Exam 30: Inductance

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)

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)

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

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)

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)

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?

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)

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.