Download Chapter 20: Radiant Energy from the Sun

12/22/12
Chapter 20: Radiant Energy from the Sun
Goals of Period 20
Section 20.1: To describe the forms of radiant energy
Section 20.2: To discuss the production of radiant energy in stars
Section 20.3: To explain the properties of waves and the transmission
of radiant energy from the Sun to the Earth
20.1 Radiant Energy
We have seen that static (motionless) electric charge produces an electric force.
Electric charge flowing through a conductor produces an electric current. Radiant
energy is produced when electric charge vibrates. We can think of radiant energy as
waves of energy. These waves can travel through a medium, such as air or water, or
through the vacuum of empty space, such as the radiant energy waves the Earth
receives from the Sun.
Radiant energy is the energy associated with an electromagnetic field; thus, it is
also known as electromagnetic radiation. We are constantly surrounded by radiant
energy. Light bulbs transfer radiant energy to our eyes in the form of visible light. A
warm oven transfers radiant energy in the form of infrared energy, which we experience
as heat. The Sun transfers radiant energy to the Earth in the form of infrared energy,
visible light, and ultraviolet rays. Microwave ovens use radiant energy to cook food.
And radio waves transfer information to our radios and televisions via radiant energy.
A moving charge (an electric current) is surrounded by a magnetic field. A
change in this magnetic field generates an electric field. This process is called
electromagnetic induction. Changing electric fields are always accompanied by a
changing magnetic field and vice versa. These changing fields allow a changing current
in a conductor or a moving charge to produce electromagnetic radiation, which is a
source of energy. The electromagnetic radiation moves outward from the source as
long as the energy that causes the charge to move is present. Figure 20.1 illustrates
waves of electromagnetic radiation.
Figure 20.1 Electromagnetic Radiation Wave
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The Electromagnetic Spectrum
While all electromagnetic waves travel at the same speed in a vacuum, they may
differ in wavelength and frequency. The electromagnetic spectrum can be divided into
regions according to wavelength or frequency. These regions are named radio waves,
microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma
rays, as illustrated in Figure 20.2.
Figure 20.2 The Electromagnetic Spectrum
Wavelength (m)
3 x 10
4
m
3m
3 x 10 – 4 m
3 x 10 – 8 m
Infrared
Ultraviolet
3 x 10 – 12 m
In
Radio waves
X – rays
Microwaves
10
4
10
6
Gamma rays
10
8
10
10
10
Visible light
12
10
14
10
16
10
18
10
20
Frequency (Hz)
The classifications of some regions of the spectrum are identified by the way that
the waves interact with matter. For example, because the typical human eye can see
over a certain range of wavelengths, we call that region visible light. Names of other
regions of the spectrum are historical. When X-rays were discovered, they were called
X-rays because it was not yet known that they were electromagnetic radiation. Next we
discuss properties of the various regions of the electromagnetic spectrum, starting with
the longest wavelengths and lowest frequencies.
Radio Waves
The longest wavelength region of the spectrum is radio waves. They have
wavelengths longer than a meter and frequencies lower than about 1 x 108 Hertz.
(Radio wave frequencies are often given in megahertz or kilohertz. A megahertz is
6
abbreviated MHz, and is equal to 1 x 10 Hz. A kilohertz is abbreviated kHz, and is
3
equal to 1 x 10 Hz.)
Microwaves
The next region is the microwave region of the spectrum. Microwaves have
wavelengths of a meter to a few millimeters, and frequencies from about 1 x 108 to 1 x
1011 Hz. You have probably used microwave ovens. Some garage door openers use
microwaves. You may also have seen microwave relay stations used by the telephone
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company for transmission of information over long distances. A small scale microwave
generator and receiver will be demonstrated in the classroom.
Infrared Radiation
The region of the spectrum with wavelengths from several millimeters down to
about 7 x 10– 7 meters (and frequencies from 1 x 1011 to 4.3 x 1014 Hz) is called the
infrared region. The fact that radiant energy is present in this region of the spectrum
can be illustrated by using a radiometer. We find that the radiometer vanes rotate when
exposed to infrared radiation. Another type of device for detecting radiation in the
infrared is the photoelectric infrared imaging device. The sniper scope, a particular
example of this type of device, will be demonstrated in class. Television remote controls
use radiation in this frequency range. The nerves of our skin are sensitive to some of
the infrared portion of the spectrum.
Visible Light
Visible light ranges in wavelength from 4 x 10– 7 meters (violet light) to 7 x 10–7
meters (red light). Our eyes do not respond to wavelengths outside this small portion of
the electromagnetic spectrum. Within this region, our eyes respond to different
wavelengths as different colors, and we see the combination of these colors as white
light. In class, we will use prisms and diffraction gratings to separate white light into the
colors of the visible spectrum.
Ultraviolet Radiation
Wavelengths of ultraviolet radiation extend from the short wavelength end of
the visible spectrum (4 x 10– 7 meters) to wavelengths as small as 1 x 10– 9 meters. The
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frequencies range from 7 x 10 Hz to about 3 x 10 Hz. Ultraviolet radiation can
induce fluorescence and can cause tanning in human skin.
X–rays
Even shorter wavelengths (down to about 1 x 10– 11 meters) are the X-ray
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region. Frequencies in this region extend from 3 x 10 Hz to about 3 x 10 Hz. X-rays
have a number of industrial and medical uses, which are associated with the ability of Xrays to penetrate matter. X-rays pass through flesh but are absorbed by bone; thus, Xray photographs can show bone structure and assist the medical profession in diagnosis.
Gamma Rays
Electromagnetic waves with wavelengths shorter than about 1 x 10–11 meters
and frequencies above 3 x 1019 Hz are called gamma rays. They may be produced by
nuclear reactions and will be discussed further in the period on nuclear energy.
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20.2 Nuclear Energy from Stars
Fission and Fusion Reactions as Sources of Energy
How can you extract energy both from fusing nuclei together and also from
breaking up nuclei? This is not a great puzzle – the same thing happens with atoms and
molecules in chemical reactions. Energy can be released when atoms or molecules
combine to form a molecule that is more tightly bound, such as when hydrogen and
oxygen combine to form water. But energy can also be released when a large, loosely
bound molecule breaks up: an example is the breakup of the explosive nitroglycerine.
The key is the relative binding energy of the reactants and the products. When
nitroglycerine breaks up, the products (N2O, O2, CO2, H2 O) are more tightly bound than
the unstable nitroglycerine molecule. The sum of the binding energies of the products is
greater than the binding energy of nitroglycerine, and energy is released in the breakup.
By contrast, the binding energy of water is greater than the sum of the binding energies
of H2 and O2. Therefore energy is released when one O2 and two H2 molecules
combine. This occurs in a fuel cell, for example, or when hydrogen burns.
In both of these chemical examples, it is necessary to supply (invest) some
activation energy to make the exothermic reactions happen. Nitroglycerine molecules
must be heated or subjected to shock or collision in order to break the weak chemical
bonds so that the atoms can rearrange themselves. Similarly, energy must be supplied
(by heating, for example) to break up H2 and O2 molecules into the H and O atoms that
recombine to form water. Once the exothermic chemical reactions get started, the
activation energy is supplied by the released energy. For example, the heat from
combining H and O atoms can break up more H2 and O2. The energetic breakup
products of one nitroglycerine molecule can bombard others, causing a chain reaction
chemical explosion.
Nuclear Fission
As described in Chapter 18, fission reactions occur when very heavy isotopes
release energy by splitting into smaller pieces. The first successful attempts to produce
energy from nuclear reactions used the process of fission and the fact that nuclei of
U-235 undergo a very small but significant number of decays through spontaneous
fission. In the fission of U-235 nuclei, excess free neutrons are produced. These
neutrons can be used to induce fission in other U-235 nuclei, increasing the number of
fissions taking place. Under controlled conditions, a chain reaction can occur, in which
enough neutrons are produced by U-235 fissions to continue the fission process until
there is no longer enough U-235 present for the process to continue. Controlled fission
is the basis of conventional nuclear power reactors.
Nuclear Fusion
Physicists have also attempted to produce energy using fusion reactions.
Nuclear fusion occurs when light isotopes release energy by combining, or fusing, into
heavier ones. The difficulty with building a fusion reactor is finding a way to confine the
nuclei long enough for them to fuse into larger, heavier nuclei. Confining nuclei is
difficult because of the very strong repulsive electric force between the positively
charged nuclei. The nuclei to be fused must have very high kinetic energies in order to
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overcome the repulsive electric force between the nuclei. But the higher the energy of
the confined particles, the harder it is to keep them confined. For many years, using a
machine called a tokamak, scientists tried unsuccessfully to use strong magnetic fields to
confine nuclei into a doughnut-shaped space to produce a fusion reaction. Only recently
has there been very limited success in this regard.
Fusion Reactions in Stars
While magnetic confinement of fusing particles has been very difficult to achieve,
there is another force that can confine particles to produce fusion – the force of gravity
acting to bind matter together in a star. As particles bind together under the
gravitational force, their binding energy is converted into kinetic energy of the particles.
As described in Chapter 5, the greater the average kinetic energy of particles, the higher
their temperature. When particles have sufficient kinetic energy to provide the required
activation energy, the matter in a star ignites and fusion begins.
Since gravity is a very weak force, a very large quantity of matter is needed to
begin nuclear fusion. If the amount of matter that coalesces into a sphere is not great
enough to produce the activation energy needed for fusion, the matter does not ignite
and become a star. In this case, a gaseous planet, such as Jupiter, forms instead of a
star. If Jupiter had only slightly more matter, it would have ignited into a second star in
our solar system.
Fusion processes in the Sun have provided energy for the Earth for billions of
years. The Sun is an average star, and the processes that take place in the Sun are
characteristic of many stars. However, stars with different masses than the Sun have
very different life histories. In fact, the fusion patterns of stars are quite different
depending on their size and age. The remainder of this chapter summarizes some of
the fusion processes in stars. In the next chapter, we will discuss how galaxies formed,
how stars formed within galaxies, and how stars similar to the Sun evolve over time.
The proton-proton fusion chain
Stars smaller than 1.2 solar masses (1.2 times the mass of our Sun) use a
hydrogen-burning proton-proton chain (PP chain) as their primary fusion process.
The following description of this chain applies to stars with central temperatures at or
below 15 million K, the central temperature of our Sun.
The first step involves the fusion of two hydrogen nuclei 1H (protons) into 2H
(deuterium). This requires that one proton change into a neutron, an antielectron and a
neutrino. Overcoming the electromagnetic repulsion between two hydrogen nuclei
requires a large amount of energy. At 15 million K, the mean proton energy is
E= 0.00129 MeV. Thus, the fraction of protons with the 1.4 MeV worth of energy
required to overcome coulomb repulsion is vanishingly small. Protons therefore must
quantum mechanically tunnel through the coulomb repulsion “barrier”. It is as if a car
climbing a mountain runs out of gas with too little energy to get it over the top, but
somehow the car just appears going down the other side. Cars are too massive for this
to happen, but it occasionally does occur for tiny subatomic particles.
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Even so, achieving a nuclear reaction is sufficiently rare that for any two protons
in the core of our Sun this reaction takes roughly 10 billion years to complete. We can
turn this around to estimate a lifetime of 10 billion years or so for our Sun, a lifetime
that is substantiated by solar models of much greater complexity. If fusion occurred
more rapidly, our Sun would have burned out long ago. However, the Sun has a lot of
protons, so reactions are going on all the time. The formula for making deuterium,
including energy released, is as follows:
1
H + 1H
2
H + e+ +  e
(+ 1.44 MeV)
As you already know, mass energy is given by the famous formula E=mc2. The
above reaction has equal mass plus motion plus radiation energies on each side of the
arrow. Such reactions are exothermic (release mass energy) when the total mass
energy on the initial (left-hand) side is larger than the total mass energy on the final
(right-hand) side.
After some time, deuterium (2H) will fuse with another hydrogen to produce
tritium (3He):
2
H + 1H
3
He + e
(+ 5.49 MeV)
After millions of years, two of the helium nuclei 3He produced will fuse together to make
the stable helium isotope 4He plus two hydrogen nuclei.
3
He +3He
4
He + 1H + 1H
(+ 12.86 MeV)
(Example 20.1)
The complete proton-proton chain involves the production of two deuterium
nuclei, two tritium nuclei and one helium nucleus. What is the net energy released by
these reactions?
2(1.44 MeV) + 2(5.49 MeV) + 12.86 MeV = 26.72 MeV
Of the 26.72 MeV produced by the PP chain, typically, half of one MeV is carried away
by two neutrinos that exit the Sun. Most of the energy remains and eventually will
contribute to the Sun’s luminosity.
How energy is released from stars
As shown in figure 20.3, stars such as the Sun can be divided into three regions
– a nuclear burning core, a convective layer and a radiative zone. The two outer layers
are named after their predominant methods of heat transfer, as shown in Figure 20.4.
Photons are released after a series of collisions within the star. If the number of
collisions for a layer becomes too large, we say that that the layer has become opaque
and convection becomes a more efficient method of heat transfer. Convection transfers
heat through hot gases that rise away from the center of the Sun, coupled with cooler
gases that fall.
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Figure 20.3 Nuclear burning, Radiative, and Convective Regions of a Star
radiative
zone
convective
zone
nuclear
burning
region
Radiation, as shown on the left of Figure 20.3, occurs when photons randomly scatter
through a layer. Convection, as shown on the right, occurs when hotter gases rise
toward the surface and colder gases drop inward.
Figure 20.4 Radiation and Convection in a Star
Layer
Layer
Photon random
motion
Convection
Large differences exist among the temperatures and pressures for the various
layers in a star. For example, the temperature in our Sun’s core is 15 million degrees
Kelvin. The pressure in the core is 250 billion times the pressure of the Earth
atmosphere. However, at its outer surface (the photosphere), the temperature and
pressure drop to 6000 K and 10-4 Earth atmospheres. Energy in the form of neutrinos
and gamma rays is generated solely in the core. Core neutrinos radiate out of the sun
in seconds, but gamma rays are quickly absorbed by surrounding material. In fact,
energy from gamma rays doesn’t arrive at the star’s surface for a considerable time,
roughly 20,000 years for our sun. The sunlight you are warmed by today started
outward from our Sun’s core when primitive man walked the Earth.
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20.3 Properties of Waves and the Transmission of Radiant Energy
One of the ways to transfer energy without the transfer of mass is to produce a
wave. A wave can be a pulse, as in the pulse of sound made by clapping your hands
together. Another example of a pulse is a tsunami, a tidal wave of energy that travels
many miles over an ocean. But many waves are generated by a cyclic vibration of some
given frequency. This type of wave is referred to as a sine wave. Sine waves are used
to describe many features of radiant energy. Electromagnetic wave refers to a model
that describes radiant energy in terms of sine waves. Figure 20.5 illustrates sine waves.
Figure 20.5 Sine Waves
Wave
Crest
Midpoint
Displacement
Distance
Wave
trough
A wave can be characterized by its wavelength, which is the distance between
two adjacent wave crests or two adjacent wave troughs, as shown in Figure 20.6. A
wave also has an amplitude, which is the maximum height or displacement of the crest
of the wave above or below its midpoint.
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Figure 20.6 Wavelength and Amplitude
Displacement
Wave Length
Wave Length
Amplitude
Distance
The time that it takes for a wave to go through one complete wave cycle is
called the period (P) of the wave. The period is the time that it takes for the wave to
go through one cycle of the wave’s crest and trough passing a particular point. For
example, if the period of a wave was 0.1 seconds, that wave would go though ten cycles
per second, or ten complete waves passing each second.
The crest of the longer wavelength of the two waves shown in Figure 20.3
travels past a given point less frequently during a specified period of time than the crest
of the shorter wavelength wave. Frequency (f) describes how often something repeats
a cycle. The longer wavelength wave has the lower frequency and the shorter
wavelength wave has the higher frequency, as shown in Figure 20.7. The horizontal
axis of Figure 20.4 is the time measured at any given point on the horizontal axis of
Figure 20.3.
Figure 20.7 Wave Frequency and Period
Displacement
Wave Period
Wave Period
Amplitude
Time
Lower Frequency Wave
Higher Frequency Wave
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The shorter the wave period P, the more cycles the wave completes in a given
amount of time, and the higher the wave frequency f. Thus, the wave period and
frequency are inversely related. This relationship can be expressed by Equation 20.1.
frequency = 1/ period
(Equation 20.1)
Since the period of a wave is expressed in seconds, the frequency of the wave is
expressed in 1/seconds, which is called a Hertz (Hz).
Wave Speed
The length of the wave L is the distance between two adjacent wave crests or
two adjacent wave troughs. In one period, a wave travels one wavelength, a distance
L. Combining the variables f and L gives the expression for the speed of a wave. As
described in Chapter 3, speed = distance/time.
In this case, distance is the wave
length L and the time is the wave period P. Substituting these variables into S = D/t
gives S = L/P. Since the period = 1/frequency, a final substitution for the period results
in S = f L, the equation for the speed of a wave.
where
s=fL
(Equation 20.2)
s = speed at which radiant energy travels (in meters/sec or feet/sec)
f = frequency (in cycles/sec, or Hertz)
L = wavelength (in meters or feet)
All electromagnetic radiation, regardless of its source, is characterized by a
frequency associated with the source and with the radiation. The speed s at which
radiant energy travels depends on the medium that it is passing through, but in a
vacuum it is about 3 x 108 meters per second, or 186,000 miles per second. This speed
is true for all frequencies of radiant energy. This constant speed, usually referred to as
the speed of light, is given the symbol c.
(Example 20.2)
a) A wave of electromagnetic radiation has a period of 2.5 x 10
Calculate the frequency of the wave in cycles/second (Hertz).
–15
seconds.
frequency = 1/period = 1/2.5 x 10–15 sec = 4.0 x 1014 cycles/sec
= 4.0 x 1014 Hz
b) Find the wavelength of this wave of electromagnetic radiation.
S = f L, or L = S = 3 x 108 m/s = 0.75 x 10 – 6 m = 7.5 x 10 – 7 m
f
4 x 1014 1/s
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Concept Check
20.1
a)
What is the frequency of electromagnetic radiation with a wavelength of 0.15
meters?
__________
b)
What is the speed of a wave with a frequency of 0.5 Hz and a wavelength of 0.6
meters? Is this a wave of electromagnetic radiation?
__________
Period 20 Summary
20.1: Vibrating electric charge produces electromagnetic radiation, or radiant energy.
This energy is associated with an electromagnetic field.
Radiant energy is produced when electric charge vibrates; it can be thought of as
a wave with a wavelength and frequency.
The electromagnetic spectrum can be divided into types of radiant energy based
on the wavelength or frequency of the radiation: radio waves, microwaves,
infrared radiation, visible light, ultraviolet light, X–rays, and gamma rays.
20.2 Energy can be released when large loosely bound nuclei break up is fission
reactions. Nuclear reactors use fission reactions.
Energy is also released when nuclei fuse to form a nucleus that is more tightly
bound. In fusion reactions, light isotopes release energy by combining
(or fusing) into heavier ones. Fusion reactions power stars.
In a star, particles are confined due to gravitational force. When the kinetic
energy of a spherical mass of particles is sufficient to provide the required
activation energy, nuclear fusion begins in the star’s core.
Stars smaller than 1.2 times the mass of the Sun use a hydrogen-burning
proton-proton chain as their primary fusion process. In this chain, two hydrogen
nuclei fuse to form a nucleus of deuterium. Deuterium fuses with another
hydrogen to form the isotope of helium called tritium. Two tritium fuse to form
a stable helium nucleus plus two hydrogen nuclei.
Energy is transferred from the star core to a radiative zone and then via
convection to the surface of the star.
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Period 20 Summary, Continued
20.3: Radiant energy is transferred from the Sun to the Earth in waves. A wave is
characterized by its wavelength (the distance between two adjacent wave crests
or two adjacent wave troughs), its frequency (how many times per second a
wave crest or trough passes a fixed point), and its amplitude (the maximum
height of the wave above or below its midpoint).
The period of a wave is the time it takes to complete one cycle.
The frequency of a wave is the inverse of its period: frequency = 1 / period
The speed of a wave = frequency x wavelength:
s =f L
Radiant energy of any frequency travels in a vacuum at 3 x 108 meters per
second, or 186,000 miles per second. This constant is known as the speed of
light and is given the symbol c.
Solutions to Chapter 20 Concept Check
20.1
s
3 x 108 m / s
a)
f 

 2.0 x 109 1 / s 
L
0.15 m
b)
s  f L
2.0 billion Hz
Waves of electromagnetic
 0.5 1 / s x 0.6 m  0.3 m / s
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radiation travel at a speed of 3 x 10 m/s. Since this wave’s speed is much
slower, it cannot be a wave of electromagnetic radiation.
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