Electrons can be used to probe the arrangement of atoms on a solid surface if the wavelength of the electrons is comparable with the spacing between the atoms. Which of the following electron velocities would be appropriate for use in this application if the atoms are separated by 0.320 nm A) 1.24 * 10³ m/s B) 8.06 * 10³ m/s C) 2.27 * 10⁶ m/s D) 4.41 * 10⁶ m/s E) 3.00 * 10⁸ m/s

Question

Quizplus · Accepted Answer

The de Broglie wavelength of electrons can be calculated using the following formula:
λ = h/mv
where λ is the wavelength, h is Planck's constant, m is the mass of the electron, and v is the velocity of the electron.
For the given spacing between atoms, the wavelength of the electron should be equal to the distance between atoms:
λ = 0.320 nm
Using the above formula and solving for v, we get:
v = h/(mλ)
The mass of an electron is 9.10938356 × 10^-31 kg.
Plugging in the given wavelength and solving for v, we get:
v = 2.27 × 10^6 m/s
Therefore, the correct answer is C.

Electrons Can Be Used to Probe the Arrangement of Atoms