A beam of 40 eV electrons traveling in the+x-directionpasses through a slit that is parallel to the y-axis and5.0 mm wide. The diffraction pattern is recorded on a screen 2.5 mfrom the slit. (a) What is the de Broglie wavelength of the electrons?(b) How much time does it take the electrons to travel from the slit tothe screen? (c) Use the width of the central diffraction pattern to calculatethe uncertainty in the y-component of momentum of an electronjust after it has passed through the slit. (d) Use the result of part(c) and the Heisenberg uncertainty principle [(Eq. 39.29) for y] toestimate the minimum uncertainty in the y-coordinate of an electronjust after it has passed through the slit. Compare your result to thewidth of the slit.
A beam of 40 eV electrons traveling in the
+x-direction
passes through a slit that is parallel to the y-axis and
5.0 mm wide. The diffraction pattern is recorded on a screen 2.5 m
from the slit. (a) What is the de Broglie wavelength of the electrons?
(b) How much time does it take the electrons to travel from the slit to
the screen? (c) Use the width of the central diffraction pattern to calculate
the uncertainty in the y-component of momentum of an electron
just after it has passed through the slit. (d) Use the result of part
(c) and the Heisenberg uncertainty principle [(Eq. 39.29) for y] to
estimate the minimum uncertainty in the y-coordinate of an electron
just after it has passed through the slit. Compare your result to the
width of the slit.
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