1. A beam of neutrons is used to study molecular structure through a series of d
ID: 1301874 • Letter: 1
Question
1.
A beam of neutrons is used to study molecular structure through a series of diffraction experiments. A beam of neutrons with a wide range of de Broglie wavelengths comes from the core of a nuclear reactor. In a time-of-flight technique, used to select neutrons with a small range of de Broglie wavelengths, a pulse of neutrons is allowed to escape from the reactor by opening a shutter very briefly. At a distance of 17.9 m downstream, a second shutter is opened very briefly 10.2 ms after the first shutter. If each shutter is open for 0.477 ms, estimate the range of de Broglie wavelengths selected.
Explanation / Answer
The slowest neutron enters the first shutter at the start of its opening and leaves the second shutter at the end, so its time of travel is 10.677 ms. its velocity is 17.9/10.677 = 1676.5 m/s
The fastest neutron enters the first shutter at the end of its opening and leaves the second shutter at the start, so its time of travel is 9.723 ms. Its velocity is 17.9/9.723 = 1841.0 m/s
Their wavelengths are h/p = h/mv so
slowest: (6.626 * 10-34 Js)/((1.675 * 10-27 kg)(1676.5 m/s)) = 2.360 * 10-10 m = 0.2360 nm
fastest: (6.626 * 10-34 Js)/((1.675 * 10-27 kg)(1841.0 m/s)) = 2.149 * 10-10 m = 0.2149 nm
which is your range.
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