Problem 1
(a) An electron moves with a speed of 4.70 \(\times\) 10\(^6\) m/s. What is its de Broglie wavelength? (b) A proton moves with the same speed. Determine its de Broglie wavelength.
Problem 2
For crystal diffraction experiments (discussed in Section 39.1), wavelengths on the order of 0.20 nm are often appropriate. Find the energy in electron volts for a particle with this wavelength if the particle is (a) a photon; (b) an electron; (c) an alpha particle (\(m\) = 6.64 \(\times\) 10\(^{-27}\) kg).
Problem 3
An electron has a de Broglie wavelength of 2.80 \(\times\) 10\(^{-10}\) m. Determine (a) the magnitude of its momentum and (b) its kinetic energy (in joules and in electron volts).
Problem 4
An alpha particle (\(m = 6.64 \times 10^{-27} kg\)) emitted in the radioactive decay of uranium-238 has an energy of 4.20 MeV. What is its de Broglie wavelength?
Problem 5
An electron is moving with a speed of 8.00 \(\times\) 10\(^6\) m/s. What is the speed of a proton that has the same de Broglie wavelength as this electron?
Problem 6
(a) A nonrelativistic free particle with mass \(m\) has kinetic energy \(K\). Derive an expression for the de Broglie wavelength of the particle in terms of \(m\) and \(K\). (b) What is the de Broglie wavelength of an 800-eV electron?
Problem 7
(a) If a photon and an electron each have the same energy of 20.0 eV, find the wavelength of each. (b) If a photon and an electron each have the same wavelength of 250 nm, find the energy of each. (c) You want to study an organic molecule that is about 250 nm long using either a photon or an electron microscope. Approximately what wavelength should you use, and which probe, the electron or the photon, is likely to damage the molecule the least?
Problem 8
What is the de Broglie wavelength for an electron with speed (a) \(v\)= 0.480\(c\) and (b) \(v\) = 0.960\(c\)? (\(Hint\): Use the correct relativistic expression for linear momentum if necessary.)
Problem 9
Calculate the de Broglie wavelength of a 5.00-g bullet that is moving at 340 m/s. Will the bullet exhibit wavelike properties?
Problem 11
(a) What accelerating potential is needed to produce electrons of wavelength 5.00 nm? (b) What would be the energy of photons having the same wavelength as these electrons? (c) What would be the wavelength of photons having the same energy as the electrons in part (a)?
