Double-Slit Experiment with Electrons
Double-Slit Experiment with Electrons Double-Slit Interference Pattern Wave-Particle Duality Sum of Two Single-Slit Patterns Interpretation Homework
Double-Slit Interference Pattern - Qualitative Consider a beam of monoenergetic electrons incident on a double-slit. The slit separation d is much greater than the width of the slits and much less than the distance between the slits and the detector. The electron detector is movable along the y direction and can detect electrons diffracted at different values of . If the detector collects electrons for a long enough time, a wave interference pattern is observed for the counts per minute.
Figure 28.16
Double-Slit Interference Pattern - Quantitative
Wave theory can be used to find the angle between the central maximum and the first minimum. The minimum occurs when the path length difference between A and B is half a wavelength
Writing the electron’s wavelength as
the small angle approximation, we have
Figure 28.16
and applying
Wave-Particle Duality The double-slit experiment with electrons clearly shows the wave-particle duality of electrons. The electrons are detected as particles at a localized position at some instant in time, but the probability of detecting the electron at that position is determined by a wave interference pattern.
Superposition of Two Single-Slit Patterns Consider an experiment in which slit 2 is blocked half of the time and then slit 1 is blocked during the remaining time. The interference pattern is lost and the result, shown by the blue curve, is just the sum of the two single-slit patterns. (The red curve shows the interference pattern when both slits are open.)
Figure 28.18
Interpretation of Results We are forced to conclude that an electron interacts with both slits simultaneously. Any attempt to determine experimentally which slit the electron goes through will result in a destruction of the interference pattern due to the act of measurement. It is impossible to determine which slit the electron goes through, and we can say only that it passes through both slits!
Single-Electron Interference
A series of images taken in a double-slit experiment with electrons as the electron current density is increased. Since there is only one electron in the apparatus at a given time, this figure shows how an interference pattern can be built up from single-electron events. (Taken from physicsweb.org/box/world/15/9/1/bologna-image)
Example Neutrons (m = 1.67 10 kg) traveling at 0.400 m/s are directed through a double-slit having a 1.00 mm separation. An array of detectors is placed 10.0 m from the slits. (a) What is the de Broglie wavelength of the neutrons? (b) How far off axis is the first zerointensity point on the detector array?
Example Neutrons (m = 1.67 10 kg) traveling at 0.400 m/s are directed through a double-slit having a 1.00 mm separation. An array of detectors is placed 10.0 m from the slits. (a) What is the de Broglie wavelength of the neutrons? (b) How far off axis is the first zerointensity point on the detector array?
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X Y (b) R>S
Double-Slit Interference Pattern - Qualitative Consider a beam of monoenergetic electrons incident on a double-slit. The slit separation d is much greater than the width of the slits and much less than the distance between the slits and the detector. The electron detector is movable along the y direction and can detect electrons diffracted at different values of . If the detector collects electrons for a long enough time, a wave interference pattern is observed for the counts per minute.
Figure 28.16
Double-Slit Interference Pattern - Quantitative
Wave theory can be used to find the angle between the central maximum and the first minimum. The minimum occurs when the path length difference between A and B is half a wavelength
Writing the electron’s wavelength as
the small angle approximation, we have
Figure 28.16
and applying
Wave-Particle Duality The double-slit experiment with electrons clearly shows the wave-particle duality of electrons. The electrons are detected as particles at a localized position at some instant in time, but the probability of detecting the electron at that position is determined by a wave interference pattern.
Superposition of Two Single-Slit Patterns Consider an experiment in which slit 2 is blocked half of the time and then slit 1 is blocked during the remaining time. The interference pattern is lost and the result, shown by the blue curve, is just the sum of the two single-slit patterns. (The red curve shows the interference pattern when both slits are open.)
Figure 28.18
Interpretation of Results We are forced to conclude that an electron interacts with both slits simultaneously. Any attempt to determine experimentally which slit the electron goes through will result in a destruction of the interference pattern due to the act of measurement. It is impossible to determine which slit the electron goes through, and we can say only that it passes through both slits!
Single-Electron Interference
A series of images taken in a double-slit experiment with electrons as the electron current density is increased. Since there is only one electron in the apparatus at a given time, this figure shows how an interference pattern can be built up from single-electron events. (Taken from physicsweb.org/box/world/15/9/1/bologna-image)
Example Neutrons (m = 1.67 10 kg) traveling at 0.400 m/s are directed through a double-slit having a 1.00 mm separation. An array of detectors is placed 10.0 m from the slits. (a) What is the de Broglie wavelength of the neutrons? (b) How far off axis is the first zerointensity point on the detector array?
Example Neutrons (m = 1.67 10 kg) traveling at 0.400 m/s are directed through a double-slit having a 1.00 mm separation. An array of detectors is placed 10.0 m from the slits. (a) What is the de Broglie wavelength of the neutrons? (b) How far off axis is the first zerointensity point on the detector array?
2 % !#"$! %'& ! (658 '7 9#%':= *& ,.-0&A/1 & 1CB 6D EFDHG I LJ KNM .3 O "$!43 "@? DPDHG Q O
X Y (b) R>S
