PHYS 1303, Chap. 4, Homework, Prof. Kaim, DMC

No astronomical object that produces a continuous visible spectrum of light has ever been observed. However, there are many astronomical objects that produce emission or absorption spectra. Read the following descriptions of astronomical objects, and then sort the labeled images into the appropriate bins according to the type of spectrum each object produces. Emission nebula: a cloud of hot, interstellar gas glowing as a result of one or more nearby young stars that ionize the gas. Planetary nebula: a glowing cloud of hot, low-density gas that is ejected from a red-giant star. Sun: a glowing ball of extremely dense gas powered by nuclear fusion in its core, but surrounded by a low-density, cooler atmosphere. Atmosphere on Titan: a layer of cool, low-density gas confined close to the surface of Titan, one of Saturn's moons.

Emission spectrum: emission nebula planetary nebula Absorption spectrum: Sun atmosphere of Titan (Spectroscopy is an extremely valuable method of astronomical study. Astronomers can determine the composition, density, and temperature of celestial objects by interpreting the light that is either emitted or absorbed by the objects.)

How many times more energy has a 0.9 nm X-ray than a 22 MHz radio photon? Express your answer using two significant figures.

Ex−ray/Eradio= 1.5×1010 Ex (f) = c/wavelength= 3x10^8 m/s / 0.9 mm= 3.3x10^17 Er = h x f= 6.626x10^-34 x 2.2x10^7= Ex/Er= 3.3x10^17 / 2.2x10^7= 1.5x10^10 Hz

An atom that has been ionized

has more protons than electrons.

What is the energy (in electron volts) of a 180 GHz (1 gigahertz = 10^9 Hz) microwave photon?

(Planck's constant x Frequency)/eV conversion(6.626x10^-34)x(180x10^9)=1.19268x10^-22 1.19268x10^-22/1.602x10^-19=0.000744 or 7.4x10^-4

Which of the following blackbody curves indicates the coldest object?

(This object has a blackbody spectrum that peaks the furthest towards the red (long-wavelength, or low-frequency) part of the spectrum. Now you should be able to compare the relative temperatures of objects just by looking at the spectrum of light they emit.)

What is the wavelength of an 0.11-eV infrared photon? Express your answer to two significant figures and include the appropriate units.

0.11 x 1.6x10^-19= 1.76x10^-20 1.9878x10^-25/1.76x10^-20 =0.000011 1.1x10^5 (My calculations) Their Answer: 1.1x10^4 nm

Relate the basic components of a simple spectroscope to their functions. 1. This turns the light into a narrow beam. 2. This spreads the beam of light out into its various wavelengths or colors. 3. This allows the spectrum to be observed and photographed.

1. A slit 2. A prism 3. An eyepiece or screen

Relate the additional components in spectrographs to their functions. 1. This captures the radiation. 2. This spreads the radiation out into a spectrum. 3. This records the result.

1. A telescope 2. A dispersing device 3. A detector

Of the three types of subatomic particles, only neutrons do not carry charge. Protons carry a positive charge, and electrons carry a negative charge. Protons and neutrons are bound in the nucleus, while electrons orbit the nucleus. When the number of each type of subatomic particle in an atom changes, the characteristics defining the atom also change. Match the appropriate phrases with the type of subatomic particle that completes the defining characteristic. 1. The number of __________________ identifies whether an atom carries a charge as an ion or is neutral. 2. The number of _____________ identifies the type of element.

1. electrons 2. protons (The number of each type of subatomic particle plays an important role in the characteristics of the atom. The general element classification (hydrogen, carbon, oxygen, etc.) is governed by the number of protons in the nucleus. If the number of protons changes in an atom, so does the type of element. The electrons are the only type of subatomic particle not in the nucleus. They orbit around the nucleus, bound by the electromagnetic force. When electrons are lost or gained by a neutral atom, the charge balance shifts, resulting in the atom becoming an ion. Ions can be either positive when electrons are lost or negative when electrons are gained.)

Suppose an electron in some atom absorbs energy and transitions from level 1 up to level 4. Which of the following is a true statement regarding the electron transitions back down to level 1?

4 to 2, followed by 2 to 1, is possible. Downward transitions can be any number of levels. (Downward transitions can indeed be any number of levels at a time. Together with the rule that each downward transition produces a photon of a particular color, you can see why each element has a unique the emission spectrum.)

How many different photons (i.e., photons of different frequencies) can be emitted as a hydrogen atom in the third excited state falls back, directly or indirectly, to the ground state? What are the wavelengths of those photons? Express your answer numerically. If there is more than one answer, enter your answers separated by commas in order of increasing wavelength.

6; λ= 97.3,103,122,486,656,1880 nm (4-3, 3-1, 2-1, 4-2, 3-2, 4-1) 4 - 3, 4 - 2, 4 - 1, 3 - 2, 3 - 1, 2 - 1, (where n=1 @ ground, n=2 @ 1st station, n=3 at 3rd station, etc.) Ground E1= 13.6(1-1/1^2) = 0 1st station E2= 13.6(1-1/2^2) = 10.2 2nd station E3= 13.6(1-1/3^2) = 12.1 (12.0889) 3rd station E4= 13.6(1-1/4^2 = 12.8 (12.75) 4th station E5= 13.6(1-1/5^2) = 13.1 (13.056) 5th station E6= 13.6(1-1/6^2) = 13.2 4 - 3 91.18nm/(1/1^2-1/4^2) = 1880 (1875.7) 4 - 2 91.18nm/(1/2^2-1/4^2) = 486 (486.293) 4 - 1 91.18nm/(1/3^2-1/4^2) = 97.3 (97.25) 3 - 2 91.18nm/(1/2^2-1/3^2) = 656 (656.496) 3 - 1 91.18nm/(1/1^2-1/3^2) = 103 (102.578) 2 - 1 91.18nm/(1/1^2-1/2^2) = 122 (121.573)

What is the wavelength of a 9000-eV (9.0-keV) X-ray? Express your answer to two significant figures and include the appropriate units.

9.0KeV=9000eV 9000 x 1.6x10^-19=1.44x10^-15 1.9878x10^-15/1.44x10^-15= 1.38042x10^-10 or .14 nm

A continuous spectrum shows the whole continuum of colors without interruption. Select the appropriate physical description of a source that would produce a continuous spectrum. Select the correct statement.

A continuous spectrum is produced by a luminous solid or liquid, or a sufficiently dense gas. (A hot, high-density light source produces a continuous spectrum.)

What the additional components in spectrographs used by astronomers for modern observations? Check all that apply.

A dispersing device A detector A telescope

What are the basic components of a simple spectroscope? Check all that apply.

A slit, a prism, and an eyepiece or screen

An absorption spectrum looks like a continuous spectrum that has narrow black lines corresponding to absorbed wavelengths of light. Select the appropriate physical description of a source that would produce an absorption spectrum. Select the correct statement.

An absorption spectrum is produced when a hot, dense source shines through a cool, thin gas. (An absorption spectrum is produced by light from a hot, high-density source passing through a cool, low-density medium.)

An emission spectrum is primarily black and has only certain narrow lines of color, corresponding to emitted wavelengths of light. Select the appropriate physical description of a source that would produce an emission spectrum. Select the correct statement.

An emission spectrum is produced by a low-density, hot gas. (An emission spectrum is produced by a hot, low-density source.)

The diagrams below show the same set of energy levels as in Parts A and B, but with a different set of electron transitions (notice that the arrows are now different). Assuming that these electron transitions were caused by the absorption of a photon, rank the atoms based on the energy of the absorbed photon, from highest to lowest.

As your answer correctly indicates, the atom in which the electron leaves (the atom is ionized) corresponds with the highest-energy photon, and the atom with the shortest arrow indicates the case where the absorbed photon had the lowest energy.

The circles in the diagrams below represent energy levels in an atom, and the arrows show electron (blue dot) transitions from one energy level to another. (The spacing between circles represents differences in energy: A larger spacing means a greater difference in energy.) Assuming that the transitions occur as photons are emitted, rank the atoms based on the photon energy, from highest to lowest.

As your answer correctly shows, the emitted photon must have exactly the same amount of energy that the electron loses in moving from the higher to the lower energy level. Therefore the ranking of the photon energies must be in the same order as the amounts of energy lost by the electrons, and longer arrows mean greater changes in energy.

There are three general types of spectra: continuous, emission, and absorption. Each is characterized by a different distribution of the wavelengths (i.e., colors) of radiation. Sort the images of the three types of spectra into the appropriate bins.

Continuous: 1 solid rainbow Emission: 2 mostly black w/some color Absorption: 2 rainbows w/black lines (Each type of spectrum is unique in the way the wavelengths (colors) of light are distributed. The continuous spectrum shows a continuum of all the colors, whereas the emission spectra show only specific lines of emitted color. The absorption spectra show only small black ranges where specific colors have been absorbed away.)

What is the energy (in electron volts - see More -Precisely 4-1 in the textbook) of a 300 nm ultra-violet photon?

E= h x c/Ephoton x λ 6.626x10^-34 J/s x 3x10^8 m/s / 4.13x10^-15 x 1.6x10^-19 =0.000001/3.0 x 10^7 =4.13281E^-14 or E = 4.1 eV

What is the energy (in electron volts - see More -Precisely 4-1 in the textbook) of a 470 nm blue photon?

E= h x c/Ephoton x λ 6.626x10^-34 J/s x 3x10^8 m/s / 4.13x10^-15 x 1.6x10^-19 =0.000001/4.7 x 10^7 =2.63796E^-14 or E = 2.6 eV

In the classical view of the atom, Bohr pictured electrons orbiting the positively charged nucleus similar to how the planets orbit the Sun. While this picture was not entirely correct, it provides a good framework in which to make calculations about the energies of electrons. Different from the predictions of Newtonian mechanics, which allows any energy to be possible, Bohr described the electron orbits (now called orbitals) as having specific energies. Rank the following electron energy states according to their electron energies. Rank from highest to lowest energies.

Left to right: third excited state second excited state first excited state ground state

The Bohr model accounted for most of the general characteristics of the atom. However, the modern model based on quantum mechanics explains that, although the energy of each orbital is fixed, the orbital radius is actually an average distance. The result is a "cloud" where the electron would most probably be located. When electrons are excited to different energy levels, the average radii from the nucleus also changes. Rank the following electron energy states according to the average distance of the electron from the nucleus.

Left to right: third excited state second excited state first excited state ground state (Excited states refer to the energy state of an electron. The higher the state, the higher the energy and the greater the distance of the electron from the nucleus. Due to the attractive force between the negatively charged electron and the positively charged nucleus, the electron requires greater energies to overcome this attraction and achieve orbits at greater distances.)

Suppose a particular spectral line has a wavelength of 500 nm in the lab. If you look at the spectrum of star A, you see this line at 480 nm. Star B exhibits this line at 510 nm, and the line is measured to be at 530 nm in star C. Which of the following statements is true?

Star C is moving away from us faster than star B, star A is moving towards us. (Since objects moving away are redshifted, and the amount of redshift tells us the speed, you can see how to tell the speed and direction of an object just by looking at its spectrum.)

The atom consists of three types of subatomic particles: protons, neutrons, and electrons. The electron is by far the lightest of the three, while the much heavier proton and neutron have masses very similar to each other. Two of the types of particles carry an electrical charge, while the third is neutral. Label the subatomic particles and appropriate charges by their relative locations.

The atom consists of three types of subatomic particles: protons, neutrons, and electrons. The electron is by far the lightest of the three, while the much heavier proton and neutron have masses very similar to each other. Two of the types of particles carry an electrical charge, while the third is neutral. Label the subatomic particles and appropriate charges by their relative locations. Identify the subatomic particles by dragging the appropriate labels to their respective targets.

Essay: List three properties of a star that can be determined from observations of its spectrum.

Three properties of a star that can be determined from spectral observation are temperature, composition, and motion (or the state). When measuring temperature, astronomers use scientific formulas to gather information on the emitted or absorbed photons. They take the information predicted by the formulas and compare them to the observed energy levels to creating a spectrum. Astronomers are able to measure the temperature and determine the composition by the strength of a spectral line. By using a pattern formed by spectral lines, astronomers can gauge the star's chemical composition by matching the lines that are formed with known atoms, ions, and molecules. The temperature of the gas plays a large role in determining how many atoms are able to go through transitions. The high and low temperatures effect whether an atom is in a calm state (associated with cooler temperatures) or excited state (hotter temperatures and fully ionized atoms). As an atom goes through these changes, a line will appear bright when it's being absorbed and dark when it's being emitted. The state or motion of the planet is calculated using the Doppler Effect. If an atom is moving away from Earth, it releases a proton and produces a redshift (a change in the visual color that is transmitted. If an atom is moving towards Earth, it will produce a blueshift. Once again, temperature plays a role - "the hotter the gas, the larger the spread of Doppler motions," which creates a wider line. When the width of the line is measured, the estimated average speed of particles and the temperature of the gas that was produced can be determined. Through observation, calculation, spectral measurements, and the Doppler Effect, astronomers have the ability to determine many things about a star including temperature, composition, and motion.

The diagrams below are the same as those from question 6. This time, rank the atoms based on the wavelength of the photon emitted as the electrons change energy levels, from longest to shortest.

You already know the ranking of the photons by energy. Because higher energy means shorter wavelength, you have correctly found that the ranking for this question is the reverse.

The visible spectrum of sunlight reflected from Saturn's cold moon Titan would be expected to be

absorption spectrum.

It is possible that an abundant element in a star does not produce strong lines, if the electrons of most of the atoms of that element ______________ a condition to absorb light of the corresponding wavelength.

are not in

There is a maximum energy that the electron can have and still be part of the atom. Once the electron acquires ________________ that maximum energy, it is no longer bound to the nucleus, and the atom is said to be _______________; an atom missing one or more of its electrons is called an ____________.

more than, ionized, ion

Figure 4.3 in the textbook ("Elemental Emission") shows the emission spectrum of neon gas. If the temperature of the gas was increased, we would observe

no significant change.

Compared with a star having many blue absorption lines, a star with many red and blue absorption lines must be

of different composition than that of the other star.

If the star is very hot, then the electrons of most the hydrogen atoms may have too much energy, and may have left the atoms entirely. Such stars are mostly hydrogen, but the ionized hydrogen has no electrons to absorb light, ___________________________________ of hydrogen is capable of absorbing, and so the lines of hydrogen are _________.

only a small part, weak

For example, the Hα absorption line of hydrogen results from electrons jumping from the second to the third atomic orbital. If a star's outer atmosphere is rather cool, relatively few atoms have electrons that have absorbed enough energy to jump to the second excited state or higher; most are in the ground state. Hence, the second to third level transition occurs _____________, and the wavelength of light corresponding to the Hα absorption line is ___________ absorbed. A __________ spectral line results.

rarely, rarely, weak

Compared with a spectrum from a ground-based observation, the spectrum of a star observed from above Earth's atmosphere would show

slightly fewer absorption lines.

List all the spectral lines of hydrogen that lie in the visible range (taken to run from 400 to 700 nm in wavelength). Express your answer numerically. If there is more than one answer, enter your answers separated by commas in order of increasing wavelength.

λ= 410,434,486,656 nm 6 - 2 91.18nm/(1/2^2-1/6^2) = 410 (410.31) 5 - 2 91.18nm/(1/2^2-1/5^2) = 434 (434.19) 4 - 2 91.18nm/(1/2^2-1/4^2) = 486 (486.293) 3 - 2 91.18nm/(1/2^2-1/3^2) = 656 (656.496)

What is the wavelength of a 1.8-eV red photon? Express your answer to two significant figures and include the appropriate units.

λ= 690 nm wavelength x c / Ephoton= 6.626x10^-34 x 3x10^8 / 1.6x10^-19 x 1.8= 1.9785x10^-25 / 2.88x10^19= 6.90104x10^7 or 690nm

What is the energy (in electron volts) of a 180 GHz (1 gigahertz = 10^9 Hz) microwave photon? Express your answer using two significant figures.

λ= 7.4×10^−4 eV λ= h x f/Ephoton λ= 6.626x10^-34 x 180x10^9= 1.19268x10^-22/1.602x10^-9=0.000745 λ= 7.4x10^-4 eV