Deck 30: Inductance

Question 1

Blackbody radiation: 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

Answer 1

λ/2

Question 2

Photon energy: A beam of red light and a beam of violet light each deliver the same power on a surface. For which beam is the number of photons hitting the surface per second the greatest?

A) the red beam
B) the violet beam
C) It is the same for both beams.

Answer 2

the red beam

Question 3

Photoelectric effect: A metal surface has a work function of 1.50 eV. Calculate the maximum kinetic energy, in eV, of electrons ejected from this surface by electromagnetic radiation of wavelength 311 nm. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, e = -1.60 × 10^-19 C, 1 eV = 1.60 × 10^-19 J)

Answer 3

2.50 eV

Question 4

Photon energy: Gamma rays are photons with very high energy. How many visible-light photons with a wavelength of 500 nm would you need to match the energy of a gamma-ray photon with energy (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

A) 1.0 × 10⁶
B) 1.4 × 10⁸
C) 6.2 × 10⁹
D) 3.9 × 10³

Question 5

Photoelectric effect: In a photoelectric effect experiment, electrons emerge from a copper surface with a maximum kinetic energy of 1.10 eV when light shines on the surface. The work function of copper is 4.65 eV. Which one of the following values is closest to the wavelength of the light? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A) 220 nm
B) 150 nm
C) 360 nm
D) 1100 nm

Question 6

Photoelectric effect: A metal having a work function of 2.5 eV is illuminated with white light that has a continuous wavelength band from 400 nm to 700 nm. For which one of the following ranges of the wavelength band in this white light are photoelectrons NOT produced? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A) 500 nm to 700 nm
B) 400 nm to 560 nm
C) 500 nm to 560 nm
D) 400 nm to 500 nm
E) 560 nm to 700 nm

Question 7

Photoelectric effect: When a certain metal is illuminated by light, photoelectrons are observed provided that the wavelength of the light is less than 669 nm. Which one of the following values is closest to the work function of this metal? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A) 1.9 eV
B) 2.0 eV
C) 2.2 eV
D) 2.3 eV

Question 8

Photoelectric effect: Monochromatic light strikes a metal surface and electrons are ejected from the metal. If the intensity of the light is increased, what will happen to the ejection rate and maximum energy of the electrons?

A) greater ejection rate; same maximum energy
B) same ejection rate; greater maximum energy
C) greater ejection rate; greater maximum energy
D) same ejection rate; same maximum energy

Question 9

Photoelectric effect: Light of wavelength 400 nm falls on a metal surface having a work function 1.70 eV. What is the maximum kinetic energy of the photoelectrons emitted from the metal? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s = 4.141 × 10^-15 ev ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 4.52 eV
B) 3.11 eV
C) 1.41 eV
D) 2.82 eV
E) 1.70 eV

Question 10

Matter waves: 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 11

Uncertainty principle: 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 12

Photoelectric effect: Upon being struck by 240-nm photons, a metal ejects electrons with a maximum kinetic energy of What is the work function of this metal? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A) 3.73 eV
B) 3.13 eV
C) 4.33 eV
D) 4.92 eV

Question 13

Photoelectric effect: When a metal surface is illuminated with light of wavelength 437 nm, the stopping potential for photoelectrons is 1.67 V. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, e = -1.60 × 10^-19 C, 1 eV = 1.60 × 10^-19 J, m_el = 9.11 × 10^-31 kg)
(a) What is the work function of the metal, in eV?
(b) What is the maximum speed of the ejected electrons?

Question 14

Photoelectric effect: A metal having a work function of 2.4 eV is illuminated with monochromatic light whose photon energy is 4.0 eV. What is the maximum kinetic energy of the photoelectrons produced by this light? (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 2.6 × 10^-19 J
B) 3.8 × 10^-19 J
C) 4.7 × 10^-19 J
D) 5.5 × 10^-19 J
E) 6.4 × 10^-19 J

Question 15

Uncertainty principle: 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 16

Photon energy: A laser emits light of wavelength 463 nm during a brief pulse that lasts for 25 ms and has a total energy of 1.2 J. How many photons are emitted in that single pulse? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A) 2.8 × 10¹⁸
B) 6.9 × 10¹⁹
C) 3.4 × 10¹⁹
D) 1.1 × 10¹⁷
E) 2.2 × 10¹⁷

Question 17

Photoelectric effect: A stopping potential of 0.50 V is required when a phototube is illuminated with monochromatic light of wavelength 590 nm. Monochromatic light of a different wavelength is now shown on the tube, and the stopping potential is measured to be 2.30 V. What is the wavelength of this new light? (c = 3.00 × 10⁸ m/s, e = -1.60 × 10^-19 C, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 320 nm
B) 300 nm
C) 340 nm
D) 360 nm
E) 410 nm

Question 18

Photon energy: A light beam from a 2.1-mW He-Ne laser has a wavelength of 633 nm. How many photons does the laser emit in one second? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

A) 6.7 × 10¹⁵
B) 8.8 × 10¹⁵
C) 1.1 × 10¹⁶
D) 1.3 × 10¹⁶

Question 19

Photon energy: An 84-kW AM radio station broadcasts at 1000 kHz. How many photons are emitted each second by the transmitting antenna? (h = 6.626 × 10^-34 J ∙ s)

A) 1.3 ×
B) 2.9 ×
C) 6.3 ×
D) 1.4 ×

Question 20

Photoelectric effect: A metal having a work function of 2.8 eV is illuminated with monochromatic light whose photon energy is 3.9 eV. What is the threshold frequency for photoelectron production? (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 6.8 × 10¹⁴ Hz
B) 2.7 × 10¹⁴ Hz
C) 7.6 × 10¹⁴ Hz
D) 8.5 × 10¹⁴ Hz
E) 9.4 × 10¹⁴ Hz

Question 21

Bohr atom: What is the orbital radius of the 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) 0.477 nm
B) 0.159 nm
C) 0.382 nm
D) 0.549 nm

Question 22

Bohr atom: 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 23

Bohr atom: 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 24

Bohr atom: 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 25

Blackbody radiation: 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 26

Compton scattering: In a particular case of Compton scattering, a photon collides with a free electron and scatters backwards. The wavelength after the collision is exactly double the wavelength before the collision. What is the wavelength of the incident photon? (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

A) 3.6 pm
B) 4.8 pm
C) 2.4 pm
D) 1.2 pm
E) 6.0 pm

Question 27

Bohr atom: 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 28

Bohr atom: 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?

Question 29

Blackbody radiation: 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 30

Bohr atom: A hydrogen atom is in its n = 2 excited state when its electron absorbs a photon of energy . 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) 7.7 eV

Question 31

Bohr atom: 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 32

Bohr atom: 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 33

Bohr atom: A hydrogen atom makes a downward transition from the 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 34

Bohr atom: 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 35

Compton scattering: A beam of X-rays at a certain wavelength are scattered from a free electron at rest and the scattered beam is observed at 45.0° to the incident beam. What is the change in the wavelength of the X-rays? (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

A) 0.175 pm
B) 0.276 pm
C) 0.000 pm
D) 0.356 pm
E) 0.710 pm

Question 36

Compton scattering: A photon of wavelength 29 pm is scattered by a stationary electron. What is the maximum possible energy loss of the photon? (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

A) 4.0 keV
B) 7.0 keV
C) 10 keV
D) 6.1 keV
E) 12 keV

Question 37

Bohr atom: 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

Question 38

Compton scattering: A photon of initial wavelength 0.651 nm, after being scattered from a free electron at rest, moves off at an angle of 120° with respect to its incident direction. (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)
(a) What is the wavelength of the scattered photon?
(b) What is the energy of the scattered photon?

Question 39

Compton scattering: A photon of wavelength 18.0 pm is scattered through an angle of 120° by a stationary electron. What is the wavelength of the scattered photon? (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

A) 19.2 pm
B) 20.4 pm
C) 21.6 pm
D) 22.9 pm
E) 24.1 pm

Question 40

Compton scattering: X-rays of energy 2.9 × 10⁴ eV are scattered by a free stationary electron through an angle of 135°. What is the energy of the scattered X-rays, in electron volts? (m_el = 9.11 × 10^-31 kg, e = -1.60 × 10^-19 C, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

Question 41

Blackbody radiation: 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 42

Matter waves: 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? (m_el = 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 43

Uncertainty principle using ΔxΔp ≥ ħ: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 (ħ = 1.055 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg)

A) 1.05 × 10⁶ m/s
B) 1.50 × 10⁶ m/s
C) 1.05 × 10⁸ m/s
D) 1.50 × 10⁸ m/s
E) 1.05 × 10¹⁰ m/s

Question 44

Matter waves: 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? (m_el = 9.11 × 10^-31 kg, m_neutron = 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 45

Matter waves: 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, m_el = 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 46

Uncertainty principle using ΔxΔp ≥ ħ: 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? (ħ = 1.055 × 10^-34 J ∙ s)

A) 0.25 m/s
B) 2.5 m/s
C) 25 m/s
D) 0.025 m/s
E) 0.0025 m/s

Question 47

Matter waves: How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (m_el = 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 48

Matter waves: 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 × m/s? (m_proton = 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 49

Uncertainty principle using ΔxΔp ≥ ħ: 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, ħ = 1.055 × 10^-34 J ∙ s, m_proton = 1.67 × 10^-27 kg)

A) 0.52 eV
B) 5.2 eV
C) 52 eV
D) 520 eV
E) 5200 eV

Question 50

Blackbody radiation: 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 51

Matter waves: 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 52

Uncertainty principle using ΔxΔp ≥ ħ: 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 × 10^{7 s}, ħ = 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 53

Matter waves: A single slit is illuminated at normal incidence with a parallel beam of light having a wavelength of 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, m_el = 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 54

Uncertainty principle using ΔxΔp ≥ ħ: 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? (ħ = 1.055 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J)

A) 0.0015 eV
B) 0.015 eV
C) 0.15 eV
D) 1.5 eV
E) 15 eV

Question 55

Matter waves: 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, m_el = 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 56

Matter waves: 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, m_el = 9.11 × 10^-31 kg)

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

Question 57

Uncertainty principle using ΔxΔp ≥ ħ: 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? (ħ = 1.055 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg)

A) 0.29 nm
B) 0.58 nm
C) 0.87 nm
D) 1.2 nm
E) 1.6 nm

Question 58

Blackbody radiation: 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 59

Matter waves: Calculate the kinetic energy (in eV) of a nonrelativistic neutron that has a de Broglie wavelength of (h = 6.626 × 10^-34 J ∙ s, m_neutron = 1.675 × 10^-27 kg, 1 eV = 1.60 × 10^-19 J)

Question 60

Blackbody radiation: 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 61

Uncertainty principle using ΔpΔx ≥ ħ/2: 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? (ħ = 1.055 × 10^-34 J ∙ s, m_el = 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 62

Uncertainty principle using ΔpΔx ≥ ħ/2: 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? (ħ = 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 63

Uncertainty principle using ΔEΔt ≥ ħ: 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. (ħ = 1.055 × 10^-34 J ∙ s = 6.59 × 10^-16 eV ∙ s)

Question 64

Uncertainty principle using ΔEΔt ≥ ħ/2: The lifetime of an excited nuclear state is 1.0 ns. What is the minimum uncertainty in the energy of this state? (ħ = 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 65

Uncertainty principle using ΔpΔx ≥ ħ/2: 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? (ħ = 1.055 × 10^-34 J ∙ s, m_el = 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 66

Uncertainty principle using ΔEΔt ≥ ħ: The excited state of a certain atom is 3.2 eV ± 0.21 eV. (ħ = 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 67

Uncertainty principle using ΔEΔt ≥ ħ: 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? (ħ = 1.055 × 10^-34 J ∙ s = 6.59 × 10^-16 eV ∙ s, c = 3.00 × 10⁸ m/s)

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

Question 68

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

A) 1.1 × 10^{-15 s}
B) 1.1 × 10^{-14 s}
C) 1.1 × 10^{-13 s}
D) 1.1 × 10^{-12 s}
E) 1.1 × 10^{-16 s}

Question 69

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

A) 1.32 × 10^{-15 s}
B) 8.28 × 10^{-15 s}
C) 1.32 × 10^{-11 s}
D) 8.28 × 10^{-11 s}
E) 1.32 × 10^{-8 s}

Question 70

Uncertainty principle using ΔEΔt ≥ ħ/2: The energy of an electron state has an uncertainty of 0.500 eV. What is the minimum uncertainty in the lifetime of the level? (ħ = 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 71

Uncertainty principle using ΔpΔx ≥ ħ/2: 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? (ħ = 1.055 × 10^-34 J ∙ s, m_el = 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 72

Uncertainty principle using ΔEΔt ≥ ħ/2: 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? (ħ = 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 73

Uncertainty principle using ΔEΔt ≥ ħ: 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? (ħ = 1.055 × 10^-34 J ∙ s = 6.59 × 10^-16 eV ∙ s)

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

Question 74

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

A) 1.0 × 10^{-9 eV}
B) 1.0 × 10^{-25 eV}
C) 6.6 × 10^{-25 eV}
D) 3.3 × 10^{-7 eV}
E) 6.6 × 10^{-7 eV}

Question 75

Uncertainty principle using ΔEΔt ≥ ħ/2: The excited state of a certain atom is 3.2 eV ±0.21 eV. ( ħ = 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 76

Uncertainty principle using ΔpΔx ≥ ħ/2: 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, ħ = 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 77

Uncertainty principle using ΔEΔt ≥ ħ/2: 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? (ħ = 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 78

Uncertainty principle using ΔpΔx ≥ ħ/2: 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, ħ = 1.055 × 10^-34 J ∙ s, m_proton = 1.67 × 10^-27 kg)

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

Question 79

Uncertainty principle using ΔEΔt ≥ ħ/2: 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? (ħ = 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 80

Uncertainty principle using ΔEΔt ≥ ħ: 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? (ħ = 1.055 × 10^-34 J ∙ s = 6.59 × 10^-16 eV ∙ s)

A) 5 × 10^-6 s
B) 5 × 10^-7 s
C) 5 × 10^-8 s
D) 5 × 10^-9 s
E) 5 × 10^-10 s