Collected by Alfred 0. Garrelt Ohio State University Columbus
The Flash of Genius,
9
The Bohr Atomic Model: Niels Bohr
A
century of research passed from the time that Dalton in 180'3 gave a clear, concise statement about the existence of atoms, in his atomic theory, until a young Danish physicist, Niels Bohr invented the first effective model and theory of the structure of atoms in 1913. Time wss ripe far this theory; all of the necessary information was available. Planek had proposed the quantum theory in 1900, the mystery of the cause of spectral lines was being studied, Rutherford had hombarded atoms with alpha particles and proposed the concept of the nuclear atom. Niels Bohr came to the University of Manchester to study with Rutherford, and thus the stage was set for the work of this brilliant young mind. His problem was most difficult. The atom is too small to be visible2000 times smaller than the smallest object visible to the eye aided by the best microscope. Bohr's solution' required an indirect approach. He had to put together tho diverse information known a t that time about the behavior of atoms, as disclosed by phenomena such as spectral lines, quantum theory, ioniaation potentials. Then he had to devise a model for this tiny particle by which the phenomena could he explained.
"In order to explain the results of experiments on scattering of n rays by matter Professor Rutherford has given a theory of the structure of atoms. According to this theory, the atoms consist of a positively charged nucleus surrounded by a system of electrons kept together by attractive forces from the nucleus; the total negative charge of the electrons is equal to the positive charge of the nucleus. "The way of considering a problem of this kind has undergone essential alterations in recent years owing to the development of the theory of the energy radiation, and the direct affirmation of the new assumptions introduced in this theory, found by experiments on very differentphenomena such as specific heats, photoelectric effect, Roentgen rays, etc. The result of the discussion of these questions seems to he a general acknowledgment of the inadeauacv " of the classical electrodvnamics in describing the behavior of systems of atomic size. Whatever the alteration in the laws of motion of the electrons may be, it seems necessary to introduce in the laws in question a quantity foreign to the classical electrodynamics, i.e., Planck's constant, or as it often is called the elementary quantum of action. . . .
This paper is an attempt to show that the application of the above ideas to Rutherford's atom-model affords a basis for a theory of the constitution of atoms. "Returning to the simple case of an electron and a positive nucleus considered above, Let us assume that the electron a t the beginning of the interaction with the nucleus was a t a great distance apart from the nucleus, and had no sensible velocity relative to the latter. Let us further assume that the electron, after the interaction has taken place, has settled down in a stationary orbit around the nucleus. We shall assume that the orbit in question is circular; this assumption will, however, make no alteration in the calculations for systems containing only a single electron. "Let us now assume that, during the biding of the electron, a homogeneous radiation is emitted of a frequency v, equal to half the frequency of revolution of the electron in its final orbit; then, from Planck's theory, we might expect that the amount of energy emitted by the process considered is equal to nhv,where his Planck's constant and n an entire number. If we assume that the radiation emitted is homogeneous, the second assumption concerning the frequency of the radiation suggests itself, since the frequency of revolution of the electron a t the beginning of the emission is 0." Bohr then calculated the amount of energy, W, required to move the electron to an infinitely great distance from the nucleus. For this calculation he derived the equation from his model of the atom:
w = -2a2rne'BZ -
z
BORE,N., Phil. Mag., July 1913, pp. 1-25.
534
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Journal o f Chemical Education
where m is the mass of the electron, e is the charge the electron, E is the charge on the nucleus, n is a whole number (1,2,3,4, etc. which was later called a quantum number) and his I'lanck'~ Bohr continues: "If we give n different values, wc get a series of values for W corresponding to a series of configurations of the system. - ~ c c o r d i n gto the above considerations, we are led to assume t,hat these On
configurations will correspond to states of the system in which there is no radiation of energy; st,ates which consequently will be stationary as long as the system is not disturbed from outside. We see that the value of W is greatest if n has its smallest value 1. This case will therefore correspond to the most stable state of the system, i.e., will correspond to the biding of the electron for the breaking up of which the greatest amount of energy is required. "Putting in the above expressions n = 1 and E = e, and introducing the experimental values
we get
=
la volt
This is the calculated ionization potential of hydrogen and compares favorably with the experimental value of 13.54 volts. "Before proceeding it may be useful to restate briefly the ideas characterizing the calculations. The principal assumptions used are: (1) That the dynamical equilibrium of the systems in the stationary states can be discussed by help of the ordinary mechanics, while the passing of the systems between different stationary states cannot be treated on that basis. (2) That the latter process is followed by the emission of a homogeneous radiation, for which the relation between the frequency and the amount of energy emitted is the one given by Planck's theory. "The first assumption seems to present itself; for it is known that the ordinary mechanics cannot have an absolute validity, but will only hold in calculations of certain mean values of the motion of the electrons. On the other hand, in the calculations of the dynamical equilibrium in a stationary state in which there is no relative displacement of the particles, we need not distinguish between the actual motions and their mean values. The second assumption is in obvious contrast to the ordinary ideas of electrodynamics, but appears to be necessary in order to account for experimental facts." The success that Bohr had with his first calculations ahout energy states in atoms, atomic radii, and ionization potentials represents the first step in testing his model of the atom. His next step was to use this model and his mathematical equations to explain spectral lines of hydrogen. Bohr describes his solution to this problem as follows: "Spectrum of Hydrogen. General evidence indicates that an atom of hydrogen consists simply of a single electron rotating round a positive nucleus of charge e. The reformation of a hydrogen atom, when the electron has been removed to great distances away from the nucleus--e.g., by the effect of electrical discharge in a vacuum tube--mill accordingly correspond to the binding of an electron by a positive nucleus. If we put E = e, we get for the total amount of energy, W, radiated out by the formation of one of the stationary states, n
"The amount of energy emitted by the passing of the system from a state corresponding t o n = nl to one corresponding to n = n ~is, consequently
"If now we suppose that the radiation in question is homogeneous, and that the amount of energy emitted is equal to h v, where v is the frequency of the radiation, we get
and from this
"We see that this expression accounts for the l a r ~ connecting the lines in the spectrum of hydrogen. If we put nz = 2 and let n, vary, we get the ordinary Balmer series. If we put n, = 3, we get the series in the ultra-red observed by Paschen and previously suspected by Rita. If we put nz = 1and E~= 4,5, . . . . . ., we get series respectively in the extreme ultraviolet and the extreme ultra-red, which are not observed, but the existence of which may be expected. "The agreement in question is quantitative as well as qualitative. "The agreement between the theoretical and observed values is inside the uncertainty due to experimental errors in the constants entering in the expression for the theoretical value. "It may be remarked that the fact, that i t has not been possible to observe more than 12 lines of the Balmer series in experiments with vacuum tubes, while 33 lines are observed in the spectra of some celestial bodies, is just what we should expect from the above theory. "We shall now return to the main object of this paper -the discussion of the 'permanent' state of a system consisting of nuclei and bound electrons. For a s y e tem consisting of a nucleus and an electron rotating round it, this state is according to the above, determined by the condition that the angular momentum of the electron round the nucleus is equal to h/2r. "On the theory of this paper the only neutral atom which contains a single electron is the hydrogen atom. Unfortunately, however, we know very little of the behavior of hydrogen atoms on account of the small dissociation of hydrogen molecules a t ordinary temperatures. In order to get a closer comparison with experiments, i t is necessary to consider more complicated systems." Bohr further assumed that the orbital angular momentum, mur = n ( h / 2 ~ )where m is the mass of the electron, v is its velocity and r is the radius of its orbit, and n is an integer (1, 2. 3, etc. now called the principal quantum number). This equation indicates that as electrons absorbn quanta of energy ( h / 2 ~units) the electrons will have more orbital angular momentum and more in wider orbitals. This validity of this assumption was proved 12 years later and is one of the basic assumptions also of the wave theory treatment of the atom leading to the electron-cloud model. Volume 39, Number 10, October 1962
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