Exam 30: Inductance

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?

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)

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

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)

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

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)

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)

Uncertainty principle using ΔpΔx ≥ h/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, h = 6.626 × 10^-34 J ∙ s, m_proton = 1.67 × 10^-27 kg)

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?

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)

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)

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?

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)

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?

Uncertainty principle using ΔpΔx ≥ h/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? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J)

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)

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)

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)

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)

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)