The Quantisation of Matter: The Bohr Model of The Atom
By the dawn of the 20th century, it was known that atoms comprise a diffuse cloud of negatively-charged electrons surrounding a small, dense, positively-charged nucleus. This understanding suggested a model in which the electrons circle around the nucleus like planets orbiting a sun. However, it was also known that the atom in this model would be unstable: according to classical theory orbiting electrons are undergoing centripetal acceleration, and should therefore give off electromagnetic radiation, the loss of energy also causing them to spiral toward the nucleus, colliding with it in a fraction of a second.
A second, related, puzzle was the emission spectrum of atoms. When a gas is heated, it gives off light only at discrete frequencies. For example, the visible light given off by hydrogen consists of four different colours, as shown in the picture below. By contrast, white light consists of a continuous emission across the whole range of visible frequencies.
In 1885 the Swiss mathematician Johann Balmer discovered that each wavelength λ (lambda) in the visible spectrum of hydrogen is related to some integer n by the equation
where B is a constant which Balmer determined to be equal to 364.56 nm. Thus Balmer's constant was the basis of a system of discrete, i.e. quantised, integers.
In 1888 Johannes Rydberg generalized and greatly increased the explanatory utility of Balmer's formula. He predicted that λ is related to two integers n and m according to what is now known as the Rydberg formula:
where R is the Rydberg constant, equal to 0.0110 nm−1, and n must be greater than m.
Rydberg's formula accounts for the four visible wavelengths of hydrogen by setting m = 2 and n = 3, 4, 5, 6. It also predicts additional wavelengths in the emission spectrum: for m = 1 and for n > 1, the emission spectrum should contain certain ultraviolet wavelengths, and for m = 3 and n > 3, it should also contain certain infrared wavelengths. Experimental observation of these wavelengths came two decades later: in 1908 Louis Paschen found some of the predicted infrared wavelengths, and in 1914 Theodore Lyman found some of the predicted ultraviolet wavelengths.
Read more about this topic: Introduction To Quantum Mechanics
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