1 Phy 3031 Modern physics, Spring 2007 Homework set #10. Due at the start of class on Wednesday, March 21, 2007. For numerical answers give two significant digits. The first should be correct, the second can be approximate. 1. Compute the de Broglie wavelength of each of the following particles with kinetic energy Ekinetic = 4.5 KeV. (a) An electron. (b) A proton. (c) An alpha particle. 2. A beam of electrons with kinetic energy 350 eV is incident on a KCl (potassium chloride) crystal whose planes of atoms are d = 0.315 nm apart. The beam of electrons comes in at an angle θ and “reflects” at the same angle θ. Use the geometry as shown in figure 3-16 on page 150 of the textbook. (a) What is the de Broglie wavelength of an electron in the beam? (b) Find all of the angles θ, of the scattering maxima. Hint: this problem is phrased to emphasize the similarity between the Davisson-Germer experiment and the Bragg effect described on pages 147-149. You get 2 points for every correct answer, and 1 point for every answer which is incorrect by a factor of 2. 3. A radar transmitter used to measure the speed of pitched baseballs emits pulses of 2.0 cm wavelength that are 0.25 µs in duration. (a) What is the length of the wave packet produced? (b) To what frequency should the detector be tuned? (c) What must be the minimum bandwidth of the receiver? 4. You are given the task of constructing a double slit experiment for 5 eV electrons. (a) If you wish for the first minimum of the diffraction pattern to occur at 5◦ , what must be the separation of the slits? (b) How far from the slits must the detector be located if the first minima on either side of the central maximum are to be separated by 1 cm? 5. A neutron in an atomic nucleus is bound to other neutrons and protons in the nucleus by the strong nuclear force when it comes within about 1 fm of another particle. (a) What is the approximate kinetic energy of a neutron localized within a box 1 fm on a side? (b) What would be the kinetic energy of an electron localized within a box of the same size?