Bohr’s Correspondence Principle

Bohr’s correspondence principle states that predictions of quantum theory must correspond to the predictions of classical physics in the region of sizes where classical theory is known to hold.

The classical sizes for length, mass, and time are on the order of centimeters, grams, and seconds and typically involve very large quantum numbers like can be seen by calculating n for hydrogen atom with a radius of 1 cm. If the quantum number becomes large because of increased size or mass, we may state the correspondence principle as:

Where n is a typical quantum number of the system such as the quantum number of hydrogen.

Also Read: The Exclusion Principle

Bohr’s correspondence principle was a powerful tool to test new quantum results as well as a source of fundamental postulates about atomic systems. For example, in Bohr’s 1913 paper, he showed that the quantization of angular momentum is a consequence of the smooth and gradual emergence of classical results from quantum theory in the limit of large quantum number. Specifically, Bohr argued that according to his correspondence principle, the quantum condition for emission (AE = hf) and Maxwell’s classical radiation theory (electronic charges with orbital frequency f radiate light waves of frequency f) must simultaneously hold for the case of very large electronic orbits.

Related Resource: Quantum Physics For Dummies