Exam 38: Particles Behaving As Waves

Calculate the kinetic energy (in eV) of a nonrelativistic neutron that has a de Broglie wavelength of 9.9 × 10^-12m. (h = 6.626 × 10^-34 J ∙ s, mneutron = 1.675 × 10^-27 kg, 1 eV = 1.60 × 10^-19 J)

How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (mel = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

Which of the following are characteristics of laser light? (There may be more than one correct choice.)

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, = 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?

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)

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)

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 collection of atoms has 20% of the sample in a state 5.9 eV above the ground state. If these emit coherent radiation, what is the wavelength of the laser light produced? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

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 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, mel = 9.11 × 10^-31 kg)

How many photons per second emerge from a laser of power 2.00 mW with wavelength 605 nm? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

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

The excited state of a certain atom is 3.2 eV ± 0.21 eV. ( = 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?

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

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)

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, mel = 9.11 × 10^-31 kg)

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? ( = 1.055 × 10^-34 J ∙ s)

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 × 10⁴ m/s? (mproton = 1.67 × 10^-27 kg, c = 3.00 × 10⁸ m/s)

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? ( = 1.055 × 10^-34 J ∙ s = 6.59 × 10^-16 eV ∙ s)

The wavelength of a ruby laser is 694.3 nm. What is the energy difference between the two energy states involved in laser action? (c = 2.9979 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.6022 × 10^-19 J)