sun is 1.496×1011m, 1ly=9.461×1015m. The inverse square law for light is: apparent brightness=(star luminosity)/(surface area of imaginary sphere)=L4πd2 Using the inverse square law for light, determine the apparent brightness our Sun would have if it were at a distance of 17 billion light-years.
1.2x10^-27 W/m^2
Daytime at "Night." According to Olbers' paradox, the entire sky would be as bright as the surface of a typical star if the universe were infinite in space, unchanging in time, and the same everywhere. However, conditions would not need to be quite that extreme for the "nighttime" sky to be as bright as the daytime sky. The luminosity of the Sun 3.8×1026W and the distance between the Earth and the Sun is 1.496×1011m, 1ly=9.461×1015m. The inverse square law for light is: apparent brightness=(star luminosity)/(surface area of imaginary sphere)=L4πd2 From your answers to parts A and B, estimate how many stars like the Sun would need to exist at a distance of 17 billion light-years for their total apparent brightness to equal that of our Sun.
1.2x10^30
The vertical axis of the graph measures the temperature of the universe in kelvin. If we move up one tick mark to the next, by what factor does the temperature increase?
100
The horizontal axis of the graph measures the time since the Big Bang in seconds. The extreme left of the horizontal axis, where it meets the vertical axis, is labeled 10−45 seconds (that is a decimal point followed by 44 zeroes and then a one). If we move along two tick marks to the right on the horizontal axis, it is labeled 10−35 seconds. By what factor does the time increase from one tick mark on the horizontal axis to the next tick mark toward the right?
1x10^5 As you move long the horizontal axis to the right, the time increases by a factor of one hundred thousand (105). So that from 105 seconds or 100000 seconds after the Big Bang to 1010 seconds (the tick mark between 105 seconds and 1015 seconds), we have increased the time since the Big Bang by a factor of one hundred thousand.
When we speak of the temperature of the universe as a whole today, we mean the temperature of the cosmic microwave background, which is about _____.
3 K
From Part B, you know that the universe's current age of about 14 billion years is equivalent to about 4×1017s . Therefore, 1 billion years ago, the age of the universe in seconds was about __________.
3.7x10^17 s
One year is equivalent to about __________. There are about 3×107s in one year, so 1 billion (109) years is about 3×1016s (because 107×109=107+9=1016).
3x10^7 s One billion years ago, the universe was about 13 billion years old, which is about 13/14 of its current age. On the powers of 10 scale used on the horizontal axis, this is almost indistinguishable from the present age of 4×1017s (see Part B). Note that this present age is about 400 times the age represented by the tick mark at 1015s, demonstrating that 13/14 of the present age must be very close to the far right along the axis.
To get your bearings on the horizontal time axis of this plot, it is useful to calculate the age of the universe in seconds today. If you multiply the age of the universe in years by the number of seconds in a year, approximately what is the current age of the universe in seconds?
4x10^17 To find this answer, multiply the age of the universe in years (14 billion years, or 1.4×1010 years) by the number of seconds in one year (about 3×107s). Note that the far right point along the red line on the graph represents this present age of the universe.
Any observation showing that the cosmic microwave background has heated up with time would contradict the Big Bang theory's prediction that it must cool as the universe expands.
An observation of dramatic change in the background temperature over a mere decade would contradict the idea that the background is a characteristic of the universe itself. A helium abundance significantly below 25% would contradict the predicted abundance.
The cosmic microwave background is essentially the thermal radiation emitted by the universe as a whole, and the laws of thermal radiation tell us that hotter objects emit light with a shorter peak wavelength (higher energy).
Because the universe cools with time (see Part A), we conclude that the peak wavelength of the cosmic microwave background must get longer as time passes.
Hydrogen nuclei are protons, and protons were formed during the particle era. During the next three minutes, many of these protons fused and then broke back apart, but by the end of that period these reactions stopped.
Essentially all the hydrogen that will ever exist was therefore present in the universe when the universe was just 3 minutes old. Subsequent fusion in stars has consumed some of this hydrogen, but it has not made any more.
Spectra of very distant galaxies show very large redshifts, and we say that the wavelengths of the photons from these galaxies are longer because of cosmological redshift. According to our modern perspective on the universe, what is the cause of cosmological redshift?
Individual photons stretch to longer wavelength as the universe expands.
How much cooler is the universe now (at an age of 4 × 1017 s) than it was at an age of 1 second?
Its current temperature is one ten-billionth (10−10) the temperature at an age of 1 second.
Classify each statement below as an observation or as an inference based on the current Big Bang model. (Note that the helium abundance is defined as the mass of helium relative to the mass of hydrogen.)
Observations: -the temperature of the cosmic microwave background varies slightly with direction -the helium abundance is at least 25% in every galaxy studied so far -the cosmic microwave background temperature is 2.73 K -large scale structure looks about the same in all directions Inferences from a model: -large scale structure grew around density variations present in the early universe -the cosmic microwave background is radiation left over from the Big Bang -photons of the cosmic microwave background have traveled through space for almost 14 billion years -fusion during the universe's first five minutes produced 75% hydrogen and 25% helium (by mass)
The Big Bang model holds that the universe began extremely hot and dense and has been cooling ever since.
Photons could first travel freely when the universe was about 380,000 years old and had a temperature of about 3,000 K. These photons are what we see today—almost 14 billion years later—as the cosmic microwave background.
Which of the following important events occurred earliest in the history of the universe?
Space-time rapidly expanded during a brief period of inflation. inflation is thought to have occurred when the universe was only a tiny fraction of a second old.
What will the temperature of the cosmic microwave background be when the average distances between galaxies are three times as large as they are today? (Hint: The peak wavelength of photons in the background will then also be three times as large as it is today.)
T = 0.91 K
Although most matter was annihilated, virtually all antimatter suffered this fate.
That is why antimatter has been very rare in the universe ever since that time, which marked the end of what is known as the "particle era."
In science, it is never enough just to say that some idea makes logical sense. Rather, a proposed model or hypothesis can become a theory only if it makes specific predictions that have been tested and verified.
The Big Bang theory gained acceptance in the early 1960s because that was when one of its key predictions—the existence of the cosmic microwave background—was first tested and verified.
Which of the following best explains why the night sky is dark?
The observable universe is not infinite.
The vertical axis shows temperature and the horizontal axis shows time, so the fact that the red line drops diagonally from left to right means the temperature is falling with time.
The universe is getting cooler with time
The tiny variations in temperature correspond to variations in density.
These variations served as "seeds" for the later formation of large-scale structure; without such seeds, gravity could not have created such large structures in only 14 billion years.
Daytime at "Night." According to Olbers' paradox, the entire sky would be as bright as the surface of a typical star if the universe were infinite in space, unchanging in time, and the same everywhere. However, conditions would not need to be quite that extreme for the "nighttime" sky to be as bright as the daytime sky. The luminosity of the Sun 3.8×1026W and the distance between the Earth and the Sun is 1.496×1011m, 1ly=9.461×1015m. The inverse square law for light is: apparent brightness=(star luminosity)/(surface area of imaginary sphere)=L4πd2 Compare your answer to part C with the estimate of the total number of stars in our observable universe. Use your answer to explain why the night sky is much darker than the daytime sky. How much larger would the total number of stars need to be for "night" to be as bright as day?
We estimated the number of stars in the observable universe to be around 10^(22), so we would need many times more stars than we have in the observable universe to make the night sky as bright as day. This explains why the night sky is dark and why even a finite number of stars would make the sky as bright as the Sun (and life as we know it impossible).
Today, the Big Bang is considered to be a scientific theory. In science, a theory is __________.
a detailed model that makes specific predictions that have been tested and verified
The current temperature of the universe as a whole is
a few K
What is the earliest time in the universe that we can directly observe?
a few hundred thousand years after the Big Bang
A hydrogen nucleus consists of __________.
a single proton
What was the approximate temperature of the universe at an age of 1015 s?
about 100 K
What was the approximate temperature of the universe at an age of 5 minutes?
about 10^9 K
Suppose you want to know what the temperature of the universe was 1 billion years ago. Where along the horizontal axis should you look?
almost all the way to the far right
The universe has been expanding since its birth in the Big Bang,
and this expansion causes the universe as a whole to cool with time.
As the universe expands, its overall temperature _____.
decreases
Compared to when the cosmic microwave background was first released, the radiation of the cosmic microwave background today is __________.
fainter and has most of its photons at longer wavelengths The universe is expanding and cooling with time, causing the cosmic microwave photons to stretch to longer wavelengths.
From Part C, you know that in basic terms, the graph shows that the temperature of the universe decreases with time. In more specific terms, this graph shows that the temperature of the universe __________.
fell very rapidly when the universe was young, but is changing very gradually today This fact leads to a very important point about any graph that is labeled with powers of 10 on either or both axes: When the graph uses a power-of-10 scale, a straight line does not have the same linear interpretation as it does on a graph that uses a linear scale on both axes.
The point along the horizontal axis that represents 1 second is __________.
halfway between the tick marks labeled 10−5 and 105
When we say that the cosmic microwave background has a temperature of 2.73 K, we mean that it __________.
has a thermal radiation spectrum characteristic of an object with temperature of 2.73
The overall helium abundance in the universe __________.
is gradually increasing
The graph shows that the temperature one billion years ago was __________.
only very slightly higher than its current temperature of about 3 K
Observations are things we actually see and measure with our eyes, telescopes, or instruments. Inferences are
proposed explanations or conclusions from models that are built with those observations in mind.
All of the following events require(d) extremely high temperature except one. Which one? -production of antimatter -merging of two or more of the four forces into one -the sudden inflation of the universe -the birth of the stars
the birth of stars
When we speak of large-scale structure in the universe, we mean __________.
the distribution of galaxies and galaxy clusters over spans of millions of light-years
An age of about five minutes marks the time in the history of the universe when __________.
the overall chemical composition of the universe was set at about 75% hydrogen and 25% helium (by mass)
Consider Object 1 with temperature 10 K and Object 2 with temperature 20 K. According to the laws of thermal radiation __________.
the spectrum of Object 2 has a shorter peak wavelength than the spectrum of Object 1
Consider Object 1 with temperature 10 K and Object 2 with temperature 20 K. According to the laws of thermal radiation, __________.
the spectrum of Object 2 has a shorter peak wavelength than the spectrum of Object 1
Which of the following does inflation help to explain?
the uniformity of the cosmic microwave background
Consider this statement from Part A: "Photons of the cosmic microwave background have traveled through space for almost 14 billion years." This statement follows from our model of the Big Bang, because the Big Bang model is based on the idea that __________.
the universe began very hot and dense and has been cooling as it expands
Individual photons stretch to longer (redder) wavelength as the universe expands;
this is the phenomenon sometimes referred to as cosmological redshift.
One of the inferred statements from Part A is that "Large-scale structure grew around density variations present in the early universe." Observational evidence that such density variations really existed comes from the fact that the cosmic microwave background exhibits __________.
tiny temperature variations in different directions
When the universe was 380,000 years old, its thermal radiation spectrum consisted mostly of
visible and infrared photons
According to the current Big Bang theory, the photons that we detect in the cosmic microwave background started their journey to us __________.
when the universe was about 380,000 years old
Although we can divide the history of the universe into many distinct "eras," sometimes it's useful just to have a broad perspective on what events occurred in the very early universe and what events occurred later. Listed following are events that occurred either before or after the first five minutes in the history of the universe. Match these events to the appropriate time period.
within the first five minutes -anti-electrons (positrons) as common as electrons -temperature fell to 10^15 K -strong force and electroweak force first became distant -inflation occurred sometime after the first five minutes -galaxies formed -carbon nuclei formed by fusion -stars formed -photons of cosmic background released
