Exam 30: Inductance

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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)

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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)

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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?

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Uncertainty principle using ΔpΔx ≥ h/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, h = 6.626 × 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?

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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)

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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)

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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, mel = 9.11 × 10-31 kg)

(Multiple Choice)
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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, mel = 9.11 × 10-31 kg)

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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

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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)

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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? (mel = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙ s, c = 3.00 × 108 m/s)

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

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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)

(Multiple Choice)
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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, mproton = 1.67 × 10-27 kg)

(Multiple Choice)
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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)

(Multiple Choice)
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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, mel = 9.11 × 10-31 kg)

(Multiple Choice)
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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)

(Short Answer)
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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)

(Multiple Choice)
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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.)

(Multiple Choice)
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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, mel = 9.11 × 10-31 kg)

(Multiple Choice)
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