.. - u .l. E :- " C-D Ill] '3' lIll tlll ilil llll I 1. Find the de Broglie wavelength of (a) a Y-Mev an electron moving at v : 1.35 x 106 mils 2. By doing a nuclear diffraction experiment. proton; (b) a 45-GeV electron; (c) you measure the de Broglie _ What is the speed of the proton? (b) nm; {c} a proton of diameter 1.2 fm. Suppose that we wish to do a doubleslit experiment with a beam of the smoke particles of Example 4.1c. Assume that we can construct a double slit whose separation is about the same size as the particles. Estimate the separation between the fringes if the double slit and the screen were on opposite coasts of the United States . A certain crystal is cut so that the rows of atoms on its surface are separated by a distance of 0.352 nm. A beam of electrons is accelerated through a potential difference of 175 V and is incident normally on the surface. lfall possible diffraction orders could be observed, at what angles (relative to the incident beam) would the diffracted beams be found? . Suppose that a traveling wave has a speed v (where v = 21f). instead of measuring waves over a distance Ax. we stay in one place and count the number of wave crests which pass in a time At. Show that Eq. 4.7 is equivalent to Eq. 4.4 for this case . A wave train of 36 vibrations covers a length of 148 m. What is the minimum uncertainty that can be measured for the wavelength? . The speed of an electron is measured to within an uncertainty of 2.8 x 104 mfs. What is the size of the smallest region of space in which the electron can be conned? . Anucleus emits a gamma ray of energy 1.2 Mev from a state that has a lifetime of 2.1 ns. What is the uncertainty in the energy of the gamma ray? The best gammaray detectors can measure gamma-ray energies to a precision of no better than a few eV. Will this uncertainty be directly measurable