35. Special Relativity

(II) What is the speed of an electron after being accelerated from rest by 28,000 V?

FIGURE EX39.16 shows the wave function of an electron. Draw a graph of |ψ(x)|².

A firecracker explodes in reference frame S at t = 1.0 s. A second firecracker explodes at the same position at t = 3.0 s. In reference frame S', which moves in the x-direction at speed v, the first explosion is detected at x' = 4.0 m and the second at x' = -4.0 m. What is the speed of frame S' relative to frame S?

The star Alpha goes supernova. Ten years later and 100 ly away, as measured by astronomers in the galaxy, star Beta explodes. An alien spacecraft passing through the galaxy finds that the distance between the two explosions is 120 ly. According to the aliens, what is the time between the explosions?

The nuclear reaction that powers the sun is the fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply 4p → ⁴He + energy. The mass of a proton, to four significant figures, is 1.673 x 10^-27 kg, and the mass of a helium nucleus is known to be 6.644 x 10^-27 kg. What fraction of the initial rest mass energy is this energy?

How many electrons, protons, and neutrons are contained in the following atoms or ions: (a) ¹⁰B, (b) ¹³N⁺, and (c) ¹⁷O⁺⁺⁺?

Identify the isotope that is 11 times as heavy as ¹²C and has 18 times as many protons as ⁶Li . Give your answer in the form ᴬS, where S is the symbol for the element. See Appendix C: Atomic and Nuclear Data.

Consider the gold isotope ¹⁹⁷Au. The gold nucleus has a diameter of 14.0 fm. What is the density of matter in a gold nucleus?

Figure 37.7 identified the wavelengths of four lines in the Balmer series of hydrogen. Predict the wavelength of the fifth line in the spectrum.

A horizontal beam of laser light of wavelength $585$ nm passes through a narrow slit that has width $0.0620$ mm. The intensity of the light is measured on a vertical screen that is $2.00$ m from the slit.

(a) What is the minimum uncertainty in the vertical component of the momentum of each photon in the beam after the photon has passed through the slit?

(b) Use the result of part (a) to estimate the width of the central diffraction maximum that is observed on the screen.

An ultrashort pulse has a duration of $9.00$ fs and produces light at a wavelength of $556$ nm. What are the momentum and momentum uncertainty of a single photon in the pulse?