Electrons are accelerated through a potential difference of 20 kV in a vacuum tube to create a beam directed along the y axis. The beam passes through a 1.0-mm-wide slit and hits a fluorescent screen 25 cm away from the slit (as in Fig. 28.13C). 

(a) What is the de Broglie wavelength of the electrons in the beam as the beam enters the slit? 

(b) Consider single-slit diffraction and calculate the expected width along the x direction of the central bright spot on the screen. (Consider the distance to the first minimum in the diffraction pattern.) 

(c) What is the uncertainty in the x component of an electron’s momentum in the beam after passing through the slit? 

(d) How long does it take for the electrons to reach the screen? 

(e) What is the uncertainty in the x position when the electrons hit the screen? 

(f) How does your answer in part (e) compare with that of part (b)? Consider the derivation in Section 28.5.

Figure 28.13C