For crystal diffraction experiments (discussed in Section...

For crystal diffraction experiments (discussed in Section 39.1$)$ , wavelengths on the order of 0.20 $\mathrm{nm}$ are often appropriate. Find the energy in electron volts for a particle with this wavelength if the particle is (a) a photon; (b) an electron; (c) an alpha particle $\left(m=6.64 \times 10^{-27} \mathrm{kg}\right) .$

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Key Concepts

Photon Energy Calculation

This concept involves the direct computation of a photon's energy from its wavelength using the formula E = hc/?, where h is Planck's constant and c is the speed of light. This relationship is central to understanding energy quantization in the electromagnetic spectrum and is fundamental in experiments involving light and radiation.

de Broglie Hypothesis

The de Broglie hypothesis posits that all matter exhibits wave-like properties, and it introduces the relation ? = h/p, where ? is the de Broglie wavelength, h is Planck's constant, and p is the momentum of the particle. This principle forms the basis for understanding the dual nature of particles and is essential when calculating properties of non-photon particles using their wavelengths.

Kinetic Energy from de Broglie Wavelength

For particles with mass, the kinetic energy can be derived from their momentum obtained via the de Broglie relation. For a non-relativistic particle, the kinetic energy is given by E = p²/(2m), where m is the particle's mass. This concept is crucial for relating the wave-like behavior of massive particles to their classical energy measures in contexts such as diffraction experiments.

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