Question 1

Two objects are moving directly away from an observer at the same speed. One object, however, is twice as far away as the other. How do their Doppler shifts compare?
A) They are the same.
B) The more distant object has the greater Doppler shift.
C) The more distant object has the smaller Doppler shift.
D) Whichever object is larger will have the greater Doppler shift.

Accepted Answer

The Doppler shift depends on the relative speed between the observer and the source, not the distance of the source from the observer. Since both objects are moving away at the same speed, their Doppler shifts will be the same, regardless of their distances.

Question 2

Because of the Doppler effect, the sound of the engines of an aircraft that flies past an observer
A) changes from a high pitch or frequency to a lower pitch as the plane passes the observer.
B) changes from a low pitch or frequency to a higher pitch as the plane passes the observer.
C) remains at the same pitch or frequency, but the intensity rises as the plane approaches and then falls as the plane moves away.
D) starts at a high pitch or frequency, drops to a low frequency when the plane is overhead, then rises again as the plane moves away.

Accepted Answer

The Doppler effect causes the sound waves to compress as an object approaches, leading to a higher pitch, and then to expand as the object moves away, leading to a lower pitch.

Question 3

The spectrum of a star shows a set of dark absorption lines equivalent to the absorption lines of the Sun but with one exception: Every line appears at a slightly longer wavelength, shifted toward the red end of the spectrum. What conclusion can be drawn from this observation?
A) A cloud of cold gas and dust surrounds the star and is absorbing light from it.
B) The star is moving toward Earth.
C) The temperature of the star's surface is higher than that of the Sun.
D) The star is moving away from Earth.

Accepted Answer

This observation is a classic example of the Doppler effect, where the wavelength of light from an object increases (redshift) if the object is moving away from the observer.

Question 4

An object is observed to show no Doppler shift. As a result, only one of these statements cannot describe the motion of the object. Which one?
A) The object is stationary.
B) The object has only a transverse motion.
C) The object has only a proper motion.
D) The object has only a radial motion.

Accepted Answer

The Doppler shift is observed when there is motion along the line of sight between the observer and the object, known as radial motion. If an object shows no Doppler shift, it means there is no motion towards or away from the observer. Options A, B, and C do not necessarily involve radial motion towards or away from the observer, but option D, radial motion, would result in a Doppler shift if it were present.

Question 5

The observed change in the wavelength of light due to the Doppler effect occurs
A) only when the temperature of an object changes.
B) only when the light source has proper motion (i.e., motion across the line of sight).
C) whenever the light source is moving with respect to the observer (regardless of direction).
D) only when the light source has a radial velocity (i.e., motion toward or away from the observer).

Accepted Answer

The answer of The observed change in the wavelength of...

Question 6

A source emitting waves of constant wavelength approaches an observer, then passes the observer, and recedes into the distance-all at a constant speed. The wavelength of the waves the observer measures from this source
A) remains constant.
B) gradually becomes longer and longer as the source approaches the observer and then becomes even longer as the source recedes from the observer.
C) gradually becomes shorter and shorter as the source approaches the observer and then gradually becomes longer and longer as the source recedes from the observer.
D) is shorter (and constant) as the source approaches the observer and then suddenly becomes longer (and constant) as the source recedes from the observer.

Accepted Answer

The answer of A source emitting waves of constant wavelength...

Question 7

Hydrogen gas emits a strong spectral line of red light with a wavelength of 656.3 nm (the Balmer$\alpha$ line). This emission line is seen in the spectrum of a distant quasar but at a wavelength of 721.9 nm. Applying Doppler's relationship, how fast is this object moving with respect to Earth, in terms of the velocity of light, c?
A) 1/10 c
B) 1.1 c
C) 1/100 c
D) 10 c

Accepted Answer

The Doppler shift formula for light is $\Delta \lambda / \lambda = v / c$, where $\Delta \lambda = 721.9 \, \text{nm} - 656.3 \, \text{nm}$, $\lambda = 656.3 \, \text{nm}$, $v$ is the velocity of the object, and $c$ is the speed of light. Solving for $v/c$ gives a value close to 0.1, or 1/10 of the speed of light.

Question 8

An electron is in the n = 3 energy level in a hydrogen atom. To ionize this atom, it is necessary for the electron to gain a minimum of how much energy? See Figure 4-11. 
A) 1.5 eV
B) 4.5 eV
C) 12.1 eV
D) 13.6 eV

Accepted Answer

The answer of An electron is in the n =...

Question 9

A police radar device bounces radio waves of wavelength 3 mm from the front of a speeding car and measures the Doppler shift in wavelength of the reflected waves. What will be the wavelength shift if the car is moving at 60 mph (80 km/h or 22.2 m/s) (in a 30 mph zone)? Note that the shift is doubled because of the reflection.
A) 0.44 nm
B) 0.44 $\mu$m
C) 4.4 $\mu$m
D) 4.4 m

Accepted Answer

The Doppler shift in wavelength can be calculated using the formula $\Delta \lambda = \frac{v}{c} \lambda$, where $v$ is the speed of the car, $c$ is the speed of light, and $\lambda$ is the original wavelength. Given that the speed of light $c \approx 3 \times 10^8$ m/s, the speed of the car $v = 22.2$ m/s, and the original wavelength $\lambda = 3$ mm = $3 \times 10^{-3}$ m, the shift $\Delta \lambda$ is calculated as follows:$$\Delta \lambda = \frac{v}{c} \lambda = \frac{22.2}{3 \times 10^8} \times 3 \times 10^{-3} = 2.22 \times 10^{-7} \text{ m}$$Since the shift is doubled due to reflection, the total shift is $2 \times 2.22 \times 10^{-7} = 4.44 \times 10^{-7}$ m, which is equal to 0.44 nm.

Question 10

An astronomer observing the spectrum of the Sun on the solar equator finds that the Balmer H _$\beta$ spectral line ($\lambda$ = 486 nm) is blueshifted by 0.0033 nm when measured at one edge of the Sun's disk compared with the same line at the center of the Sun's disk and is redshifted by the same amount on the equator at the other side of the Sun's disk. If this Doppler shift is due to the Sun rotating (try drawing a diagram), then the rotational speed of the Sun at its equator is A) 1 km/s. B) 0.5 km/s. C) 2 km/s. D) 4 km/s.

Accepted Answer

The Doppler shift formula for velocity is $v = \frac{\Delta \lambda}{\lambda}c$, where $\Delta \lambda = 0.0033 \, \text{nm}$, $\lambda = 486 \, \text{nm}$, and $c = 3 \times 10^8 \, \text{m/s}$. Substituting these values gives a rotational speed of approximately 2 km/s for the Sun at its equator.

Question 11

When electromagnetic radiation (e.g., light) is Doppler-shifted by motion of the source away from the detector, the measured
A) speed of the radiation is less than the emitted speed.
B) frequency is higher than the emitted frequency.
C) frequency of the radiation remains the same, but its wavelength is shortened, compared to the emitted radiation.
D) wavelength is longer than the emitted wavelength.

Accepted Answer

The Doppler effect causes the wavelength of electromagnetic radiation to lengthen (redshift) when the source is moving away from the observer, leading to a lower observed frequency but the speed of light remains constant in a vacuum.

Question 12

The orbits of electrons in an atom are sometimes compared to the orbits of the planets around the Sun. However, only one of these characteristics of electron orbits is shared with planetary orbits. Which one?
A) Larger orbits are associated with higher energies.
B) The particle motions must be described by quantum mechanics.
C) Only certain allowed orbits exist with certain allowed energies and allowed distances.
D) The orbiting particles exhibit both particle and wave properties.

Accepted Answer

Electron orbits in an atom and planetary orbits share the characteristic that larger orbits are associated with higher energies. In the context of an atom, electrons in larger orbits (further from the nucleus) have higher energy levels. Similarly, in the solar system, planets in orbits further from the Sun have higher potential energy due to gravity.

Question 13

An electron is in the n = 3 energy level in a hydrogen atom. What can be said about the spectral series in which it can participate by making a single atomic transition?
A) If the electron gains energy, it can participate in the Lyman series; if it loses energy, it can participate in the Balmer series.
B) If the electron gains energy, it can participate in the Lyman series or the Paschen series; if it loses energy, it can participate in the Balmer series.
C) If the electron gains energy, it can participate in the Balmer series; if it loses energy, it can participate in the Paschen series.
D) If the electron gains energy, it can participate in the Paschen series; if it loses energy, it can participate in the Lyman series or the Balmer series.

Accepted Answer

When an electron in a hydrogen atom is in the n = 3 level, it can move to a higher energy level (n > 3) by gaining energy, which would result in emission lines in the Paschen series (transitions to n = 3 from higher levels). If it loses energy, it can drop to n = 2 (Balmer series) or n = 1 (Lyman series), depending on the final energy level.

Question 14

An astronomer measures the spectrum of a star and finds a spectral line at 499 nm wavelength. In the laboratory, this spectral line occurs at 500 nm. According to the Doppler effect, this object is moving _____ Earth at _____the speed of light.
A) toward; 1/500
B) away from; 1/500
C) toward; 499/500
D) away from; 499/500

Accepted Answer

The star's spectral line is blue-shifted (shifted to a shorter wavelength) from 500 nm to 499 nm, indicating it is moving toward Earth. The speed can be approximated by the change in wavelength divided by the original wavelength, which is (500 - 499)/500 = 1/500 of the speed of light.

Question 15

According to modern atomic theory, light emitted by atoms originates from
A) photons emitted directly from the nucleus.
B) transitions of electrons between electron levels of the same atom.
C) collisions between atoms.
D) electrons emitted from the nucleus.

Accepted Answer

Light emitted by atoms is due to transitions of electrons between different energy levels within the same atom. When an electron moves from a higher energy level to a lower one, it emits a photon of light corresponding to the energy difference between those levels.

Question 16

The Doppler effect is the
A) change in the wavelength of peak emission of light when the source temperature changes.
B) increase in the observed wavelength of light if the source of light is moving away from you.
C) increase in the observed wavelength of light if the light source is moving toward you.
D) splitting of spectral lines into two or more wavelengths because the source of the light is in a strong magnetic field.

Accepted Answer

The Doppler effect refers to the change in the observed frequency (or wavelength) of a wave in relation to an observer who is moving relative to the wave source. Specifically, if the source of light is moving away from the observer, the observed wavelength increases (redshift).

Question 17

The series of spectral absorption lines in the infrared part of the spectrum that result from atomic transitions in hydrogen atoms in which electrons are lifted from the n = 3 level to all other atomic energy levels is known as
A) ionization transitions.
B) the Lyman series.
C) the Paschen series.
D) the Balmer series.

Accepted Answer

The Paschen series refers to the spectral lines in the infrared part of the spectrum that are produced when electrons transition from higher energy levels to the n = 3 level in hydrogen atoms.

Question 18

The wavelength $\lambda$₀ of light emitted by a moving object is detected as a different wavelength $\lambda$ by a stationary observer. If v is the velocity of the object and c is the velocity of light, this Doppler shift can be described by the equation A) ($\lambda$ - $\lambda$₀ = v - c.) B) ($\lambda$/$\lambda$₀ = v/c.) C) ($\lambda$$\lambda$₀ = vc.) D) ($\lambda$ - $\lambda$₀)/$\lambda$₀ = v/c.)

Accepted Answer

The correct equation for the Doppler shift in terms of wavelength involves the observed wavelength minus the source wavelength over the source wavelength, equal to the velocity of the object divided by the speed of light. This is accurately represented in choice D.

Question 19

The Doppler effect is the change in the wavelength of light caused by the source
A) being in a high gravitational field.
B) being embedded in a cloud of dust and gas.
C) being in an intense magnetic field.
D) moving with respect to the observer.

Accepted Answer

The Doppler effect refers to the change in frequency (or wavelength) of a wave in relation to an observer who is moving relative to the wave source. This effect is observed for all types of waves, including light. When the source of light is moving towards the observer, the wavelengths appear shorter (blue-shifted); when it is moving away, the wavelengths appear longer (red-shifted).

Question 20

According to the Doppler effect,
A) spectral lines are split into two or more wavelengths when the source of the light is in a strong magnetic field.
B) the wavelength of light is shifted to a longer wavelength if the source of the light is moving toward the observer.
C) the wavelength of peak emission of light from a source changes as the temperature of the source changes.
D) the wavelength of light is shifted to a shorter wavelength if the source of light is moving toward the observer.

Accepted Answer

The Doppler effect describes how the wavelength of light (or sound) changes due to the relative motion of the source and the observer. If the source is moving toward the observer, the wavelengths are compressed, leading to a shift to shorter wavelengths.

Quiz 4: Atomic Physics and Spectra

Two objects are moving directly away from an observer at the same speed. One object, however, is twice as far away as the other. How do their Doppler shifts compare?

Because of the Doppler effect, the sound of the engines of an aircraft that flies past an observer

The spectrum of a star shows a set of dark absorption lines equivalent to the absorption lines of the Sun but with one exception: Every line appears at a slightly longer wavelength, shifted toward the red end of the spectrum. What conclusion can be drawn from this observation?

An object is observed to show no Doppler shift. As a result, only one of these statements cannot describe the motion of the object. Which one?

The observed change in the wavelength of light due to the Doppler effect occurs

A source emitting waves of constant wavelength approaches an observer, then passes the observer, and recedes into the distance-all at a constant speed. The wavelength of the waves the observer measures from this source

An electron is in the n = 3 energy level in a hydrogen atom. To ionize this atom, it is necessary for the electron to gain a minimum of how much energy? See Figure 4-11.

When electromagnetic radiation (e.g., light) is Doppler-shifted by motion of the source away from the detector, the measured

The orbits of electrons in an atom are sometimes compared to the orbits of the planets around the Sun. However, only one of these characteristics of electron orbits is shared with planetary orbits. Which one?

An electron is in the n = 3 energy level in a hydrogen atom. What can be said about the spectral series in which it can participate by making a single atomic transition?

An astronomer measures the spectrum of a star and finds a spectral line at 499 nm wavelength. In the laboratory, this spectral line occurs at 500 nm. According to the Doppler effect, this object is moving _ Earth at _the speed of light.

According to modern atomic theory, light emitted by atoms originates from

The Doppler effect is the

The series of spectral absorption lines in the infrared part of the spectrum that result from atomic transitions in hydrogen atoms in which electrons are lifted from the n = 3 level to all other atomic energy levels is known as

The wavelength $\lambda$ ₀ of light emitted by a moving object is detected as a different wavelength $\lambda$ by a stationary observer. If v is the velocity of the object and c is the velocity of light, this Doppler shift can be described by the equation

The Doppler effect is the change in the wavelength of light caused by the source

According to the Doppler effect,