Astronomy: Chapter 4

What is a blackbody? What does it mean to say that a star appears almost like a blackbody? If stars appear to be like blackbodies, why are they not black?

A blackbody is a hypothetical object that completely absorbs all the electromagnetic radiation that strikes it. A star is described as almost like a blackbody when the continuous part of that star's spectrum follows the shape of a blackbody spectrum. Stars are not black because they are hot and emit large amounts of electromagnetic radiation. They would be black only if they gave off no electromagnetic radiation.

Continuous Spectrum (Continuum)

A complete rainbow of colors without any spectral lines. This is a blackbody spectrum. The light emitted by a hot iron rod & by an incandescent lightbulb are examples of continuous spectra that are bright enough for us to see.

Emission Line Spectrum

A series of bright spectral lines against a dark background. The light emitted by neon lights & by low-pressure sodium vapor lights are examples of emission line spectra. The neon has bright-red emission lines, while the low pressure sodium has bright-yellow lines.

Absorption Line Spectrum

A series of dark spectral lines among the colors of the rainbow. Sunlight & the light from other stars pass through several cooler gases on their way to us. Hence, light from stars produce absorption line spectra.

Using Wien's law & the Stefan-Boltzmann law, state the color & intensity changes that are observed as the temperature of a hot, glowing object increases.

According to Wien's law, the peak of the emission spectrum shifts to shorter wavelengths as the temperature increases. Which means that the color changes from red to yellow to green to violet to blue as the object gets hotter. The Stefan-Boltzmann Law says that the energy radiated per unit area increases as the 4th power of the temperature meaning as the temperature goes up, the object gets brighter and brighter, emitting more energy.

Redshift

All of the colors in the spectrum of a receding source, regardless of its distance, are shifted toward the longer-wavelength (red) end of the spectrum, producing a redshift.

Blueshift

All the colors in the spectrum of an approaching source, such as a star, are shifted toward the short-wavelength (blue) end of the spectrum, regardless of its distance.

What is an element? List the names of 5 different elements, & briefly explain what makes them different from each other.

An element is a fundamental substance that can't be broken down into more basic units while still retaining its properties. 1. Hydrogen 2. Helium 3. Carbon 4. Gold 5. Iron What makes them different from each other is the amount of protons & electrons they contain.

Stefan-Boltzman Law

An object emits energy per unit area at a rate proportional to the 4th power of its temperature. As a device becomes hotter, it gets brighter, meaning it emits more energy. Stefan's result says that if the temperature of an object doubles, the energy emitted each second from each piece of the object's surface increases by 2⁴, or 16 times. If you triple the temperature, the rate at which energy is emitted increases by a factor of 3⁴, or 81 times. Stefan's results were put on a firm theoretical foundation by Ludwig Boltzmann in 1885. In their honor, the intensity-temperature relationship for blackbodies is named the Stefan-Boltzmann law.

The spectrum of which of the following objects will show a blueshift?

An object moving directly toward Earth.

Molecules

Atoms can share electrons &, by doing so, become bound together. Such groups of atoms are called molecules. Like atoms, molecules have unique spectra. They are the essential building blocks of all complex structures, including life.

Luminosity

Because F is the energy emitted per second from each square meter of an object, multiplying F by the surface area, 4πr², where r is the object's radius, yields the total energy emitted by a spherical object each second. This quantity, denoted L, is called luminosity: L = F × 4πr² = σT⁴4πr². Luminosity is the total energy emitted per second by an entire object.

Spectroscope

Bunsen & Kirchhoff collaborated in designing & constructing the 1st spectroscope. This device consists of a narrow slit, a prism, & several lenses that straighten the light rays & magnify the spectrum so that it can be closely examined.

Blackbody Curves

By measuring the intensity of radiation emitted by a blackbody at several wavelengths, it's possible to plot a curve of its emissions over all wavelengths. Ideal blackbodies have smooth blackbody curves, whereas objects that approximate blackbodies, such as the Sun, have more jagged curves whose variations from the ideal blackbody are caused by other physics.

Kirchhoff's Laws

By the early 1860s, Kirchhoff had discovered the condition under which different types of spectra are observed. His description is summarized as Kirchhoff's Laws: Law 1: Solid, liquid, or gas produces a continuous spectrum (continuum), a complete rainbow of colors without any spectral lines. This is a blackbody spectrum. Law 2: Rarefied (opposite of dense) gas produces an emission line spectrum-a series of bright spectral lines against a dark background. Law 3: The Light from an object with a continuous spectrum that passes through a cool gas produces an absorption line spectrum-a series of dark spectral lines among the colors of the rainbow.

Spectrograph

Device for photographing a spectrum. This instrument, in its numerous variations, is the astronomer's most important tool. In its earliest form, it was attached directly to a telescope. It consisted of a slit, 2 lenses, & a prism arranged to focus the spectrum of an object on film. Although conceptually straightforward, this early type had severe drawbacks. A prism doesn't spread colors evenly: The blue & violet portions of the spectrum are spread out more than the red portion. In addition, because the blue & violet wavelengths must pass through more glass than the red wavelengths, light's absorbed unevenly across the spectrum. Practical spectrographs used in research today separate light from objects in space into the colors of the rainbow using diffraction grating.

Isotope

Each different combination of protons & neutrons. In contrast to each atom of a given element always having the same number of protons in their nuclei, the nuclei of most elements can have different numbers of neutrons. For example, hydrogen, with 1 proton, can have 0, 1, or 2 neutrons; oxygen, with 8 protons, can have 8, 9, or 10 neutrons. There are 3 isotopes of hydrogen & 3 isotopes of oxygen. Hydrogen with no neutrons is the most common hydrogen isotope, while oxygen with 8 neutrons is the most abundant isotope of oxygen. Some are stable, meaning that the number of protons & neutrons in their nuclei do not change. However, many elements have isotopes that are unstable & come apart spontaneously. These isotopes are radioactive. For example, carbon with 6 neutrons, C ("Carbon 12"), is stable, while carbon with 8 neutrons, C ("Carbon 14"), is unstable. C ("Carbon 14") decays into nitrogen with 7 neutrons, N.

Explain how the spectrum of hydrogen is related to the structure of the hydrogen atom.

Electrons have only certain allowed orbits around their nuclei. The allowed orbits, which are associated with unique energy levels, are different in all different types of atoms. The wavelengths of any atom's spectral lines are determined by the differences in the energies of the orbits between which its electrons transfer. The higher the energy difference, the shorter the wavelength of the photon that is emitted or absorbed. When electrons descend in orbit, they emit photons, creating emission spectra. When they go to higher orbits, they absorb photons, creating absorption spectra. Since all elements have allowed orbits with different energy levels, the emission and absorption spectra of each element, such as hydrogen, has a unique set of wavelengths.

Absorption Line

Fine dark line in the solar spectrum where light of these colors has been absorbed by gases between the sun's emitting surface & the viewer from Earth. Fraunhofer counted more than 600 such lines, & today physicists have detected more than 30,000 of them.

Elements

Fundamental substance that can't be broken down into 2 or more basic units while still retaining its properties. By the mid-1800s, chemists had already identified such familiar elements as hydrogen, oxygen, carbon, iron, gold, & silver. Spectral analysis promptly led to the discovery of additional elements, many of which are quite rare.

Spectral Analysis

Identification of chemical substances by their spectral lines. It promptly led to the discovery of additional elements, many of which are quite rare.

Of the following photons, which has the lowest energy?

Infrared

Weak Nuclear Force

Many scientists find it fascinating that all of the interactions between matter and energy in nature occur as a result of just 4 forces, the above 3 + the weak nuclear force. It is involved in some radioactive decays, such as when a neutron transforms into a proton.

Ground State

Normally, the electron is in the lowest-energy allowed orbit or energy level, commonly called the ground state; this is labeled n = 1. Each allowed orbit with successively higher energy is labeled n = 2, n = 3, n = 4, & so on.

Atomic Number

Number of protons in an atom's nucleus that determines the element of that atom. All hydrogen nuclei have 1 proton, all helium nuclei have 2, all carbon nuclei have 6 protons, and so forth. There are 92 different types of elements that form naturally. Uranium is the most massive, with 92 protons. The fact that neutrons can transform into neutrons by absorbing an electron is vital for the formation of elements with more than 26 elements.

Which is hotter, a "red-hot" or a "blue-hot" object?

Of all objects that glow visibly from heat generated or energy stored inside them, those that glow red are the coolest. So, a "blue-hot" object is hotter.

Wein's Law

Often called Wien's displacement law, is the mathematical relationship between the location of the peak for each curve & that blackbody's temperature. It proves useful in determining the surface temperature of a star. It says that to find that temperature, all we need to determine is the peak wavelength of its electromagnetic radiation-we don't need to know the star's size, distance, or any other physical property. The peak wavelength of radiation emitted by a blackbody is inversely proportional to its temperature. The peak moves down as temperature rises. As temperature goes down, the peak goes up.

Neutron

Particle in atomic nuclei with protons but without an electrical charge.

Proton

Particle in the atomic nuclei. All protons have the exact same positive charge & they attract electrons & it is this attraction that keeps electrons in orbit around nuclei.

Emission Lines

Pattern of bright spectral lines, against a dark background.

Diffraction Grating

Piece of glass or plastic on which thousands of closely spaced parallel grooves are cut or etched. Some of the finest have more than 10,000 grooves per centimeter. The spacing of the grooves must be very regular. Light waves are diffracted by the grooves in the diffraction grating, just as light or water waves are diffracted when passing through slits. Some have the light pass through them, while others have the light reflect off their surfaces.

Ionization

Process of creating an ion. Ions are denoted by the atomic symbol followed by a Roman numeral that's 1 greater than the number of missing electrons. Positively ionized hydrogen (missing its 1 electron) is denoted H II, while positively ionized iron with 7 electrons missing is denoted Fe VIII.

Quantum Mechanicsi

Protons, neutrons, & electrons are not tiny solid bodies. Rather, like photons, they both have wave & particle properties. The science that accurately describes their complex behavior is called quantum mechanics. It explains that electrons in atoms can exist in only certain allowed orbits around their nuclei, except when they are making a transition from 1 allowed orbit to another.

What color will an interstellar gas cloud composed of hydrogen glow, & why?

Red, because it will absorb the energy of close by stars & the energy is re-emitted by the nebula as red.

Planck's Law

Relationship between intensity of electromagnetic radiation at every wavelength emitted by a given blackbody & its temperature. Planck's law gives the shape of the curves. A cool object emits primarily long-wavelength photons that carry little energy, while a hot object emits mostly short wavelength photons that carry much more energy.

Proper Motion

Since astronomers can't measure the transverse velocity directly, they measure the angle that the body moves along the more distant stars on the celestial sphere, which appear to move much less rapidly than do stars that are closer to us. Often a matter of arcseconds per year or arcseconds per century. It doesn't affect the perceived wavelength of an object observed here on Earth & so proper motion can't be determined by Doppler shift.

Explain why the Doppler shift tells us only about the motion directly along the line of sight between a light source & an observer, but not about motion across the celestial sphere.

Since motion is perpendicular to the line of sight, it won't change the wavelength (compression or lengthening). This is because there is no component in the direction it is going.

Atom

Smallest particle of a chemical element that still has the properties of that element. At the time of Kirchoff's discoveries, scientists knew that all matter is composed of atoms, but they did not know how atoms were structured. Furthermore, scientists saw that atoms of a gas somehow extract light of specific wavelengths from continuum spectra that pass through gas, leaving dark absorption lines, & they perceived that the atoms then radiate light of precisely the same wavelengths-the bright emission lines.

Transverse Velocity

Speed in KM per hour perpendicular to the radial velocity, which does not affect the star's spectrum.

Radial Velocity

Speed of an object toward or away from us is called its radial velocity because the motion is along our line of sight, or put another way, along the "radius" drawn from Earth to the object. Measured in KM per hour. This creates a Doppler shift in the star's spectrum.

Blackbody

Stars, molten rock, & iron bars, are approximations of an important class of objects that scientists call blackbodies. An ideal blackbody absorbs all of the electromagnetic radiation that strikes it. This incoming radiation heats it up, which then reemits the energy it has absorbed, but with different intensities at each wavelength than it received. Furthermore, the pattern of radiation emitted by blackbodies is independent of their chemical compositions. By measuring the intensity of radiation emitted by a blackbody at several wavelengths, it is possible to plot a curve of its emissions over all wavelengths.

Electron

Subatomic particle in an atom that has a negative charge. Newton's 2nd law explains that electrons move much more than the nuclei they orbit because the electrons have only 1/2000 the mass of a proton or neutron. The number of electrons that orbit an atom is normally equal to the number of protons in its nucleus, thus making the atom electrically neutral.

What is the Stefan-Boltzmann Law? How do astronomers use it?

The Stefan-Boltzmann law deals with blackbody radiation. It states that the total energy radiated per unit surface area of a blackbody in unit time is directly proportional to the 4th power of the blackbody's thermodynamic temperature. It's primary importance that it is one way for scientists to measure the temperature of stars based on a star's luminosity. It also provides an easy way for us to estimate the radius of a star too.

What color does the Sun emit most brightly?

The Sun emits all wavelengths of electromagnetic radiation. The colors it emits most intensely are in the blue-green part of the spectrum. Because the human eye is less sensitive to blue-green than to yellow, & because Earth's atmosphere scatters blue-green wavelengths more readily than longer wavelengths, we normally see the Sun as yellow.

Doppler Shift

The amount of Doppler shift varies directly with approaching or receding speed: When the speeds are small compared to the speed of light, an object that approaches twice as fast as another has all of its colors (or wavelengths) blueshifted twice as much as does the slower-moving object. An object moving away twice as fast as another object has its colors redshifted twice as much as the slower-moving object. Doppler shift applies to spectral lines as well.

Periodic Table

The chemical elements are most conveniently displayed in the form of a periodic table. In addition to the 92 naturally occurring elements, 26 more have been produced artificially. All of the human elements are heavier than uranium (U), & all are highly radioactive, meaning that they spontaneously decay into lighter elements shortly after being created in the lab.

Why do different elements have different patterns of lines in their spectra?

The electrons occupy different energy levels in the atom. What we see in the spectral lines is what frequencies of light are being absorbed by the elements that are reflecting or producing the light.

Electromagnetic Force

The interaction between charged particles, the 2nd of 4 fundamental forces in nature. Particles with the same type of charge, such as a pair of electrons, repel each other. For atoms that have more than 1 portion in their nuclei (& many do), the protons are pushing away from each other.

Radioactive

The internal structure of an atoms 1st came into focus in 1908 when New Zealand native & 1908 Nobel laureate Ernest Rutherford & his colleagues at the University of Manchester in England were investigating radioactivity. They were expanding on work done earlier by Polish physicist (& double Nobel laureate, 1903 & 1911) Marie Curie (1867-1934), among others. Over time, a radioactive element naturally & spontaneously transforms into another element by emitting particles. Certain radioactive elements, such as uranium & radium, were known to emit such particles with considerable speed. It seemed plausible that a beam of these high-speed particles would penetrate a thin sheet of gold. Rutherford & his associates found that almost all of the particles did pass through the gold sheet with little or no deflection.

What is the Doppler shift, & why is it important to astronomers?

The motion of an object toward or away from an observer causes the observer to see all of the colors from the object blueshifted or redshifted, respectively. This effect is generically called a Doppler shift. It is important to astronomers because you can approximate how far away a star is by measuring the redshift or blueshift of the star's light that reaches Earth.

Strong Nuclear Force

These nuclei must experience an attractive force stronger than the repulsion of protons to keep them glued together. The electrically neutral neutrons in the nucleus help provide that attractive force.

Transition (of an electron)

These orbital conditions are completely unlike planets, which can exist at any distance (in any orbit) around the Sun. Each allowed electron orbit has a well-defined energy associated with it, & every different type of atom & molecule has a unique set of allowed orbits. These orbits & the transitions between them are the key to understanding the spectra.

How are the 3 isotopes of hydrogen different from each other?

They have the same amount of protons & electrons but different amount of neutrons. Which means that they also have a different atomic mass. Hydrogen 3 is also more reactive.

Energy Flux

Total energy emitted from each square meter of an object's surface each second. In this context, flux means "rate of flow." The energy flux is related to the temperature, T, by the equation F = σT ⁴ where σ (lowercase Greek sigma) is called the Stefan-Boltzmann constant. It has a value of σ = 5.67 × 10^-8J/(m²×K⁴×s) with J being the energy unit joules, m the unit meters, k the unit kelvins, & s the unit seconds.

A blackbody glowing with which of the following colors is hottest?

Violet

How can we determine the age of space debris found on Earth?

We measure how much the long-lived radioactive elements, such as 238U, have decay in the object. Carbon dating is only reliable for organic materials that formed within the past 100,000 years. It can't be used for determining the age of rocks & minerals on Earth or from space. These substances were formed more than 4.5 billion years ago. Radioactive carbon in them has long since decayed to stable isotopes.

Ion

When an atom contains a different number of electrons than protons. Negative ions also exist, in which nuclei have more electrons orbiting than they have protons.

Excited State

When an electron is in an orbit with more energy than the lowest energy state available to it. Electrons change orbits by absorbing or emitting photons. However, orbiting electrons cannot absorb just any photon that they encounter. These electrons can absorb only photons with energies exactly enough to boost them up to a higher-energy allowed orbit. That is, the photons that are absorbed are those with energies = to the difference between the energies of 2 allowed orbits. All photons that don't satisfy this condition pass straight through the atom. If the electron starts in its ground state, then it must get exactly the energy necessary to move it to an excited state. If it's already in an excited state, then by absorbing a photon, it must transition to a higher-energy excited state. Electrons in this state are unstable. They lose energy by bumping into other particles & suddenly having either too much or too little energy than is necessary to be in that state.

What is Wien's Law? How could you use it to determine the surface of a star's surface?

Wien's Law is the mathematical relationship between the dominant wavelength & the temperature of a blackbody. You can use it to determine the temperature of a star's surface by finding the peak wavelength of its' electromagnetic radiation because it is inversely proportional to its temperature.

Nucleus (of an atom)

Within a few decades, the structure of atoms became evident. That dense "something" is now called the nucleus of an atom, & it consists of particles called protons & neutrons. Surrounding the nucleus, 1 or more electrons normally orbit.