Bohr Model of the Atom
January 3, 2012
My introduction to
atomic physics was as a child watching the many
science-oriented editions of
Walt Disney Presents on Sunday nights on a
monochrome (a.k.a.,
black-and-white)
television receiver. The atomic model, presented as an
animation, was the
Bohr model in which the
electrons travel in orbits around the
nucleus.
The Bohr model was readily understandable to those of us who had learned enough
astronomy to know that the
planets orbit the
Sun. At the time it was presented, it was also quite reasonable to
physicists, who just needed to replace
gravitational force with
electrostatic force in the same model. Both forces followed an
inverse-square law, so what could be simpler?
The Bohr atom, as depicted in the 1946-1974 logo of the United States Atomic Energy Commission.
(Via Wikimedia Commons))
The Bohr model was one of many early atomic models spawned from the realization that atoms had
positive and
negative elements that were separable; that is, they were entities unto themselves. The history of the Bohr model has been summarized in a
very nice paper on the
arXiv Preprint Server.[1]
Atomic models leading up to the Bohr model included
• The cubic atom, proposed by Gilbert N. Lewis in 1902 to explain valence and bonding. I wrote about Lewis in a previous article (Gilbert N. Lewis, November 16, 2011.
• The plum-pudding model, proposed by J.J. Thompson, who had discovered the electron, in 1904. This model had electrons embedded in a positively-charged liquid. This model was proposed before the discovery of a point-like nucleus. The electrons were allowed to orbit internally in this liquid. Thompson was awarded the Nobel Prize in Physics in 1906, primarily because of his discovery of the electron.
• The Saturnian model, proposed in 1904 by the Japanese physicist, Hantaro Nagaoka. As its name implies, the electrons move in orbits very close to the nucleus, very much like Saturn's rings. The atomic stability derives from this close orbit that dominates the electrostatic forces, just as Saturn's gravitational field stabilizes its rings.
• The Rutherford model, proposed by Ernest Rutherford in 1911. Based on his scattering experiments of alpha particles striking gold foils that showed the existence of a compact nucleus, Rutherford proposed a planetary model of the atom. Rutherford didn't attempt to reconcile this model with physical features of atoms, such as their spectra. This was left to Bohr, whose planetary model made this connection.
Separated at Birth? Edgar Allan Poe (left) and J.J. Thompson (right). Image sources for Poe and Thompson via Wikimedia Commons.
As any
undergraduate physics student knows (or, should know), the planetary models have a fundamental problem; that is, an
accelerating charge will
radiate energy. Electrons in orbit about a nucleus will lose energy and spiral into the nucleus. This calculation was actually a back-of-the-chapter
homework problem in
Resnick and Halliday that I needed to solve as an undergraduate.
This radiation is readily calculated from the
Larmor's equation.
P = e2a2 / 6 π εo c3
in which
P is the radiated
power,
e is the charge,
a is the acceleration,
εo is the
permittivity of free space, and
c is the
speed of light. The acceleration in this case is the
centripetal acceleration,
a = v2 / r
in which
v is the electron velocity, and
r is the radius of its orbit.
Eventually,
quantum mechanics cleared this problem by making the electron
fuzzy, which is about as confusing as things can get. Fortunately, it all worked out for the best, and we have all our
electronic gadgets as proof.
Frontpiece of H. A. Kramers and H. Holst, 'The Atom and the Bohr Theory of its Structure,' (Gyldendal, London), 1923. (Fig. 2 of ref. 1, via arXiv Preprint Server). This book helped to popularize Bohr's atomic model.[1]
Reference:
- Helge Kragh and Kristian Hvidtfelt Nielsen, "Spreading the gospel: The Bohr atom popularised," arXiv Preprint Server, December 12, 2011.
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