The Bohr Theory and Atomic Spectra of Hydrogen

The Bohr Theory and Atomic Spectra of Hydrogen - Atomic structure and the periodic table

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When atoms are heated or subjected to an electric discharge, they absorb energy, which is subsequently emitted ~s radiation. For example, if sodium chloride is heated in the flame of a bunsen burner' sodium atoms are produced which gives rise to the characteristic yellow flame coloration. (There are two lines in the emission spectrum of sodium corresponding to wavelengths of589.0nm and 589.6nm.) Spectroscopy is a study of either the radiation absorbed or the radiation emitted. Atomic spectroscopy is an important technique for studying the energy and the arrangement of electrons in atoms.
If a discharge is passed through hydrogen gas (H₂) at low pressure, some hydrogen atoms (H) are formed, which emit light in the visible region. This light can he studied with u spectrometer and is found to comprise a series of lines of different wavelengths. Four lines can be seen by eye, but many more are observed photographically in the ultraviolet region. The lines become increasingly close together as the wavelength (A.) decreases until the continuum is reached (Figure 1.3). Wavelengths, in meters, are related to the frequency, v, in Hertz (cycles/second) by the equation:

Figure 1.3 Spectrum of hydrogen in the visible region (Bahner series.)

where R is the. Rydberg constant and n has the values 3, 4. 5 ...• thus giving a series of lines. The lines observed in the visible region are called the Balmer series. but several other series of lines may be observed in different regions of the spectrum (Table 1.1). Similar equations were found to hold for the lines in the other series in the hydrogen spectrum

In the early years of this century, attempts were made to obtain a physical picture of the atom from this and other evidence. Thomson had shown in 1896 that the application of a high electrical potential across a gas gave electrons, suggesting that these were present in atoms. Rutherford suggested from alpha-particle scattering experiments that an atom consisted of a heavy positively charged nucleus with a sufficient number of electrons around it to make the atom electrically neutral. In 1913, Niels Bohr combined these ideas and suggested that the atomic nucleus was surrounded by electrons moving in orbits like planets around the sun. He was awarded the Nobel Prize for Physics in 1922 for his work on the structure of the atom. Several problems arise with this concept:

I. The electrons might be expected to slow down gradually.
2. Why should electrons move in an orbit around t~e nucleus? ·
3. Since the nucleus and electrons have opposite charges, they should attract each other. Thus one would expect the electrons to spiral inwards until eventually, they collide with the nucleus.
To explain these problems Bohr postulated:
l. An electron did not radiate energy if it stayed in one orbit, and therefore did not slow down. ·
2. When an electron moved from one orbit to another it either radiated or absorbed energy. If it moved towards the nucleus energy was radiated and if it moved away from the nucleus energy was absorbed.
3. For an electron to remain in its orbit the electrostatic attraction between the electron and the nucleus which tends to pull the electron towards the nucleus must be equal to the centrifugal force which tends to throw the electron out of its orbit. For an electron of mass m, moving with a velocity v in an orbit of radius r

According to Planck's quantum theory, energy is not continuous but is discrete. This means that energy occurs in 'packets' called quanta, of magnitude h/2rt, where h is Planck's constant. The energy of an electron in an orbit, that is its angular momentum mvr, must be equal to a whole number n of quanta.

The experimental value of R is 1.097373 x 10⁷ m ^{- 1} , in good agreement with the theoretical value of 1.096776 x 10⁷ m^{- 1} • The Bohr theory provides an explanation of the atomic spectra of hydrogen. The different series of spectral lines can be obtained by varying the values of ni and fir in equation (1.4). Thus with nr = 1 and n_i = 2, 3, 4 ... we obtain the Lyman series of lines in the UV region. With nr = 2 and n_i = 3, 4, 5 ... we get the Balmer series of lines in the visible spectrum. Similarly, nr = 3 and n; = 4, 5, 6 . .. gives the Paschen series, nr = 4 and n_i = 5, 6, 7 ... gives the Brackett series, and nr = 6 and n;- = 7, 8, 9 ... gives the Pfund series. The various transitions which are possible between orbits are shown in Figure 1.4.