Neutron diffraction is an important technique for determining the structures of molecules. Calculate the velocity of a neutron needed to achieve a wavelength of 125 pm. (Refer to the inside cover for the mass of the neutron.)

검증된 단계별 안내

First, recall the de Broglie wavelength equation, which relates the wavelength (\( \lambda \)) of a particle to its momentum (\( p \)): \( \lambda = \frac{h}{p} \), where \( h \) is the Planck constant.

Next, express the momentum (\( p \)) in terms of mass (\( m \)) and velocity (\( v \)) of the neutron: \( p = m \cdot v \).

Substitute the expression for momentum into the de Broglie equation to relate wavelength, mass, and velocity: \( \lambda = \frac{h}{m \cdot v} \).

Rearrange the equation to solve for velocity (\( v \)): \( v = \frac{h}{m \cdot \lambda} \).

Finally, use the given wavelength (125 pm) and the mass of a neutron (refer to the inside cover of your textbook or a reliable source) to calculate the velocity.

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주요 개념

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De Broglie Wavelength

The De Broglie wavelength is a fundamental concept in quantum mechanics that relates the wavelength of a particle to its momentum. It is given by the formula λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. For neutrons, this relationship is crucial for understanding how their wave-like properties can be utilized in diffraction experiments.

Momentum of a Particle

Momentum is a vector quantity defined as the product of an object's mass and its velocity (p = mv). In the context of neutron diffraction, the momentum of the neutron is essential for calculating its wavelength. Understanding how to manipulate this relationship allows for the determination of the velocity required to achieve a specific wavelength.

Neutron Properties

Neutrons are subatomic particles found in the nucleus of an atom, possessing a mass approximately equal to that of a proton but no electric charge. Their unique properties, including their ability to penetrate materials without causing ionization, make them particularly useful in diffraction techniques for studying molecular structures. Knowing the mass of the neutron is vital for calculations involving its velocity and wavelength.