A beam of neutrons is used to study molecular structure...

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-offlight 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 $16.4 \mathrm{~m}$ downstream, a second shutter is opened very briefly $13.0 \mathrm{~ms}$ after the first shutter. (a) What is the speed of the neutrons selected? (b) What is the de Broglie wavelength of the neutrons? (c) If each shutter is open for $0.45 \mathrm{~ms}$, estimate the range of de Broglie wavelengths selected.

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-offlight 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 $16.4 \mathrm{~m}$ downstream, a second shutter is opened very briefly $13.0 \mathrm{~ms}$ after the first shutter. (a) What is the speed of the neutrons selected?
(b) What is the de Broglie wavelength of the neutrons?
(c) If each shutter is open for $0.45 \mathrm{~ms}$, estimate the range of de Broglie wavelengths selected.

Key Concepts

Kinematics in Particle Motion

Kinematics in particle motion deals with the relationships between displacement, velocity, and time. In the context of neutron experiments, it allows researchers to compute particle speeds by measuring the distance traveled and the time taken, which is an essential step in linking macroscopic experimental data to microscopic properties such as the de Broglie wavelength.

Neutron Diffraction

Neutron diffraction is an experimental technique in which a beam of neutrons is scattered by a material to produce an interference pattern. This pattern provides detailed information about the arrangement of atoms within a material, making neutron diffraction a powerful tool for studying molecular structures, lattice dynamics, and other properties in solid-state physics and chemistry.

Time-of-Flight Technique

The time-of-flight (TOF) technique is a method used to determine the velocity of particles by measuring the time they take to travel a known distance. This approach is particularly useful in experiments where particles (such as neutrons) are released in pulses, allowing researchers to select or classify particles based on their speeds and, consequently, on their energy or wavelength ranges.

de Broglie Wavelength

The de Broglie wavelength is a fundamental concept in quantum mechanics that describes the wave-like behavior of particles, relating a particle’s momentum to its wavelength via the equation ? = h/p. This principle is central to diffraction experiments, where knowing a particle’s wavelength permits analysis of its interaction with matter and helps elucidate the structure of materials at the molecular or atomic scale.

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