A nickel crystal is used as a diffraction grating for x- rays. Then the same crystal is used to

Step 1: Determine the wavelength of the x-ray photons. We know the energy of each x-ray photon i

A nickel crystal is used as a diffraction grating for x-...

A nickel crystal is used as a diffraction grating for $\mathrm{x}-$ rays. Then the same crystal is used to diffract electrons. If the two diffraction patterns are identical, and the energy of each $x$ -ray photon is $E=20.0 \mathrm{keV}$, what is the kinetic energy of each electron?

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Key Concepts

kinetic energy and momentum relation for electrons

In the context of non-relativistic particles, an electron's kinetic energy is related to its momentum by K.E. = p²/(2m), where m is the mass of the electron. Combining this with the de Broglie wavelength formula allows one to equate the wavelength of electrons with that of x-rays, ultimately linking the electron's kinetic energy to the energy of the photon.

photon energy-wavelength relationship

The energy of a photon is inversely proportional to its wavelength, expressed as E = hc/?, where E is the photon energy, h is Planck's constant, and c is the speed of light. This relationship is key when comparing the wavelengths of x-rays to those of electrons in diffraction experiments.

de Broglie wavelength

This concept describes the wave-like behavior of matter, specifically stating that any particle with momentum has an associated wavelength given by ? = h/p, where h is Planck's constant and p is the momentum. It is fundamental in explaining diffraction of electrons and other particles.

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