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?

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.

For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 0.010a_B at distance (a) ½ a_B, (b) a_B, and (c) 2a_B 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 > a_B from the proton?

A sample of 1.0 x 10¹⁰ atoms that decay by alpha emission has a half-life of 100 min. How many alpha particles are emitted between t = 50 min and t = 200 min?