Deck 38: Particles Behaving As Waves

Question 1

What is the frequency of the light emitted by atomic hydrogen with m = 8 and n = 12? (The Rydberg constant is R = 1.097 × 10⁷ m^-1, c = 3.00 × 10⁸ m/s)

A) 2.86 × 10¹³ Hz
B) 1.43 × 10¹³ Hz
C) 7.46 × 10¹³ Hz
D) 8.82 × 10¹³ Hz
E) 1.05 × 10¹³ Hz

Answer 1

2.86 × 10¹³ Hz

Question 2

Suppose that in a parallel universe, the proton and electron were identical to their counterparts in our own universe EXCEPT that the electron had twice as much charge as our electron. In our present universe, the radius of the first Bohr orbit for hydrogen is a0 and the speed of an electron in that orbit is v₀. In the parallel universe
(a) what would be the radius (in terms of a₀) of the first Bohr orbit for hydrogen?
(b) what would be the speed (in terms of v₀) of an electron in the first Bohr orbit for hydrogen?

Answer 2

(a) a₀/2
(b) 2v₀

Question 3

What is the orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom? The ground-state radius of the hydrogen atom is 0.529 × 10^-10 m.

A) 0.476 nm
B) 0.159 nm
C) 0.381 nm
D) 0.548 nm

Answer 3

0.476 nm

Question 4

What is the wavelength of peak emission for a black body at 37°C? (c = 3.0 × 10⁸ m/s, Wien displacement law constant is 2.9 × 10^-3 m ∙ K, σ = 5.67 × 10^-8 W/m² ∙ K⁴)

A) 94 µm
B) 9.4 µm
C) 29 µm
D) 7.8 µm
E) 78 µm

Question 5

A hydrogen atom is in its n = 2 excited state when its electron absorbs a photon of energy 8.5 eV. What is the energy of the resulting free electron? The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 5.1 eV
B) 6.6 eV
C) 6.9 eV
D) 7.6 eV

Question 6

A perfectly black body at 100°C emits light of intensity I that has the strongest intensity near wavelength λ. The temperature of this body is now increased to 200°C.
(a) In terms of I, what is the intensity at which this hotter body radiates?
(b) In terms of λ, near what wavelength does light radiated from this hotter body have the strongest intensity?

Question 7

The Bohr radius of the hydrogen atom is 0.529 × 10^-10 m. What is the radius of the n = 2 state?

A) 1.06 × 10^-10 m
B) 2.12 × 10^-10 m
C) 0.265 × 10^-10 m
D) 0.529 × 10^-10 m
E) 4.23 × 10^-10 m

Question 8

A hydrogen atom makes a downward transition from the n = 20 state to the n = 5 state. Find the wavelength of the emitted photon. The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s)

A) 2.43 μm
B) 1.46 μm
C) 1.94 μm
D) 2.92 μm

Question 9

The energy of the ground state in the Bohr model of the hydrogen atom is -13.6 eV. The energy of the n = 2 state of hydrogen in this model is closest to

A) -3.4 eV.
B) -6.8 eV.
C) -1.7 eV.
D) -13.6 eV.
E) -4.5 eV.

Question 10

If the accuracy in measuring the position of a particle increases, the accuracy in measuring its velocity will

A) increase.
B) decrease.
C) remain the same.
D) It is impossible to say since the two measurements are independent and do not affect each other.

Question 11

A hydrogen atom is excited to the n = 10 stated. It then decays to the n = 4 state by emitting a photon which is detected in a photographic plate. What is the frequency of the detected photon? The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 3.46 × 10¹⁴ Hz
B) 0.865 × 10¹⁴ Hz
C) 1.27 × 10¹⁴ Hz
D) 4.05 × 10¹⁴ Hz
E) 1.73 × 10¹⁴ Hz

Question 12

In the vicinity of what frequency does an object with a temperature of 1000 K radiate the largest amount of power? (c = 3.00 × 10⁸ m/s, Wien displacement law constant equals 2.90 × 10^-3 m ∙ K, σ = 5.670 × 10^-8 W/m² ∙ K⁴)

A) 1.0 × 10¹⁴ Hz
B) 8.0 × 10¹⁴ Hz
C) 2.3 × 10¹⁴ Hz
D) 6.7 × 10¹⁴ Hz
E) 4.1 × 10¹⁴ Hz

Question 13

At absolute temperature T, a black body radiates its peak intensity at wavelength λ. At absolute temperature 2T, what would be the wavelength of the peak intensity?

A) 16λ
B) 2λ
C) λ
D) λ/2
E) λ/16

Question 14

Which of the following are characteristics of laser light? (There may be more than one correct choice.)

A) It is coherent.
B) It is produced by an inverted population of atoms.
C) It contains a full spectrum of wavelengths.

Question 15

Light excites atomic hydrogen from its lowest level to the n = 4 level. What is the energy of the light? The energy of the lowest level is -13.6 eV.

A) 12.8 eV
B) 3.40 eV
C) 0.850 eV
D) 26.4 eV

Question 16

Light shines through atomic hydrogen gas. It is seen that the gas absorbs light readily at a wavelength of 91.63 nm. What is the value of n of the level to which the hydrogen is being excited by the absorption of light of this wavelength? Assume that the most of the atoms in the gas are in the lowest level. (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J, the Rydberg constant is R = 1.097 × 10⁷ m^-1)

A) 14
B) 16
C) 11
D) 21

Question 17

The energy of the ground state in the Bohr model of the hydrogen atom is -13.6 eV. In a transition from the n = 2 state to the n = 4 state, a photon of energy

A) 3.40 eV is emitted.
B) 3.40 eV is absorbed.
C) 2.55 eV is emitted.
D) 2.55 eV is absorbed.
E) 0.85 eV is absorbed.

Question 18

A hydrogen atom initially in the n = 6 state decays to the n = 2 state. The emitted photon is detected in a photographic plate. What is the wavelength of the detected photon? The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s)

A) 410 nm
B) 93.8 nm
C) 1090 nm
D) 93.1 nm

Question 19

If the accuracy in measuring the velocity of a particle increases, the accuracy in measuring its position will

A) increase.
B) decrease.
C) remain the same.
D) It is impossible to say since the two measurements are independent and do not affect each other.

Question 20

A nonrelativistic electron and a nonrelativistic proton have the same de Broglie wavelength. Which of the following statements about these particles are accurate? (There may be more than one correct choice.)

A) Both particles have the same speed.
B) Both particles have the same kinetic energy.
C) Both particles have the same momentum.
D) The electron has more kinetic energy than the proton.
E) The electron has more momentum than the proton.

Question 21

A perfectly black sphere 18.0 cm in diameter is held at a temperature of 215°C. (σ = 5.670 × 10-8 W/m² ∙ K⁴, Wien displacement law constant is 2.90 × 10^-3 m ∙ K, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)
(a) Near what wavelength does this sphere radiate most strongly?
(b) If all the radiated energy were at the wavelength found in part (a), how many photons would the sphere emit each second?

Question 22

A small dust particle of mass 7.90 × 10^-6 g is being observed under a magnifying lens. Its position is determined to within 0.0050 mm. (1 y = 3.156 × 10⁷ s, = 1.055 × 10^-34 J ∙ s)
(a) Find the minimum uncertainty in its velocity implied by the uncertainty in its position.
(b) Assuming the dust particle is moving at the speed you just found, how many years would it take for the particle to move 1.0 mm?

Question 23

In a double slit experiment, a beam of electrons strikes a pair of slits. The slits are 15 μm apart, and the first interference maximum lies at an angle of 0.50 µrad from the center of the interference pattern. What is the momentum of the incoming electrons? (h = 6.626 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg)

A) 4.4 × 10^-23 kg ∙ m/s
B) 2.2 × 10^-23 kg ∙ m/s
C) 1.1 × 10^-23 kg ∙ m/s
D) 6.6 × 10^-23 kg ∙ m/s
E) 8.8 × 10^-23 kg ∙ m/s

Question 24

A nonrelativistic electron is confined to a length of 500 pm on the x-axis. What is the kinetic energy of the electron if its speed is equal to the minimum uncertainty possible in its speed? ( = 1.055 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J)

A) 0.00038 eV
B) 0.0038 eV
C) 0.038 eV
D) 0.38 eV
E) 3.8 eV

Question 25

What is the energy of a photon that has a wavelength equal to the de Broglie wavelength of a proton having a speed of 7.1 × 10⁴ m/s? (mproton = 1.67 × 10^-27 kg, c = 3.00 × 10⁸ m/s)

A) 220 keV
B) 150 keV
C) 290 keV
D) 360 keV
E) 440 keV

Question 26

A gas of helium atoms (each of mass 6.65 × 10^-27 kg) are at room temperature of 20.0°C. What is the de Broglie wavelength of the helium atoms that are moving at the root-mean-square speed? (h = 6.626 × 10^-34 J ∙ s, the Boltzmann constant is 1.38 × 10-23 J/K)

A) 5.22 × 10^-11 m
B) 7.38 × 10^-11 m
C) 1.04 × 10^-10 m
D) 2.82 × 10^-10 m
E) 3.99 × 10^-10 m

Question 27

A nonrelativistic electron is accelerated from rest through a potential difference. After acceleration the electron has a de Broglie wavelength of 880 nm. What is the potential difference though which this electron was accelerated? (h = 6.626 × 10^-34 J ∙ s, e = - 1.60 × 10^-19 C, mel = 9.11 × 10^-31 kg)

A) 1.9 µV
B) 1.7 µV
C) 2.2 µV
D) 2.5 µV

Question 28

A nonrelativistic electron has a kinetic energy of 5.4 eV. What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? (mel = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A) 2.4 keV
B) 2.2 keV
C) 2.0 keV
D) 2.5 keV
E) 2.7 keV

Question 29

An electron inside a hydrogen atom is confined to within a space of 0.110 nm. What is the minimum uncertainty in the electron's velocity? ( = 1.055 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg)

A) 5.26 × 10⁵ m/s
B) 7.50 × 10⁵ m/s
C) 5.26 × 10⁷ m/s
D) 7.50 × 10⁷ m/s
E) 5.26 × 10⁹ m/s

Question 30

How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (mel = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A) 2000 m/s
B) 1900 m/s
C) 1700 m/s
D) 1600 m/s
E) 1400 m/s

Question 31

An electric current through a tungsten filament maintains its temperature at 2800 K. Assume the tungsten filament behaves as an ideal radiator at that temperature. Near what wavelength does the filament emit the greatest power? (σ = 5.67 × 10-8 W/m² ∙ K⁴, Wien displacement law constant is 2.9 × 10^-3 m ∙ K)

A) 1000 nm
B) 1200 nm
C) 1400 nm
D) 1600 nm
E) 1800 nm

Question 32

A single slit is illuminated at normal incidence with a parallel beam of light having a wavelength of 411 nm. The entire central band of the diffraction pattern is observed at ±90°. The illumination is now replaced by a nonrelativistic beam of electrons, each having a kinetic energy of 980 eV. When this beam hits the slit at normal incidence, at what angle will the first minimum of the electron diffraction pattern occur? (h = 6.626 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J)

A) 0.095 mrad
B) 0.071 mrad
C) 0.046 mrad
D) 0.12 mrad
E) 0.14 mrad

Question 33

A molecule of roughly spherical shape has a mass of 6.10 × 10^-25 kg and a diameter of 0.70 nm. The uncertainty in the measured position of the molecule is equal to the molecular diameter. What is the minimum uncertainty in the speed of this molecule? ( = 1.055 × 10^-34 J ∙ s)

A) 0.12 m/s
B) 1.2 m/s
C) 12 m/s
D) 0.012 m/s
E) 0.0012 m/s

Question 34

Electrons emerge from an electron gun with a speed of 2.0 × 10⁶ m/s and then pass through a pair of thin parallel slits. Interference fringes with a spacing of 2.7 mm are detected on a screen far from the double slit and fairly close to the center of the pattern. What would the fringe spacing be if the electrons were replaced by neutrons with the same speed? (mel = 9.11 × 10^-31 kg, mneutron = 1.67 × 10^-27 kg)

A) 1.5 µm
B) 4.9 µm
C) 0.93 nm
D) 1.1 µm
E) 1.5 nm

Question 35

A measurement of an electron's speed is 2.0 × 10⁶ m/s and has an uncertainty of 10%. What is the minimum uncertainty in its position? ( = 1.055 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg)

A) 0.15 nm
B) 0.29 nm
C) 0.44 nm
D) 0.60 nm
E) 0.80 nm

Question 36

A nonrelativistic proton is confined to a length of 2.0 pm on the x-axis. What is the kinetic energy of the proton if its speed is equal to the minimum uncertainty possible in its speed? (1 eV = 1.60 × 10^-19 J, = 1.055 × 10^-34 J ∙ s, mproton = 1.67 × 10^-27 kg)

A) 0.13 eV
B) 1.3 eV
C) 13 eV
D) 130 eV
E) 1300 eV

Question 37

An electric current through a tungsten filament maintains its temperature at 2800 K. Assume the tungsten filament behaves as an ideal radiator at that temperature. If the radiating area of the filament is 2.0 × 10^-6 m², at what rate does it radiate energy? (σ = 5.670 × 10^-8 W/m² ∙ K⁴, Wien displacement law constant is 2.90 × 10^-3 m ∙ K)

A) 5.5 W
B) 7.0 W
C) 8.5 W
D) 10 W
E) 11.5 W

Question 38

The excited state of a certain atom is 3.2 eV ± 0.21 eV. ( = 1.055 × 10^-34 J ∙ s = 6.591 × 10^-16 eV ∙ s, 1 eV = 1.60 × 10^-19 J)
(a) What is the average lifetime of this state?
(b) If the excited energy were doubled to 6.4 eV ± 0.21 eV, how would the lifetime be affected?

Question 39

Calculate the kinetic energy (in eV) of a nonrelativistic neutron that has a de Broglie wavelength of 9.9 × 10^-12m. (h = 6.626 × 10^-34 J ∙ s, mneutron = 1.675 × 10^-27 kg, 1 eV = 1.60 × 10^-19 J)

Question 40

Light of wavelength 105 nm falls on a metal surface for which the work function is 5.00 eV. What is the minimum de Broglie wavelength of the photoelectrons emitted from this metal? (h = 6.626 × 10^-34 J ∙ s = 4.14 × 10^-15 eV ∙ s, c = 3.00 × 10⁸ m/s, mel = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J)

A) 0.24 nm
B) 0.33 nm
C) 0.47 nm
D) 0.66 nm
E) 0.94 nm

Question 41

The wavelength of a ruby laser is 694.3 nm. What is the energy difference between the two energy states involved in laser action? (c = 2.9979 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.6022 × 10^-19 J)

A) 1.537 eV
B) 1.646 eV
C) 1.786 eV
D) 1.812 eV
E) 3.572 eV

Question 42

You need 14 W of infrared laser light power with wavelength 1270 nm to bore a hole in a diamond. How many downward atomic transitions per second must occur in the laser if all of them result in light directed onto the diamond? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A) 8.9 × 10¹⁹
B) 8.9 × 10¹⁸
C) 5.9 × 10¹⁹
D) 2.7 × 10¹⁸

Question 43

The lifetime of an excited nuclear state is 1.0 ns. What is the minimum uncertainty in the energy of this state? ( = 1.055 × 10^-34 J ∙ s = 6.591 × 10^-16 eV ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 5.0 × 10^-10 eV
B) 5.0 × 10^-26 eV
C) 3.3 × 10^-25 eV
D) 1.6 × 10^-7 eV
E) 3.3 × 10^-7 eV

Question 44

The energy of an electron state has an uncertainty of 0.500 eV. What is the minimum uncertainty in the lifetime of the level? ( = 1.055 × 10^-34 J ∙ s = 6.591 × 10^-16 eV ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 6.59 × 10^-16 s
B) 4.14 × 10^-15 s
C) 6.59 × 10^-12 s
D) 4.14 × 10^-11 s
E) 6.59 × 10^-9 s

Question 45

In a ruby laser, an electron jumps from a higher energy level to a lower one. If the energy difference between the two levels is 1.8 eV, what is the wavelength of the emitted photon? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 350 nm
B) 470 nm
C) 650 nm
D) 690 nm
E) 960 nm

Question 46

A laser produces a beam of 4000-nm light. A shutter allows a pulse of light, 30 ps in duration, to pass. Which of the following is closest to the uncertainty in the energy of a photon in the pulse? ( = 1.055 × 10^-34 J ∙ s = 6.59 × 10^-16 eV ∙ s)

A) 10^-6 eV
B) 10^-5 eV
C) 10^-4 eV
D) 10^-3 eV
E) 10^-2 eV

Question 47

A certain particle's energy is measured by a detector to within 1.0 × 10-18. What is the minimum uncertainty we can have in its arrival time at the detector? ( = 1.055 × 10^-34 J ∙ s)

A) 5.3 × 10^-16 s
B) 5.3 × 10^-15 s
C) 5.3 × 10^-14 s
D) 5.3 × 10^-13 s
E) 5.3 × 10^-17 s

Question 48

An ultraviolet source produces a monochromatic beam of 200-nm light. A shutter allows a pulse to pass that is 10,000 wavelengths long. The uncertainty in the energy of a photon in this pulse is closest to which of the following? ( = 1.055 × 10^-34 J ∙ s = 6.59 × 10^-16 eV ∙ s, c = 3.00 × 10⁸ m/s)

A) 5 × 10^-7 eV
B) 5 × 10^-6 eV
C) 5 × 10^-5 eV
D) 5 × 10^-4 eV
E) 5 × 10^-3 eV

Question 49

An unstable particle produced in a high-energy collision is measured to have an energy of 483 MeV and an uncertainty in energy of 84 keV. Use the Heisenberg uncertainty principle to estimate the lifetime of this particle. ( = 1.055 × 10^-34 J ∙ s = 6.59 × 10^-16 eV ∙ s)

Question 50

A collection of atoms has 20% of the sample in a state 5.9 eV above the ground state. If these emit coherent radiation, what is the wavelength of the laser light produced? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 210 nm
B) 91 nm
C) 340 nm
D) 34 nm

Question 51

A 440-nm spectral line is produced by a transition from an excited state to the ground state. The natural line width of the spectral line is 0.020 pm. The average time the atom spends in the excited state is closest to which of the following? ( = 1.055 × 10^-34 J ∙ s = 6.59 × 10^-16 eV ∙ s)

A) 2.5 × 10^-6 s
B) 2.5 × 10^-7 s
C) 2.5 × 10^-8 s
D) 2.5 × 10^-9 s
E) 2.5 × 10^-10 s

Question 52

How many photons per second emerge from a laser of power 2.00 mW with wavelength 605 nm? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A) 6.09 × 10¹⁵ photons/s
B) 5.03 × 10¹² photons/s
C) 3.07 × 10¹⁵ photons/s
D) 3.07 × 10¹³ photons/s