24.3. Uncertainty Principle http://www.ck12.org
24.3 Uncertainty Principle
Objectives
The student will:
- Understand the uncertainty principle.
- Solve problems involving the uncertainty principle.
Vocabulary
- Heisenberg uncertainty principle:A fundamental constraint, upon any such set of measurements, made with
any tool. The more narrowly we define the position∆x, the lesswell defined we know the momentum,∆p. - Quantum mechanics:Changed the view of the atom from the orderly arrangement of the planetary atom to
what is known today as an electron cloud model.
Introduction
Bohr’s model of the atom established the principle that electrons could only orbit the nucleus in a limited number of
levels, or quantized levels. This matched previous evidence forquantum mechanics, such as:
- Black body radiation like heated iron was shown to have very many different tiny wavelengths.
- The photoelectric effect showed that light could act like a particle.
- Diffraction of electrons showed that electrons could act like waves.
The essence of early quantum mechanics was two principles:
- At tiny scales, waves could act like particles, and particles could act like waves.
- Those waves could only have certain distinct (quantized) wavelengths, rather than a smooth range of wave-
lengths.
There was no connection established yet between this and electrons in orbit around the nucleus.
Electrons as Standing Waves
The connection between waves and electron orbits was only suggested more than ten years after Bohr’s model of
the atom, by French physicist Louis de Broglie (1892-1987). The reason that the properties of Bohr atom had to be
quantized, according to de Broglie, was to accommodate a standing wave condition around the nucleus of the atom.
From wave theory, a standing wave is also called a harmonic, and consists of a stable state with distinct numbers for
how many wavelengths fit into the fixed length.