BackThe energy-level scheme for the hypothetical one-electron element Searsium is shown in Fig. . The potential energy is taken to be zero for an electron at an infinite distance from the nucleus. An -eV photon is absorbed by a Searsium atom in its ground level. As the atom returns to its ground level, what possible energies can the emitted photons have? Assume that there can be transitions between all pairs of levels.
-g marble is gently placed on a horizontal tabletop that is m wide.
(a) What is the maximum uncertainty in the horizontal position of the marble?
(b) According to the Heisenberg uncertainty principle, what is the minimum uncertainty in the horizontal velocity of the marble?
(c) In light of your answer to part (b), what is the longest time the marble could remain on the table? Compare this time to the age of the universe, which is approximately billion years. (Hint: Can you know that the horizontal velocity of the marble is exactly zero?)
In one experiment, 2000 photons are detected in a 0.10-mm-wide strip where the amplitude of the electromagnetic wave is 10 V/m. How many photons are detected in a nearby 0.10-mm-wide strip where the amplitude is 30 V/m?
When 5×1012 photons pass through an experimental apparatus, 2.0×109 land in a 0.10-mm-wide strip. What is the probability density at this point?
FIGURE EX39.12 shows the probability density for an electron that has passed through an experimental apparatus. If 1.0×106 electrons are used, what is the expected number that will land in a 0.010-mm-wide strip at 2.000 mm?
FIGURE EX39.13 shows the probability density for an electron that has passed through an experimental apparatus. What is the probability that the electron will land in a 0.010-mm-wide strip at x = 0.000 mm?
A 1.5-μm-wavelength laser pulse is transmitted through a 2.0-GHz-bandwidth optical fiber. How many oscillations are in the shortest-duration laser pulse that can travel through the fiber?
What minimum bandwidth is needed to transmit a pulse that consists of 100 cycles of a 1.0 MHz oscillation?
What is the minimum uncertainty in position, in nm, of an electron whose velocity is known to be between 3×105 m/s and 4 ×105 m/s? Give your answer to one significant figure.
FIGURE P39.28 shows a pulse train. The period of the pulse train is T = 2 Δt, where Δt is the duration of each pulse. What is the maximum pulse-transmission rate (pulses per second) through an electronics system with a 200 kHz bandwidth? (This is the bandwidth allotted to each FM radio station.)
Consider a single-slit diffraction experiment using electrons. (Single-slit diffraction was described in Section 33.4.) Using Figure 39.5 as a model, draw A graph of |ψ(x)|2 for the electrons on the detection screen.
A pulse of light is created by the superposition of many waves that span the frequency range f₀ − (1/2) Δf ≤ f ≤ f₀ + (1/2) Δf, where f₀ = c/λ is called the center frequency of the pulse. Laser technology can generate a pulse of light that has a wavelength of 600 nm and lasts a mere 6.0 fs (1 fs = 1 femtosecond =10−15 s). What is the spatial length of the laser pulse as it travels through space?
For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 0.010aB at distance (a) ½ aB, (b) aB, and (c) 2aB from the proton?
What is the angular momentum of a hydrogen atom in (a) a 6s state and (b) a 4f state? Give your answers as a multiple of ℏ .
What is the probability of finding a 1s hydrogen electron at distance r > aB from the proton?