Electrons from a weak source pass a screen with two slits and are recorded
PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Quantum Mechanics · Origins of quantum theory
Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Matter waves and wave-particle duality
Problem
Electrons from a weak source pass a screen with two slits and are recorded, one click at a time, by a small detector fixed at a point P on the far screen. The source strength is the same in every run. With only slit 1 open, the detector clicks 900 times per minute. With only slit 2 open, it clicks 400 times per minute. Following the rule of this chapter, each open slit sends a wave to P whose amplitude squared is that slit's own click rate; with both slits open the two waves add and the click rate is the square of the summed amplitude. At P the two waves differ in phase by δ, and opening one slit does not change the amplitude from the other.
((a)) Predict the click rate at P with both slits open if δ=0.
((b)) Predict it if δ=π.
((c)) An experimenter now records which slit each electron passed, so that the cross term is absent and the rates from the two slits simply add. What rate is then found at P?
((d)) For which smallest positive δ, in degrees, does the two-slit rate with no which-slit record equal the answer to (c)?