Calculating de Broglie's Wavelength

We can now use the following relationship to find the wavelength of various particles.

Since h = 4.14 ´ 10^-15 eV and mass of an electron is 9.1 ´ 10^-34 kg, for electrons only we can write:

Where the wavelength is in nanometers and the kinetic energy is in eV.

Question 1
An electron coming out of a television electron gun has an energy of 1000 eV, what is it's wavelength?

Question 2
While wave behavior is exhibited by electrons, pions, neutrons and protons; we do not observe similar behavior for large objects such as gnats or humans. As an example, we will consider why diffraction doesn't cause a gnat to look like several gnats as it flies through window blinds. Suppose the gnat's mass is .001 kg, and its speed is 0.10 m/s.

• What is the gnat's momentum?
• What is the gnat's de Broglie wavelength?
• Approximately what would the spacing between the window blinds have to be for the gnat to create a pattern as it flew through? Why?
• Is it necessary for a gnat to worry about creating a pattern as it flies through the blinds? Why?

For patterns to be formed, the separation between the slits must be comparable to the wavelength of the waves passing through them. Thus, as your separation became very large, the pattern was not easy to see.

Question 3

• How would a human being's de Broglie wavelength compare to that of a gnat? Why?
• Why do we not create a pattern similar to that created by electrons or protons when we walk through two doors that are next to each other?