Test 1

Express the following in common notation (with zeros): (a) 1.90 × 1027 (mass of Jupiter in kg) (b) 3.16 × 107 (number of seconds in a year) (c) 9.46 × 1012 (number of km in 1 light year)

(a) 1,900,000,000,000,000,000,000,000,000 (b) 31,600,000 (c) 9,460,000,000,000

Express the following numbers in scientific notation: (a) 0.000001 (wavelength of near infrared radiation in m) (b) 0.00000035 (wavelength of near ultraviolet radiation in m) (c) 0.00000000000000000000000000167 (mass of proton in kg)

(a) 10−6 (b) 3.5 × 10−7 (c) 1.67 × 10−27

Express the following numbers in scientific notation: (a) 673,948,000 (b) 84,261,000,000,000 (c) 9,241,000,000

(a) 6.73948 × 108 (b) 8.4261 × 1013 (c) 9.241 × 109

What is a nanometer (nm)?

A nanometer is one-billionth (10−9) of a meter.

What is a spectral line? Describe the difference between emission and absorption lines.

A spectral line is a sharp peak or dip in a spectrum at a particular wavelength. A peak is called an emission line, while a dip is called an absorption line.

What is a spectrum? Why are spectra useful to astronomers?

A spectrum is a separation of light (electromagnetic radiation) into its constituent wavelengths, using a prism or grating. Obtaining a spectrum allows us to determine how much light is received at each wavelength. This allows astronomers to determine the physical nature of the object that emits the light, e.g. a gas cloud, star, or galaxy.

Is a water wave transverse or longitudinal?

A water wave combines both transverse (vertical) and longitudinal (horizontal) mo-tion. The latter motion is a back and forth oscillation parallel to direction of wave travel. The combination of these two motions causes the water to move in a small circle about its equilibrium position.

What is a photon? What are its properties?

All forms of electromagnetic radiation consist of individual energy packets called pho-tons, which have some of the characteristics of particles. A photon is the smallest unit of electro-magnetic radiation and cannot be divided. The energy of a photon is proportional to its frequency and thus inversely proportional to its wavelength.

Define the term Astronomical Unit (AU).

An Astronomical Unit (AU) is the average distance between the Earth and the Sun. It is approximately equal to 150 million km. We typically measure distances in the solar system in units of AU.

Explain why we see different constellations at different times of the year.

As the Earth orbits the Sun, we see the Sun projected against different parts of the sky. We are not able to see the constellations in the region where the Sun appears. Instead, we see the stars in the direction of the night side of the Earth, i.e. the side that faces away from the Sun. The constellations on the night side of the Earth thus change through the year.

What do astronomers mean by a "constellation"?

Astronomers divide the sky into 88 contiguous regions called constellations. Thus any point in the sky lies within one of these constellations. The modern system of 88 constellations is based on the traditional constellation patterns, which are determined by bright stars. It is important to note that the stars within a constellation are usually not physically associated with each other and are usually at a wide range of distances from Earth.

How does the visible series of spectral lines of hydrogen (the Balmer series) arise? What are the wavelengths and colors of the first three lines in the Balmer series?

Balmer photons are emitted when electrons drop from higher levels into the second energy level of a hydrogen atom, i.e. the second smallest orbit. Balmer photons are absorbed when an electron in a hydrogen atom moves from the second energy level into a higher level.

Explain what black body radiation is.

Black body radiation is produced by an ideal absorber and emitter of electromagnetic radiation. Real-world objects, such as kilns and stars, provide approximations to a perfect black body. An ideal black body produces a continuous spectrum, i.e. there are no sharp dips or peaks.

Describe the situations in which the following types of spectrum are produced: (1) continuous spectra, (2) emission-line spectra, and (3) absorption-line spectra. Give examples of objects that produce each of these types of spectra.

Continuous: A hot solid object or dense gas produces a continuous spectrum. Examples: incan-descent light filament, heated bar of iron, ideal black body. Emission-Line: A low-density, hot gas produces an emission line spectrum. Examples: vacuum discharge tube (as used in class), fluorescent lights, "neon" signs, bright interstellar gas clouds. Absorption-Line: A low-density, cool gas produces an absorption line spectrum when viewed in front of a continuous source. Examples: photosphere of Sun, photospheres of other stars, galaxies

What is electromagnetic radiation? What effect does it have on electrons?

Electromagnetic radiation (light) is a means by which energy is transported through space as a wave. This wave causes electrons to oscillate back and forth as it passes, in a direction that is perpendicular to the wave travel direction.

List the types of electromagnetic radiation in order of increasing wavelength.

Electromagnetic radiation from shortest to longest wavelength: gamma-ray, X-ray, ultraviolet, visible, infrared, microwave, radio

For photons 1 and 2, if λ1/λ2 = 5, find the ratios ν1/ν2 and E1/E2.

Frequency varies inversely with wavelength and that energy varies directly with frequency. Thus, the ratio ν1/ν2 is the inverse of λ1/λ2, i.e. ν1/ν2 = 1/5. The ratio E1/E2 is equal to ν1/ν2, i.e. E1/E2 = 1/5.

What is an absorption-line spectrum?

Normal stars show an absorption-line spectrum. It is a continuous spectrum (rainbow of colors) with absorption lines (dips) at certain wavelengths. The dips are caused by absorption of energy by atoms and (for cool stars) molecules.

What causes photons to be emitted and absorbed by atoms?

Photons are emitted by atoms when electrons drop to lower energy levels, releasing energy. Photons are absorbed by atoms when electrons move to higher energy levels, which requires energy input.

Sketch approximate black body curves (spectra) for stars with temperatures of 3000 K, 6000 K, and 12,000 K. Label the axes. Indicate the wavelengths of peak emission on your figure. On which side of the peak do the curves fall faster?

See Figure 4-2 on page 108 of the text. The curves fall off much faster on the short wavelength side of the peak.

What is an emission-line spectrum?

Some astronomical objects show an emission-line spectrum. Rather than a continuous spectrum, there are emission lines (sharp peaks) at certain wavelengths, with little or no radiation between the peaks. The peaks are caused by emission of energy by atoms.

What is the Doppler effect?

The Doppler effect is caused by the motion of a light source either toward or away from an observer. When a light source moves toward or away from an observer, the observed wavelength is shifted from the emitted wavelength by an amount proportional to the speed of the object. Motion toward the observer results in a blue shift (shift to shorter wavelengths). Motion away from the observer results in a red shift (shift to longer wavelengths).

Explain how the Kelvin (absolute) temperature scale is defined. Give the temperatures for the following in the Fahrenheit, Celsius, and Kelvin scales: (a) absolute zero (b) the freezing point of water (c) the boiling point of water

The Kelvin scale is defined so that its zero corresponds to absolute zero and the degree size is the same as for the Celsius scale. There are no negative temperatures on the Kelvin scale. Fahrenheit Celsius Kelvin absolute zero: −459◦ F, −273◦ C, 0 K freezing pt. of water: 32◦ F, 0◦ C, 273 K boiling pt. of water: 212◦ F, 100◦ C, 373 K

For what type of radiation is the particle-like nature least apparent? For what type is it most apparent?

The higher the photon energy, the more the particle-like nature of photons is apparent. Thus, radio photons have the least particle-like nature and gamma-ray photons have the most particle-like nature.

What is the relation between the size of an electron orbit in an atom and the energy of the orbit?

The larger the orbit, the higher its energy. Thus, the smallest possible orbit corresponds to the lowest energy level (i.e. the ground state).

Describe how the pointer stars in the Big Dipper are used to find Polaris.

The pointer stars are the two stars at the far end of the bowl from the handle. Motion along the line defined by these stars, out of the bowl, leads to Polaris—the North Star.

Describe the features of the sky chart that was distributed in class. What does the outer circle represent? How should the chart be oriented when you are looking in a certain direction, e.g. North?

The sky chart shows the part of the sky that is above the horizon. The outer circle represents the horizon. The chart should be turned so that the direction in which you are looking is at the bottom.

What is the physical significance of the speed of light?

The speed of light (in a vacuum) is the absolute speed limit in the universe. Nothing can go faster than this limit

What is meant by "near infrared" and "near ultraviolet"?

The term "near" indicates location relative to the visible spectrum. The near infrared region of the electromagnetic spectrum is just to the long wavelength side of red. The near ultra-violet region is just to the short wavelength side of violet.

What is the zodiac?

The zodiac is the band of sky where the Sun, Moon, and planets are found. There are 12 classical constellations that lie along the zodiac.

Consider an ultraviolet photon with wavelength λUV = 300 nm and an infrared photon with wavelength λIR = 1200 nm. Compute the ratios νUV/νIR and EUV/EIR.

This problem is similar to the previous one. First calculate the ratio λUV/λIR = 300 nm/1200 nm = 1/4. Then follow the same approach as in the previous problem, which leads to νUV/νIR = 4 and EUV/EIR = 4.

Describe the difference between a transverse wave and a longitudinal wave. Give examples of both types of wave

Transverse Wave: Direction of oscillation is perpendicular to direction of wave travel. Exam-ples: waves on a string, sideways Slinky wave, electromagnetic radiation. Longitudinal Wave: Direction of oscillation is parallel to direction of wave travel. Examples: compression wave on a Slinky, sound wave

Suppose that an astronomical object emits light with a rest wavelength of λrest = 400 nm that is observed to have a wavelength of λobs = 360 nm What is the speed of the object and in what direction is it moving?

Use the Doppler formula: v c = λobs − λrest λrest v c = 360 nm − 400 nm 400 nm = − 1 10 The negative sign indicates motion toward the observer, i.e. the wavelength is blueshifted (ob-served wavelength is shorter than emitted wavelength). Thus, the object is approaching the observer at 0.1 c, i.e. 10% of the speed of light.

What is the approximate range of wavelength for visible light?

Visible light ranges in wavelength from about 700 nm (red) to 400 nm (violet).

Explain what actually moves outward with a water wave that is generated by dropping a pebble in a pond.

Wave crests and energy move outward with the wave. However, the water itself does not move outward with the wave. It just moves in a small circle about its original position.

Suppose that ocean waves travel at 2 meters per second. If the wavelength is 4 meters, what is the frequency of the waves?

Wavelength (λ), frequency (ν), and speed (v) are related by λν = v . Thus, ν = v/λ ν = 2 m/s 4 m ν = 0.5 1 s The frequency is 0.5 waves per second.

Define the terms wavelength, frequency, and amplitude.

Wavelength is the distance between successive wavecrests. Frequency is the number of wavecrests passing a point per time. Amplitude is the height of the wave above the undisturbed level.

For two stars with the following surface temperatures, calculate the ratio of wavelengths of peak emission, λmax,1/λmax,2. T1 = 3000 K, T2 = 12, 000 K

Wavelength of peak emission, λmax, varies inversely with temperature, T. Thus, since T1/T2 = 3000/12, 000 = 1/4, it follows that λmax,1/λmax,2 = 4.

The wavelength of peak emission of the Sun is approximately 500 nm and the surface temperature of the sun is approximately 6000 K. Use this information to find the wavelength of peak emission for a star that has a surface temperature of 3000 K.

λmax =const. T Thus, λmax varies inversely with T. Since the Sun has a temperature of about 6000 K, a star with a temperature of 3000 K is approximately half as hot as the Sun. Thus, the wavelength of peak emission for this star is approximately twice as large as that of the Sun, i.e. λmax = 1000 nm.