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Atoms hvif E niE nf (12.11) Since both n fnd n aie integers, this immediately shows that in transitions between different atomic levels, light is radiated in various discrete frequencies. The various lines in the atomic spectra are produced when electrons jump from higher energy state to a lower energy state and photons are emitted. These spectral lines are called emission lines. But when an atom absorbs a photon that has precisely the same energy needed by the electron in a lower energy state to make transitions to a higher energy state, the process is called absorption. Thus if photons with a continuous range of frequencies pass through a rarefied gas and then are analysed with a spectrometer, a series of dark spectral absorption lines appear in the continuous spectrum. The dark lines indicate the frequencies that have been absorbed by the atoms of the gas. The explanation of the hydrogen atom spectrum provided by Bohr’s model was a brilliant achievement, which greatly stimulated progress towards the modern quantum theory. In 1922, Bohr was awarded Nobel Prize in Physics. 12.6 D E B ROGLIE ’S E XPLANATION OF B OHR ’S S ECOND P OSTULATE OF Q UANTISATION Of all the postulates, Bohr made in his model of the atom, perhaps the most puzzling is his second postulate. It states that the angular momentum of the electron orbiting around the nucleus is quantised (that is, Ln= nh/2p; n = 1, 2, 3 …). Why should the angular momentum have only those values that are integral multiples of h/2p? The French physicist Louis de Broglie explained this puzzle in 1923, ten years after Bohr proposed his model. We studied, in Chapter 11, about the de Broglie’s hypothesis that material particles, such as electrons, also have a wave nature. C. J. Davisson and L. H. Germer later experimentally verified the wave nature of electrons in 1927. Louis de Broglie argued that the electron in its circular orbit, as proposed by Bohr, must be seen as a particle wave. In analogy to waves travelling on a string, particle waves too can lead to standing waves under resonant conditions. From FIGURE 12.8 A standing wave Chapter 14 of Class XI Physics textbook, we know that when is shown on a circular orbit a string is plucked, a vast number of wavelengths are excited. where four de Broglie wavelengths fit into the However only those wavelengths survive which have nodes circumference of the orbit. at the ends and form the standing wave in the string. It means that in a string, standing waves are formed when the total distance travelled by a wave down the string and back is one wavelength, two wavelengths, or any integral number of wavelengths. Waves with other wavelengths interfere with themselves upon reflection and theith amplitudes quickly drop to zero. For an electron moving in n circular orbit of radius rn, the total distance is the circumference of the orbit, 2prn. Thus 301 Reprint 2026-27