AtomsMind Map

Rutherford’s model came from the alpha particle scattering experiment, where fast alpha particles were directed at a very thin gold foil. Most alpha particles passed straight through, a few were slightly deflected, and a very small number rebounded through large angles. Rutherford concluded that most of the atom is empty space, positive charge and nearly all mass are concentrated in a tiny central nucleus, and electrons revolve around it. The nuclear size was found to be much smaller than atomic size, about 10⁻¹⁵ m compared with atomic size around 10⁻¹⁰ m. However, the model failed to explain atomic stability and line spectra because revolving electrons should radiate energy continuously according to classical electromagnetic theory.

Atomic spectra are the patterns of light obtained when radiation from atoms is separated by a prism or diffraction grating. A hot solid, liquid, or dense gas usually gives a continuous spectrum containing all wavelengths. A low-pressure excited gas gives an emission line spectrum consisting of bright lines at specific wavelengths. When white light passes through a cooler gas, the gas absorbs its characteristic wavelengths and forms a dark-line absorption spectrum. For isolated atoms, spectra are not continuous because atomic energy is quantized. Hydrogen shows several spectral series produced by electron transitions to fixed lower levels. These spectral lines were among the strongest evidences against classical atomic models and led to Bohr’s quantized energy levels.

Bohr’s model corrected Rutherford’s instability problem by introducing quantum postulates. According to Bohr, electrons revolve around the nucleus only in certain permitted stationary orbits without radiating energy. The angular momentum of the electron is quantized as mvr = nh/2π. Radiation is emitted or absorbed only when an electron jumps between two stationary orbits, with photon energy hν equal to the energy difference. For hydrogen-like atoms, Bohr derived formulas for orbit radius, electron velocity and energy. The model explains hydrogen spectrum, excitation energy and ionization energy very well. Its limitations are that it fails for multi-electron atoms, fine structure, Zeeman effect and the full wave nature of electrons.

Hydrogen spectrum is the most important application of Bohr’s model. When an electron in hydrogen jumps from a higher energy level to a lower energy level, it emits a photon whose wavelength is determined by the Rydberg formula. A group of lines ending at the same lower level is called a spectral series. Transitions ending at n = 1 form the Lyman series in the ultraviolet region. Transitions ending at n = 2 form the Balmer series, partly visible. Transitions ending at n = 3, 4 and 5 form the Paschen, Brackett and Pfund series respectively in the infrared region. Series limit occurs when the initial level n₂ becomes infinity, giving the shortest wavelength and maximum energy in that series.

de Broglie proposed that moving particles have wave nature along with particle nature. The wavelength associated with a particle is λ = h/p = h/mv. For an electron moving in a Bohr orbit, only those circular paths are stable in which the electron wave forms a standing wave. This means the circumference of the orbit must contain a whole number of wavelengths: 2πr = nλ. Substituting λ = h/mv gives mvr = nh/2π, which is exactly Bohr’s quantization of angular momentum. Thus de Broglie’s idea gives a physical explanation for why only certain electron orbits are allowed. Wave-particle duality is experimentally supported by electron diffraction and is fundamental to modern quantum physics.