It is desired to obtain a diffraction pattern for electrons using a diffraction grating with lines separated by 10 nm.The mass of an electron is 9.11 × 10^-³¹ kg.
-What is the approximate kinetic energy of electrons that would be diffracted by such a grating?

Question

Quizplus · Accepted Answer

To observe diffraction, the de Broglie wavelength of the electrons should be comparable to the spacing of the grating, which is 10 nm. The de Broglie wavelength $\lambda$ is given by $\lambda = \frac{h}{p}$, where $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{m}^2 \, \text{kg} \, \text{s}^{-1}$) and $p$ is the momentum of the electron. The momentum $p$ can be related to kinetic energy $E$ through the relation $p = \sqrt{2mE}$, where $m$ is the mass of the electron. Substituting the given values and solving for $E$ gives a kinetic energy in the order of $10^2$ eV, making option C the closest match.

It Is Desired to Obtain a Diffraction Pattern for Electrons