Which principle states that it is impossible to know the exact velocity and position of an electron at the same time?

The Heisenberg uncertainty principle is a fundamental concept in quantum mechanics that articulates a critical limit on the precision with which certain pairs of physical properties can be known simultaneously. Specifically, it asserts that the more accurately we know an electron's position, the less accurately we can know its velocity, and vice versa. This principle emphasizes the inherent limitations in measuring the state of subatomic particles, such as electrons, which do not behave like classical objects. Instead of possessing a defined position and velocity at the same time, electrons are described by a probability distribution, indicating the likelihood of finding them in various locations around the nucleus.

In contrast, the Pauli exclusion principle pertains to the behavior of fermions, specifically addressing how no two identical fermions can occupy the same quantum state simultaneously, impacting the structure of electron shells in atoms. Max Planck's hypothesis relates to the quantization of energy and the foundational ideas of quantum theory, while the Bohr model of the atom provides a simplified view of electron orbits around the nucleus, which does not encompass the complexities highlighted by the uncertainty principle. This is key in understanding the nature of electrons and their behavior within atoms according to modern quantum theories.