Final answer:
For the double-slit experiment with matter waves, an individual electron goes through either one slit or the other, and if the observer does not measure this, a double-slit interference pattern emerges. Option b is the correct answer.
Step-by-step explanation:
In the context of matter waves in a double-slit experiment, an electron that is fired one at a time will exhibit behavior that suggests wave-particle duality. When not observed, the electron seems to interfere with itself, as evidenced by the double-slit interference pattern, which builds up statistically even when electrons pass one by one.
This implies that the electron's probability distribution spans both slits. However, if we determine which slit the electron passes through, the interference pattern collapses to a single-slit pattern.
Thus, the correct description from the options provided is: the electron goes through either one or the other slit, but the observer does not know which one it actually goes through, as knowing this information changes the observed interference pattern due to the peculiarities of quantum measurement dictated by the Heisenberg Uncertainty Principle.