Part of JPC-07 — Atomic Structure: Quantum Numbers & Electronic Config

Heisenberg Uncertainty Principle

by Notetube Official102 words7 views

deltaxdelta_x * deltapdelta_p >= h4pi\frac{h}{4*pi}, where deltaxdelta_x = uncertainty in position, deltapdelta_p = m*deltavdelta_v = uncertainty in momentum. This is a fundamental limit, not an experimental limitation. Consequence: the concept of well-defined orbits (Bohr model) is replaced by probability distributions (orbitals). For an electron confined to 1 angstrom: deltavdelta_v >= h4pimdeltax\frac{h}{4*pi*m*delta_x} = 6.626x10^-$$\frac{34}{4 x 3.14 x 9.1x10^-31 x 10^-10} = 5.8 x 10^5 m/s — comparable to the electron's actual velocity. For a 1 kg ball confined to 1 mm: deltavdelta_v >= 5.3 x 10^-32 m/s — immeasurably small. This explains why quantum effects are significant for electrons but not macroscopic objects.

Like these notes? Save your own copy and start studying with NoteTube's AI tools.

Sign up free to clone these notes