In the equation for the time-dependent wave function I ( x, t) = V(x)e int - Aci(kx-wt) + Be i(katut) keep both terms, putting A = B = Vo. The equation then describes the superposition of two matter waves of equal amplitude, traveling in opposite directions. (Recall that this is the condition for a standing wave.) (a) Find IT (x, t) 12. IT ( 20, t ) 12 = (b) Find the positions of the nodes of this standing wave in terms of 1, the de Broglie wavelength of the particle. C = (c) Find a similar expression for the most probable locations of the particle. OC = ? 57You will find in Chapter 39 that electrons cannot move in definite orbits within atoms, like the planets in our solar system. To see why, let us try to "observe" such an orbiting electron by using a light microscope to measure the electron's presumed orbital position with a precision of, say, 5 pm (a typical atom has a radius of about 100 pm). The wavelength of the light used in the microscope must then be about 5 pm. - Your answer is partially correct. (a) What would be the photon energy of this light? Number 62.2 Units keV (b) How much energy would such a photon impart to an electron in a head-on collision? Number i 12.0 Units keV