# Bohr Model: Definition & Equation

Instructor: Marion Carroll

Marion is a 30-year veteran of industry and academia primarily in the fields of biochemistry and genomics.

Explore the problem of the Saturnian atomic model, how the Bohr equation addresses this problem using the hydrogen atom, and what current theory has taken from the Bohr model to refine and improve on it.

## Neils Bohr

Neils Bohr was born in Copenhagen, Denmark in 1885 to a well-to-do family; his father was a prominent professor of physiology. Neils earned a Master's and Ph.D from the University of Copenhagen, and then joined J.J. Thomson at Cambridge University in 1912. Over the next 10 years, he worked on the problems of atomic structure, which earned him the Nobel Prize in 1922. He opened his own Institute for Theoretical Physics in 1920 from which many prominent physicists were trained.

## Refining a Modeled Structure

The model described by Bohr was not far removed from the prevailing model in which electrons revolved around the atomic nucleus, like the rings that revolve around Saturn. The Saturnian model described by Bohr's mentor Ernest Rutherford consisted of applying electromagnetic radiation and electrostatic repulsion to describe the distribution and arrangement of electrons around a central positive nucleus. This is the model that is still generally recognized today to represent the atomic structure.

What was known about electromagnetic radiation or radioactivity at the time would then imply that every element was unstable and would decay over time. To address this weakness in the Saturnian model, Bohr used his work with hydrogen gas and its emission spectrum of light. The emission of light by hydrogen has a specific wavelength. Max Planck's experimentation on the emission of light by heating solid bodies resulted in the description of energy as being gained or lost in whole-number intervals. This quantity, hv, is Planck's constant (h) multiplied by the frequency (v) of the electromagnetic radiation. The concept of a 'quantum' change of energy rests in this equation:

where delta E is the change in energy of a system and n is a whole number. The quantum is measured in discrete whole number units and associates the properties of electromagnetic radiation or photons of light with the properties of a particle with angular momentum. In the following diagram 'f' is the same as 'v' or frequency.

## Challenging Classical Physics

Before the Bohr equation could be complete, Neils Bohr made some challenging assumptions regarding the emission of light or energy. The primary assumption was regarding the movement of electrons. In classical physics, the movement of electrons around the nucleus would result in constant acceleration, emission of light and loss of energy, therefore decaying its revolution toward the nucleus. To account for this instability, Bohr assumed that the angular movement of electrons occurs within energy levels. This movement is equal to the product of mass, velocity and orbital radius. Each level must exceed -2.178 x 10^-18 J/atom for an electron to enter (large negative value) or leave (smaller negative value) the next level as observed in Bohr's work on the hydrogen atom. The ideal equation to represent the atomic structure that also accounts for the emission of radiation (light) and the maintenance of atomic stability is as follows:

where Z is the nuclear charge, n is an integer for the orbital radius, 1 being the ground state with the smallest negative value being the most tightly bound orbital around the nucleus.

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