Final answer:
Quantum tunneling is negligible for macroscopic objects like humans due to extremely low probabilities associated with their short wavelengths, contrasted with effective tunneling observed in microscopic particles like electrons.
Step-by-step explanation:
The physics student's chances of tunneling out of her prison cell using quantum mechanics are negligible because quantum tunneling is a phenomenon that rarely occurs in macroscopic objects. Quantum tunneling allows particles to penetrate a potential energy barrier that they classically shouldn't be able to overcome, due to the wave-like nature of particles at quantum scales. However, for macroscopic objects such as a human, the probabilities of tunneling are so small that they are effectively zero because their associated wavelengths are incredibly short, leading to an extremely low tunneling probability.
This principle explains why in classical situations we never observe objects like balls tunneling through walls, as the potential barriers in everyday life are too thick and the objects too large. In contrast, quantum tunneling is observed at the atomic scale, such as electrons in a scanning tunneling microscope or in certain radioactive decays, where particles may tunnel through thin potential barriers.