Section 3 - Observing matter waves
3.1 A beam of neutrons, all moving at the same speed, is directed through a pair of slits whose centers are 2.00×10í^6 m apart.
An array of detectors is located 49.9 m from the slits. The intensity pattern of received neutrons is measured, and the first
zero-intensity point is 1.76 mm off-axis. The mass of a neutron is 1.68×10í^27 kg. (a) What is the de Broglie wavelength of a
neutron in the beam? (b) What is the speed of the neutrons in the beam?
(a) m
(b) m/s
Section 6 - Heisenberg uncertainty principle
6.1 A barrier contains a vertical slit of width 5.0×10í^6 m. An electron approaches the barrier and passes through the slit. (a) What
is the uncertainty in the horizontal position of this electron (measured parallel to the barrier, not in the direction of the
electron's motion) as it emerges on the other side? (b) What is the minimum uncertainty in its corresponding horizontal
momentum?
(a) m
(b) kg·m/s6.2 The position of a 900 kg boulder's center of mass has been determined to within an uncertainty of 1.0 nm. (a) What is the
minimum uncertainty in the boulder's velocity? (b) Repeat the calculation, but for a proton with the same uncertainty in
position. (c) Repeat the calculation, but for an electron with the same uncertainty in position.
(a) m/s
(b) m/s
(c) m/s
6.3 They-component of a dust particle's velocity is measured with an uncertainty of 1.0×10í^6 m/s. The particle has a mass of
1.6eí9 kg. (a) What is the limit of the accuracy to which we can locate the particle along the y-axis? That is, what is the
minimum uncertainty in the y-position? (b) Does this place any limitation on the accuracy with which we can locate its position
along the x or z axes?
(a) m
(b) Yes No