Exam 30: Inductance

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)

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?

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?

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)

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)

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)

Uncertainty principle using ΔEΔt ≥ ħ/2: 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)

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)

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)

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)

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?

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)

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)

Uncertainty principle using ΔpΔx ≥ h/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? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg)

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?

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)

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)

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)

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)

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)