The Hydrogen Atom. Quantum Theory of Atom. Lecture 16 The Hydrogen Atom. Quantum Theory of Atom. Atomic Spectra The Bohr Model of the Atom Quantum Theory of Atom

Atomic Spectra When an electric current is passed through a gas, electrons in the gas atoms absorb energy from the current. The excited this way gas emits colored light. If we disperse the emitted light into different frequencies, we will see series of bright lines, some of which are more intense. The color of the most intense lines gives the excited gas its color (red to neon). This is an emission spectrum.

Absorption Spectra Absorption spectra occur when light from a hot source passes through a cool gas before entering the spectroscope. The light source alone would give a continuous spectrum, but atoms of the gas absorb certain frequencies from the light. The lines in the emission and absorption spectrum of the same chemical element have the same frequencies. It was shown that frequencies in the spectrum of an element fall into sets called spectral series.

The Bohr Model In 1913 Niels Bohr proposed a theory of the hydrogen atom that could account for its stability and for the frequencies of its spectral lines. Bohr proposed than an electron can circle the nucleus without losing energy only in certain specific orbits. The energy of the electron depends on which orbit it is in. Thus Bohr suggested that atomic electrons can have only certain particular energies.

The Bohr Model An electron in the innermost orbit has the least energy. The larger the orbit, the more the electron has energy. The orbits are identified by a quantum number, n. Each orbit corresponds to an energy level of the atom. An electron can absorb only those photons whose energy will permit it to jump from orbit to another, farther out. When an electron jumps from an orbit to another one, closer to the nucleus, it emits a photon. The difference in energy between the 2 orbits is hf, where f is the frequency of the emitted or absorbed photon.

Electron Waves and Orbits Why does an atomic electron follow certain orbits only? The de Broglie wavelength of the electron is exactly equal to the circumference of its ground state (the innermost orbit with n=1). If we consider the vibrations of a wire loop, we find that their wavelengths always fit a whole number of times into the loop’s circumference. Thus, an electron can circle a nucleus only in orbits that contain a whole number of de Broglie wavelengths.

Quantum Theory of the Atom The Bohr’s model has some severe limitations. It correctly predicts the spectral series for hydrogen, but fails predicting the same for atoms with 2 or more electrons. A more general approach was developed in 1925/6 by Erwin Schrodinger, Werner Heisenberg, and others, and is called quantum mechanics.

Classical versus Quantum Mechanics Classical mechanics takes such quantities of an object as its position, mass, velocity, and acceleration for granted. Quantum mechanics uses the uncertainty principle instead and explores probabilities. It deals only with quantities which can actually be measured. The measurable quantities are mass of the electron, its electric charge, frequencies of spectral lines, etc. But we cannot measure the precise diameter of an electron’s orbit. Quantum mechanics includes Newtonian mechanics as a special case.

Quantum Numbers In the quantum theory of atom, an electron has no fixed orbit but is free to move about 3 dimensions. It circulates in a probability cloud that forms a certain pattern in space and can be found where the cloud is the most dense. Three quantum numbers determine the size and shape of the probability cloud of an atomic electron. n  the principal quantum number l  the orbital quantum number ml  the magnetic quantum number

Exclusion Principle The fourth quantum number is ms  spin magnetic quantum number. In an unexcited hydrogen atom, the electron is in its quantum state of the lowest energy. For more complex atoms, the exclusion principle is valid: Only one electron can exist in a given quantum state. Each electron in an atom must have a different set of the 4 quantum numbers.

Summary The Bohr model correctly explained properties of only hydrogen atoms. Quantum theory of atom is a probabilistic approach, which enlarges applications of the classical mechanics. Quantum mechanics shows that four quantum numbers are needed to specify the physical state of each atomic electron.