| What is the difference between luminosity and apparent magnitude? Solution: Luminosity is the actual amount of electromagnetic energy (i.e. the total energy of photons of all wavelengths) emitted by the star, and it does not depend on where the star is located. Apparent magnitude is how bright the star looks like to us on Earth, so two stars with the same luminosity but at different distances would have different apparent magnitude. Star A has apparent magnitude 5.5. Star B has apparent magnitude 8.5. Which star is brighter? Solution: Star A is brighter, since lower magnitude means brighter. Star A has apparent magnitude -2.6. Star B has apparent magnitude -6.1. Which star is brighter? Solution: Star B is brighter. In this case, note that the numbers are negative, and -6.1 is actually lower than -2.6. Star A has apparent magnitude -7.2. Star B has apparent magnitude 1.5. Which star is brighter? Solution: Star A is brighter. A negative number is always lower than a positive one. A star is located 20 ly away from Earth. How bright will the same star look to aliens living on a planet 100 ly away from the star? Solution: Brightness decreases with the square of the distance. The aliens are 5 times farther away from the star than we are, so they will see the star 52 = 25 times less bright. Vega has an apparent magnitude of +0.03. Under what conditions is it visible? Solution: According to the slides in the lecture, magnitude under -2.5 means "visible during the day when the Sun is very low in the sky" and magnitude under +3.5 means "visible to the naked eye at night from an urban neighborhood". Vega is between -2.5 and +3.5, so it is not visible during the day, but it is visible to the naked eye at night. What is the difference between apparent and absolute magnitude? Solution: Apparent magnitude represents the brightness of the star as seen from Earth, while absolute magnitude represents the actual brightness of the star itself. Two stars with the same absolute magnitudes will have the same luminosity, but if one star is farther away from Earth then its apparent magnitude will be dimmer. Is light a continuous wave, or is it made of discrete particles? Solution: Neither! It is something completely different, which can only be described by quantum mechanics. But since we live in a classical world, it's easier for us to talk about it in terms of either a wave or a collection of photons, depending on the context. Wave A has frequency 100 Hz. Wave B has frequency 50 Hz. Which wave has a longer wavelength? Solution: Wavelength is inversely proportional to frequency, so wave B, with the lower frequency, will have the longer wavelength. Photon A has energy 30 eV. Photon B has energy 20 eV. Which photon has a higher frequency? Solution: Energy is proportional to frequency, so photon A, with with the higher energy, will have the higher frequency. I am wearing a green shirt. What range of wavelengths of light is being reflected from my shirt? Solution: 500-565 nm. Which has a higher frequency: microwaves or X-rays? Solution: X-rays. Body A has temperature 1000 K. Body B has temperature 2000 K. Which body's blackbody radiation has a longer peak wavelength? Solution: The peak wavelength, according to Wien's law, is inversely proportional to temperature. Therefore, body A, which has the lower temperature, will have the longer wavelength. Explain why the sky is blue and why the Sun appears red/orange/yellow. Solution: Light from the Sun scatters in the atmosphere. Shorter (blue) wavelengths scatter more than longer (red/orange/yellow) wavelengths. So the blue light scatters and we see it coming from all directions, while the red/orange/yellow light does not scatter and we see it coming from the direction of the Sun. What is the speed of light in meters per second? The average human walking speed is around 1.5 meters per second; how long will it take a human to walk the distance that light travels in one second? Solution: The speed of light is 300,000,000 (300 million) meters per second. If we divide this by 1.5, we get 200,000,000. Therefore it will take us 200 million seconds, or around 6.5 years, to walk the distance light travels in just one second. Light is very fast! If I double the frequency of an electromagnetic wave, what happens to its wavelength? Solution: It gets halved, since the frequency and wavelength are inversely proportional. How would the intensity of a distant star change if the distance to the star was tripled? Solution: The intensity will decrease by a factor of 9 (the square of the distance), or in other words, it will be 1/9 times the original intensity. Why did humans and other animals on Earth evolve to see the 400-700 nm range of the electromagnetic spectrum? Solution: Because most of the light that gets to us from the Sun is in that specific range. How does a photon's wavelength relate to its energy? Solution: Wavelength is inversely proportional to frequency. Frequency is proportional to energy (higher-energy waves have a higher frequency). Therefore, wavelength is inversely proportional to energy. I heat two containers of gas. One is helium and the other is neon. Do they emit the same wavelengths of electromagnetic radiation? Solution: No, each gas has its own spectral signature of emission lines. What's the difference between an absorption spectrum and an emission spectrum? Solution: An absorption spectrum is a continuous spectrum from which certain wavelengths have been removed, resulting in dark lines where those wavelengths of light should be. These "missing colors" are due to the light passing through a gas which absorbs light at these specific wavelengths. An emission spectrum is the opposite: it consists of bright lines of different wavelengths on a black background. These lines of color a due to a gas emitting light at only these specific wavelengths. The same wavelengths are absorbed or emitted in both cases, determined by the specific type of gas. What happens if I put an absorption spectrum on top of an emission spectrum? Solution: I will get the full continuous spectrum without any dark lines, since all the dark lines in the absorption spectrum will be "filled out" by the bright lines in the emission spectrum, as they are of the same wavelengths. What is an energy level? Solution: In Bohr's model of the atom, electrons can only occupy specific orbits. Each orbit is associated with an energy level. For the electron to move from one orbit to another, it must either absorb or emit a photon with energy equal to the difference between the energy levels of each orbit. An electron moves from an orbit with energy level 1 eV to an orbit with energy level 3 eV. Will it emit or absorb a photon? What would be the energy of this photon? Solution: Since the electron has increased its energy, something had to give it the extra energy. Therefore, the electron must have absorbed a photon with an energy equal to the difference, which is 3 - 1 = 2 eV. What produces a photon with a longer wavelength: an electron moving from energy level 5 eV to 4 eV or from 5 eV to 3 eV? Solution: In the first case, the photon will have energy 5 - 4 = 1 eV. In the second case, it will have energy 5 - 3 = 2 eV. A higher energy means higher frequency and thus shorter wavelength, as frequency is inversely proportional to wavelength. Therefore, the first photon, with the lower energy of 1 eV, will have a longer wavelength. What is the difference between the ground state and an excited state? Solution: The ground state has the lowest possible energy. All other states are excited states. What is ionization? When does it happen? Solution: When the electron obtains enough energy, whether by absorbing a photon or by colliding with something, it can escape the atom completely - essentially, it goes beyond the highest possible energy level. This is called ionization, and an atom with missing electrons is called ionized. A car is driving from Alice to Bob. The car sounds its horn, which produces sound waves that propagate in all directions. According to the Doppler effect, what is the difference between what Alice hears and what Bob hears, in terms of wavelength, frequency, and pitch? Solution: The car is driving away from Alice, so this stretches the waves, and Alice will hear a sound with a longer wavelength (and thus lower frequency and pitch). The car is driving towards Bob, so this compresses the waves, and Bob will hear a sound with a shorter wavelength (and thus higher frequency and pitch). A white spaceship is moving away from Earth at a very high speed. What will happen to its color as seen by people observing it from Earth? Solution: It's moving away from Earth, so the light waves get stretched, which means wavelengths get longer. This is called redshift, since red has the longest wavelength. The spaceship will not necessarily appear red, but its color will be shifted towards the red side of the visible spectrum. There is a certain velocity where its color will be exactly red, but at other velocities it might be, for example, yellow or infrared. How can we detect the elements inside a star even though their spectral lines have been shifted due to the Doppler effect? Solution: We don't detect the wavelength of a single line, we detect a specific pattern of lines. This pattern will always look the same, since each line in the pattern will be shifted by the same amount. In fact, by comparing this pattern's wavelengths to those of the same pattern generated on Earth, we can deduce the speed of the star. Rank the following stars from hottest to coolest: F2, K9, F8, A4, A3, K7. Solution: A3, A4, F2, F8, K7, K9. Summarize how astronomers use spectrography to measure the size, composition, velocity, and rotation of stars. Solution: Size: larger stars have lower density and pressure, which results in narrower spectral lines. Composition: each element leaves a distinct pattern of spectral lines, and if a specific element is more abundant, then the lines corresponding to that element would be stronger. Velocity: the radial velocity (the component of the velocity in the direction toward or away from us) is determined by the Doppler shift of the spectral lines, but to find the space velocity (the actual velocity of the star) we also need to find the transverse velocity (via the proper motion) and distance to the star, and then combine them together to find the space velocity. Rotation: the Doppler shift will cause the spectral lines to broaden in proportion to the rotational speed of the star. |