Exam 30: Inductance

Uncertainty principle using ΔEΔt ≥ ħ: 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)

Bohr atom: The Bohr radius of the hydrogen atom is 0.529 × 10^-10 m. What is the radius of the n = 2 state?

Matter waves: A gas of helium atoms (each of mass 6.65 × 10^-27 kg) are at room temperature of 20.0°C. What is the de Broglie wavelength of the helium atoms that are moving at the root-mean-square speed? (h = 6.626 × 10^-34 J ∙ s, the Boltzmann constant is 1.38 × 10^-23 J/K)

Bohr atom: Light excites atomic hydrogen from its lowest level to the n = 4 level. What is the energy of the light? The energy of the lowest level is -13.6 eV.

Photoelectric effect: A metal surface has a work function of 1.50 eV. Calculate the maximum kinetic energy, in eV, of electrons ejected from this surface by electromagnetic radiation of wavelength 311 nm. (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)

Bohr atom: Suppose that in a parallel universe, the proton and electron were identical to their counterparts in our own universe EXCEPT that the electron had twice as much charge as our electron. In our present universe, the radius of the first Bohr orbit for hydrogen is a₀ and the speed of an electron in that orbit is v₀. In the parallel universe, (a) what would be the radius (in terms of a₀) of the first Bohr orbit for hydrogen? (b) what would be the speed (in terms of v₀) of an electron in the first Bohr orbit for hydrogen?

Matter waves: Calculate the kinetic energy (in eV) of a nonrelativistic neutron that has a de Broglie wavelength of (h = 6.626 × 10^-34 J ∙ s, m_neutron = 1.675 × 10^-27 kg, 1 eV = 1.60 × 10^-19 J)

Compton scattering: A photon of initial wavelength 0.651 nm, after being scattered from a free electron at rest, moves off at an angle of 120° with respect to its incident direction. (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s) (a) What is the wavelength of the scattered photon? (b) What is the energy of the scattered photon?

Uncertainty principle using ΔEΔt ≥ ħ: A certain particle's energy is measured by a detector to within 1.0 × 10^-18 J. What is the minimum uncertainty we can have in its arrival time at the detector? (ħ = 1.055 × 10^-34 J ∙ s)

Photoelectric effect: A stopping potential of 0.50 V is required when a phototube is illuminated with monochromatic light of wavelength 590 nm. Monochromatic light of a different wavelength is now shown on the tube, and the stopping potential is measured to be 2.30 V. What is the wavelength of this new light? (c = 3.00 × 10⁸ m/s, e = -1.60 × 10^-19 C, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

Bohr atom: Light shines through atomic hydrogen gas. It is seen that the gas absorbs light readily at a wavelength of 91.63 nm. What is the value of n of the level to which the hydrogen is being excited by the absorption of light of this wavelength? Assume that the most of the atoms in the gas are in the lowest level. (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J; the Rydberg constant is R = 1.097 × 10⁷ m^-1.)

Uncertainty principle using ΔxΔp ≥ ħ: 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)

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

Uncertainty principle using ΔEΔt ≥ ħ: 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? (ħ = 1.055 × 10^-34 J ∙ s = 6.59 × 10^-16 eV ∙ s)

Bohr atom: A hydrogen atom initially in the n = 6 state decays to the n = 2 state. The emitted photon is detected in a photographic plate. What is the wavelength 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, c = 3.00 × 10⁸ m/s)

Uncertainty principle using ΔEΔt ≥ ħ/2: 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? (ħ = 1.055 × 10^-34 J ∙ s = 6.59 × 10^-16 eV ∙ s)

Matter waves: 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.)

Uncertainty principle using ΔEΔt ≥ ħ/2: 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)

Photon energy: A light beam from a 2.1-mW He-Ne laser has a wavelength of 633 nm. How many photons does the laser emit in one second? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

Matter waves: Electrons emerge from an electron gun with a speed of 2.0 × 10⁶ m/s and then pass through a pair of thin parallel slits. Interference fringes with a spacing of 2.7 mm are detected on a screen far from the double slit and fairly close to the center of the pattern. What would the fringe spacing be if the electrons were replaced by neutrons with the same speed? (m_el = 9.11 × 10^-31 kg, m_neutron = 1.67 × 10^-27 kg)