Lecture 24 The Hydrogen Atom Chapter 28.4  28.9 Outline Atomic Spectra The Bohr Model Modifications to the Bohr Model

Summary of Early Atomic Models The Thomson Model Description: Electrons are embedded in a wide positively charged area, like raisins in a cookie. Problem: Does not agree with the Rutherford -particles experiment. The Rutherford Model Description: Miniature Solar system with electrons orbiting the nucleus at any distance. Problem: Electrons experience acceleration and should lose energy by radiating photons and eventually fall onto the nucleus.

Three Types of Spectra When a material object is heated, electrons in the atoms absorb energy from the current and emit colored light, which can be dispersed into a spectrum. At high densities, the emission is continuous with no peaks within a short wavelength range. At lower densities, 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)  emission spectrum.

Three Types of 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. 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. 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.  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 has an energy level En = 13.6/n2 eV. An electron can absorb only those photons whose energy permit it to jump from one orbit (ni) to another, farther out (nf). When an electron jumps to an orbit, closer to the nucleus, it emits a photon of a wavelength . 1 1 1  = RH     nf2 ni2 RH  Rydberg constant RH = 1.097 107 m1

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. An electron can circle a nucleus only in orbits that contain an integral 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 as position, mass, velocity, and acceleration for granted. Quantum mechanics uses the uncertainty principle instead and explores probabilities. It deals only with quantities that 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 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 The 4th, spin quantum number (ms) determines the maximum number of electrons allowed on an orbit.

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.