Deck 7: Quantum Theory and Atomic Structure

Question 1

Who was the first scientist to propose that the atom had a dense nucleus which occupied only a small fraction of the volume of the atom?

A) Planck
B) Bohr
C) Rydberg
D) Rutherford
E) Thomson

Answer 1

Rutherford

Question 2

Which word best describes the phenomenon which gives rise to a rainbow?

A) reflection
B) dispersion
C) diffraction
D) interference
E) deflection

Answer 2

dispersion

Question 3

The interference pattern seen when light passes through narrow, closely spaced slits, is due to

A) diffraction.
B) reflection.
C) refraction.
D) dispersion.
E) deflection.

Answer 3

diffraction.

Question 4

Who was the first scientist to propose that an object could emit only certain amounts of energy?

A) Planck
B) Einstein
C) Bohr
D) Rydberg
E) de Broglie

Question 5

Electromagnetic radiation of 500 nm wavelength lies in the __________ region of the spectrum.

A) infrared
B) visible
C) ultraviolet
D) X-ray
E) ( $\gamma$ )-ray

Question 6

Electromagnetic radiation can be specified by its wavelength ( $\lambda$ ), its frequency (v) or its period ( $\tau$ ). The period $\tau$ is the time it takes one complete wavelength to pass a point in space. Based on this information, what is the mathematical relationship between v and $\tau$ ?

A) (v = 1/ $\tau$ )
B) (v = $\tau$ )
C) ( $\tau$ = v/c)
D) c = $\tau$ x v
E) ( $\tau$ = c/v)

Question 7

Select the arrangement of electromagnetic radiation which starts with the lowest energy and increases to greatest energy.

A) radio, infrared, ultraviolet, gamma rays
B) radio, ultraviolet, infrared, gamma rays
C) gamma rays, infrared, radio, ultraviolet
D) gamma rays, ultraviolet, infrared, radio
E) infrared, ultraviolet, radio, gamma rays

Question 8

Select the arrangement of electromagnetic radiation which starts with the lowest energy and increases to greatest energy.

A) radio, visible, infrared, ultraviolet
B) infrared, visible, ultraviolet, microwave
C) visible, ultraviolet, infrared, gamma rays
D) X-radiation, visible, infrared, microwave
E) microwave, infrared, visible, ultraviolet

Question 9

Which scientist first proposed that particles of matter could have wave properties?

A) Einstein
B) Planck
C) de Broglie
D) Compton
E) Heisenberg

Question 10

Interference of light waves

A) separates light into its component colors.
B) creates a pattern of light and dark regions.
C) focuses a broad beam of light into a point.
D) bends light as it passes the edge of an object.
E) creates a laser beam.

Question 11

Which scientist first proposed that the electron in the hydrogen atom can have only certain energies?

A) Planck
B) Einstein
C) Bohr
D) Rydberg
E) Heisenberg

Question 12

Who proposed a model that successfully explained the photoelectric effect?

A) Planck
B) Einstein
C) Compton
D) Rydberg
E) Bohr

Question 13

The FM station KDUL broadcasts music at 99.1 MHz. Find the wavelength of these waves.

A) 1.88 × 10^-2 m
B) 0.330 m
C) 3.03 m
D) 5.33 × 10² m
E) > 10³ m

Question 14

The AM station KBOR plays your favorite music from the 20's and 30's at 1290 kHz. Find the wavelength of these waves.

A) 4.30 × 10^-2 m
B) 0.144 m
C) 6.94 m
D) 232 m
E) > 10³ m

Question 15

Which scientist demonstrated that photons transferred momentum during collisions with matter?

A) Bohr
B) de Broglie
C) Planck
D) Compton
E) Billiard

Question 16

Contact lenses can focus light due to the ____________ of the waves.

A) diffraction
B) reflection
C) refraction
D) dispersion
E) interference

Question 17

Who developed an empirical equation from which the wavelengths of lines in the spectrum of hydrogen atoms can be calculated?

A) Planck
B) de Broglie
C) Bohr
D) Rutherford
E) Rydberg

Question 18

Who proposed the principle which states that one cannot simultaneously know the exact position and velocity of a particle?

A) Einstein
B) Planck
C) Heisenberg
D) Compton
E) de Broglie

Question 19

Select the arrangement of electromagnetic radiation which starts with the lowest wavelength and increases greatest wavelength.

A) radio, infrared, ultraviolet, gamma rays
B) radio, ultraviolet, infrared, gamma rays
C) gamma rays, radio, ultraviolet, infrared
D) gamma rays, infrared, radio, ultraviolet
E) gamma rays, ultraviolet, infrared, radio

Question 20

Which of the following frequencies of electromagnetic radiation has the shortest wavelength?

A) 1 kilohertz
B) 1 terahertz
C) 1 dekahertz
D) 1 gigahertz
E) 1 megahertz

Question 21

Use the Rydberg equation to calculate the frequency of a photon absorbed when the hydrogen atom undergoes a transition from n₁ = 2 to n₂ = 4. (R = 1.096776 × 10⁷ m^-1)

A) 2.056 × 10⁶ s^-1
B) 2.742 × 10⁶ s^-1
C) 6.165 × 10¹⁴ s^-1
D) 8.226 × 10¹⁴ s^-1
E) > 10¹⁵ s^-1

Question 22

Green light has a wavelength of 5200 Å. Calculate the energy of one photon of green light.

A) 3.4 × 10^-40 J
B) 3.4 × 10^-30 J
C) 3.8 × 10^-29 J
D) 3.4 × 10^-27 J
E) 3.8 × 10^-19 J

Question 23

The ionization energy is the energy needed to remove an electron from an atom. In the Bohr model of the hydrogen atom, this means exciting the electron to the n = $\infty$ state. What is the ionization energy in kJ/mol, for hydrogen atoms initially in the n = 2 energy level?

A) 290 kJ/mol
B) 328 kJ/mol
C) 656 kJ/mol
D) 983 kJ/mol
E) 1311 kJ/mol

Question 24

According to the Bohr theory of the hydrogen atom, the minimum energy (in J) needed to ionize a hydrogen atom from the n = 2 state is

A) 2.18 × 10^-18 J.
B) 1.64 × 10^-18 J.
C) 5.45 × 10^-19 J.
D) 3.03 × 10^-19 J.
E) none of the above.

Question 25

In the photoelectric effect, a photon with an energy of 5.3 × 10^-19 J strikes an electron in a metal. Of this energy, 3.6 × 10^-19 J is the minimum energy required for the electron to escape from the metal. The remaining energy appears as kinetic energy of the photoelectron. What is the velocity of the photoelectron, assuming it was initially at rest?

A) 3.7 × 10¹⁴ m/s
B) 3.7 × 10¹¹ m/s
C) 1.9 × 10⁶ m/s
D) 6.1 × 10⁵ m/s
E) 1.7 × 10^-19 m/s

Question 26

A modern compact fluorescent lamp contains 1.4 mg of mercury. If each mercury atom in the lamp were to emit a single photon of wavelength 254 nm, how many joules of energy would be emitted?

A) 7.8 × 10^-19 J
B) 3.3 J
C) 6.6 × 10² J
D) 3.3 × 10³ J
E) 4.2 × 10¹⁸ J

Question 27

An electron in the n = 6 level emits a photon with a wavelength of 410.2 nm. To what energy level does the electron move?

A) n = 1
B) n = 2
C) n = 3
D) n = 4
E) n = 5

Question 28

Platinum, which is widely used as a catalyst, has a work function $\Phi$ (the minimum energy needed to eject an electron from the metal surface) of 9.05 × 10^-19 J. What is the longest wavelength of light which will cause electrons to be emitted?

A) 2.196 × 10^-7 m
B) 4.553 × 10^-6 m
C) 5.654 × 10² m
D) 1.370 × 10¹⁵ m
E) > 10⁶ m

Question 29

Consider the following adjectives used to describe types of spectrum: continuous line atomic emission absorption
How many of them are appropriate to describe the spectrum of radiation given off by a black body?

A) none
B) one
C) two
D) three
E) four

Question 30

What type of spectrum, if any, would be produced if the light radiated by a heated atomic gas were to be dispersed through a prism?

A) a continuous band of color
B) a continuous band of color with some dark lines (missing wavelengths)
C) only blue light
D) only red light
E) discrete lines of different colors

Question 31

According to the Rydberg equation, the longest wavelength (in nm) in the series of H-atom lines with n₁ = 3 is

A) 1875 nm.
B) 1458 nm.
C) 820. nm.
D) 656 nm.
E) 365 nm.

Question 32

Line spectra from all regions of the electromagnetic spectrum, including the Paschen series of infrared lines for hydrogen, are used by astronomers to identify elements present in the atmospheres of stars. Calculate the wavelength of the photon emitted when the hydrogen atom undergoes a transition from n = 5 to n = 3. (R = 1.096776 × 10⁷ m^-1)

A) 205.1 nm
B) 384.6 nm
C) 683.8 nm
D) 1282 nm
E) > 1500 nm

Question 33

A radio wave has a frequency of 8.6 × 10⁸ Hz. What is the energy of one photon of this radiation?

A) 7.7 × 10^-43 J
B) 2.3 × 10^-34 J
C) 5.7 × 10^-25 J
D) 1.7 × 10^-16 J
E) > 10^-15 J

Question 34

Excited hydrogen atoms radiate energy in the

A) infrared region only.
B) visible region only.
C) ultraviolet region only.
D) visible and ultraviolet regions only.
E) infrared, visible, and ultraviolet regions.

Question 35

For potassium metal, the work function $\Phi$ (the minimum energy needed to eject an electron from the metal surface) is 3.68 × 10^-19 J. Which is the longest wavelength of the following which could excite photoelectrons?

A) 550. nm
B) 500. nm
C) 450. nm
D) 400. nm
E) 350. nm

Question 36

An infrared wave has a wavelength of 6.5 × 10^-4 cm. What is this distance in angstroms, Å?

A) 6.5 × 10^-4 Å
B) 2.2 × 10^-4 Å
C) 4.6 × 10³ Å
D) 6.5 × 10⁴ Å
E) 6.5 × 10⁶ Å

Question 37

According to the Rydberg equation, the line with the shortest wavelength in the emission spectrum of atomic hydrogen is predicted to lie at a wavelength (in nm) of

A) 91.2 nm.
B) 1.10 × 10^-2 nm.
C) 1.10 × 10² nm.
D) 1.10 × 10¹⁶ nm.
E) none of the above.

Question 38

A photon has an energy of 5.53 × 10^-17 J. What is its frequency in s^-1?

A) 3.66 × 10^-50 s^-1
B) 1.20 × 10^-17 s^-1
C) 3.59 × 10^-9 s^-1
D) 2.78 × 10⁸ s^-1
E) 8.35 × 10¹⁶ s^-1

Question 39

Consider the following adjectives used to describe types of spectrum: continuous line atomic emission absorption
How many of them are appropriate to describe the spectrum of radiation absorbed by a sample of mercury vapor?

A) one
B) two
C) three
D) four
E) five

Question 40

The Bohr theory of the hydrogen atom predicts the energy difference (in J) between the n = 3 and the n = 5 state to be

A) 8.72 × 10^-20 J.
B) 1.36 × 10^-19 J.
C) 2.42 × 10^-19 J.
D) 1.55 × 10^-19 J.
E) 1.09 × 10^-18 J.

Question 41

The size of an atomic orbital is associated with

A) the principal quantum number (n).
B) the angular momentum quantum number (l).
C) the magnetic quantum number (m_l).
D) the spin quantum number (m_s).
E) the angular momentum and magnetic quantum numbers, together.

Question 42

a. What is the frequency of microwave radiation which has a wavelength of 10.7 cm?
b. What is the energy of one photon of this radiation?

Question 43

Which of the following is a correct set of quantum numbers for an electron in a 3d orbital?

A) n = 3, l = 0, m_l = -1
B) n = 3, l = 1, m_l = +3
C) n = 3, l = 2, m_l = 3
D) n = 3, l = 3, m_l = +2
E) n = 3, l = 2, m_l = -2

Question 44

a. Use Bohr's equation to calculate how much energy (in J) is needed to promote an electron from the H-atom ground state to the n = 4 level.
b. If a photon provides the energy in (a), what is its wavelength in nm?

Question 45

A sprinter must average 24.0 mi/h to win a 100-m dash in 9.30 s. What is his wavelength at this speed if his mass is 84.5 kg?

A) 7.29 × 10^-37 m
B) 3.26 × 10^-37 m
C) 5.08 × 10^-30 m
D) 1.34 × 10^-30 m
E) none of the above

Question 46

For all the allowed vibration(s) (wavelength(s)) of a plucked guitar string, what is the correct relationship between the length of the string, L, and the wavelength, $\lambda$ ?

A) L = $\lambda$ /2
B) L = $\lambda$
C) L = n $\lambda$ /2 where n is a positive integer
D) L = n $\lambda$ where n is a positive integer
E) L = 1/ $\lambda$

Question 47

The shape of an atomic orbital is associated with

A) the principal quantum number (n).
B) the angular momentum quantum number (l).
C) the magnetic quantum number (m_l).
D) the spin quantum number (m_s).
E) the magnetic and spin quantum numbers, together.

Question 48

The energy of an electron in the hydrogen atom is determined by

A) the principal quantum number (n) only.
B) the angular momentum quantum number (l ) only.
C) the principal and angular momentum quantum numbers (n & l ).
D) the principal and magnetic quantum numbers (n & m_l).
E) the principal, angular momentum and magnetic quantum numbers.

Question 49

According to the Heisenberg uncertainty principle, if the uncertainty in the speed of an electron is 3.5 × 10³ m/s, the uncertainty in its position (in m) is at least

A) 1.7 × 10^-8 m.
B) 6.6 × 10^-8 m.
C) 17 m.
D) 66 m.
E) none of the above.

Question 50

Which one of the following sets of quantum numbers can correctly represent a 3p orbital?

A) n = 3 l = 1 m_l = 2
B) n = 1 l = 3 m_l = 3
C) n = 3 l = 2 m_l = 1
D) n = 3 l = 1 m_l = -1
E) n = 3 l = 0 m_l = 1

Question 51

a. Calculate the wavelength in nm of a photon whose energy is 6.00 × 10^-19 J.
b. Would the photon in (a) have enough energy to ionize a hydrogen atom in its ground state (i.e., to separate the proton and electron completely)? Use the Bohr equation to explain your answer.

Question 52

The de Broglie equation predicts that the wavelength (in m) of a proton moving at 1000. m/s is

A) 3.96 × 10^-10 m.
B) 3.96 × 10^-7 m.
C) 2.52 × 10⁶ m.
D) 2.52 × 10⁹ m.
E) > 10¹⁰ m.

Question 53

For the following equations
a. name the scientist to whom the equation is attributed.
b. in not more than three lines, explain clearly what the equation means or represents.
1. E = nhv
2. $\lambda$ = h/mu
3. H $\varPsi$ = E $\varPsi$
4. $\Delta$ x.m $\Delta$ u $\ge$ h/4 $\pi$
5. E_photon = hv

Question 54

In an atom, the square of an electron's wave function

A) becomes zero at the nucleus.
B) is smallest near the nucleus.
C) is largest near the nucleus.
D) may be zero at more than one point.
E) tends to infinity at large distances from the nucleus.

Question 55

Atomic orbitals developed using quantum mechanics

A) describe regions of space in which one is most likely to find an electron.
B) describe exact paths for electron motion.
C) give a description of the atomic structure which is essentially the same as the Bohr model.
D) allow scientists to calculate an exact volume for the hydrogen atom.
E) are in conflict with the Heisenberg Uncertainty Principle.

Question 56

Which of the following is a correct set of quantum numbers for an electron in a 5f orbital?

A) n = 5, l = 3, m_l = +1
B) n = 5, l = 2, m_l = +3
C) n = 4, l = 3, m_l = 0
D) n = 4, l = 2, m_l = +1
E) n = 5, l = 4, m_l = 3

Question 57

The orientation in space of an atomic orbital is associated with

A) the principal quantum number (n).
B) the angular momentum quantum number (l).
C) the magnetic quantum number (m_l).
D) the spin quantum number (m_s).
E) none of the above.

Question 58

In the quantum mechanical treatment of the hydrogen atom, which one of the following combinations of quantum numbers is not allowed?

Question 59

In not more than three lines for each answer, briefly outline one important scientific contribution of each of the following:
a. Planck
b. de Broglie
c. Heisenberg

Question 60

Use the Rydberg equation to calculate the wavelength, in nm, of the least energetic (longest wavelength) line in the visible series (n₁ = 2) of the spectrum of atomic hydrogen.

Question 61

Use the Bohr equation to calculate the energy of
a. the largest energy absorption or emission process involving the n = 2 state of the hydrogen atom.
b. the smallest energy absorption or emission process involving the n = 2 state of the hydrogen atom.

Question 62

For the following orbitals, state the values or n, l and m_l which apply, and draw a sketch showing the shape and orientation of the orbital.
a. 3s
b. 2p_x

Question 63

Other factors being constant, a heavy object will have a longer de Broglie wavelength than a light object.

Question 64

Continuous spectra are characteristic of heated solids.

Question 65

As the frequency of electromagnetic radiation increases, its wavelength also increases.

Question 66

The energy of a photon is directly proportional to the wavelength of the radiation.

Question 67

Continuous spectra are characteristic of molecules in the gas phase.

Question 68

What is the speed of an electron in m/s if its wavelength is 0.155 nm?

Question 69

The Rydberg equation is an example of an empirical equation.

Question 70

The following combinations of quantum numbers are not allowed.

Question 71

a. Calculate the momentum of a photon of green light, wavelength 515 nm.
b. If this photon is traveling in a vacuum, what is its "mass"?

Question 72

Line spectra are characteristic of atoms in the gas phase.

Question 73

In the Bohr model of the hydrogen atom, the electron moves in a circular path which Bohr referred to as an orbital.

Question 74

What is the minimum uncertainty in the position of a neutron if the uncertainty in its speed is 0.0250 m/s?

Question 75

In the Rydberg equation, for a fixed value of n₁, the longest wavelength line has n₂ = $\infty$ .

Question 76

The Rydberg equation, giving the wavelengths of lines in the spectrum of the hydrogen atom, was obtained by assuming that energy is quantized.

Question 77

In the quantum mechanical treatment of the hydrogen atom, the functions $\varPsi$ and $\varPsi$ ² both feature prominently. Briefly explain (in principle) how they are obtained and what, if anything, their physical meanings are.

Question 78

Explain the context and meanings of the terms "orbit" and "orbital", making a clear distinction between them.

Question 79

What are the possible values for the following quantum numbers in an atom?
a. n
b. l
c. m_l

Question 80

a. Use the Bohr equation to calculate the energy needed to ionize a hydrogen atom from its ground state.
b. What is the minimum wavelength of a photon needed for it to have the energy needed in (a)?