Question

As Prof. Greene indicated in his lecture, the double slit experiment teaches us that microscopic objects, like electrons, are both particles and waves. In fact, as Prof. Greene also described, Louis de Broglie suggested in 1923 that all material objects display wave-like properties and have wavelengths associated with them. According to de Broglie, these "matter waves" have a wavelength given by the equation 2 =; , where à is the wavelength of the object, h is Planck's constant, m is the mass of the object, and v is its speed. Let's consider what this formula and its application tell us about the electrons in our double slit experiment. mv' C. (i) Suppose that in your double slit experiment, your electrons are moving at a speed of 900 m/s. What is the wavelength of these electrons in units of nm? (ii) Do the electrons in the double slit experiment behave ONLY as waves?

Answer 1

λ = h / (m v) de Broglie wavelength

i) λ = 6.63E-34 / (9.11E-31 kg * 9.00E^2)

λ = 6.63 / (9.11 * 9.00) * 10^-5 m = .809E-7 m = 80.9 nm

If no determination of the slit thru which the electrons pass an interference pattern will appear on the screen - as if an electron went thru each slit simultaneously

If a determination is made thru which slit the electrons passed there will be no interference pattern on the screen (only 2 slit images)