BACKGROUND TO QUANTUM MECHANICS Flashcards
Light is wave-like:
refraction, diffraction, and two-slit experiment
Light is particle-like:
photoelectric effect and Compton scattering
In 1024, Louis de Broglie, considering the nature of light and matter, offered a startling proposition:
Small particles of matter may at times display wave-like properties
How did de Broglie come up with such a suggestion?
- combined the equation of Einstein with the Planck relationship for the enery of a photon, E =hv
- substituted for the momentum, p, its equivalent the product of the mass of the particle, m and its velocity, v.
Experimental observation of de Broglie Waves
X-ray Diffraction
- a beam of x-rays is directed at a crystalline substance, the beam is scattered in a definite manner characteristic of the atomic structure of the crystalline substance.
- The wavelength of the electrons revealed by the diffraction pattern matched that predicted by de Broglie’s hypothesis
- x-rays and electrons do indeed behave like analogously in these experiment; electron has a wave-like property
Rutherford model of the atom
- assumed that the positive charge was spread throughout the atom, forming a kind of paste or pudding in which the negative electrons were suspended like plums
- hypothesis: alpha particles would be expected to pass nearly straight through the foil
- Experimental result: not all alpha particles passed straight through the foil; some were deflected at large angles, even backward.
- Conclusion: the positive charge, instead of being distributed thinly and uniformly throughout the atom, was concentrated in a small region called the nucleus.
- hydrogen atom can be pictured as a central, rather massive nucleus with one electron; the nucleus can be considered fixed and the electron to be revolving about it.
How could the electron in the atom remain separated from the positively charged nucleus?
- the force holding the electron in a circular orbit is supplied by the coulombic force of attraction between the proton and the electro.
- a particle revolving around a fixed point experiences an outward acceleration, and requires an inward force to keep it moving in a circular orbit.
Proven to be wrong in the Rutherford model of the atom:
- because the electron is constantly being accelerated, it should emit EM radiation and lose energy just as electrons accelerated in an antenna.
- an electron revolving around a nucleus will lose energy and spiral into the nucleus, and so a stable orbit is classically forbidden.
Line spectra of Hydrogen
- every atom when subjected to high temp. or an electrical charge, emits electromagnetic radiation of characteristic frequencies; each atom has a characteristic emission spectrum
Johannes Balmer
- tried to find a pattern in the wavelengths or frequencies of the lines in the hydrogen atomic spectrum
Balmer series
- occurs in the visible and near ultraviolet regions
- series of line similar to the Balmer series appear in the ultraviolet and infrared regions
Johannes Rydberg
Swiss spectroscopist that accounted for all the lines in the hydrogen atomic spectrum by generalizing the Balmer formula
Ritz combination rule
all the observed lines could be expressed as the difference between the terms in the Rydberg formula
Niels Bohr
- theoretical explanation of the atomic spectrum of the hydrogen
- resolved the problem of Rutherford model of the atom
- incorporated the quantization of Planck into his theory of the hydrogen atom
Bohr model of the atom:
- Assumption: the angular momentum of the electron must be quantized according to (see formula in ppt)
- thus, we see that the radii of the allowed orbits (Bohr orbits), are quantized.
- the total energy of the electron = sum of its kinetic energy and potential energy
- hydrogen atoms and as well as most other atoms and molecules, will be found almost exclusively in their ground electronic state
- excited states - unstable; will usually relax back to the ground state and give off the energy as electromagnetic radiation
- assumed that the observed emission spectrum of the hydrogen atom was due to the transitions from one allowed energy state to a lower state
Bohr frequency condition
the basic assumption that as the electron falls from one level to another, the energy evolved is given off as a photon of energy, E =hv
Limitations of the Bohr theory:
- it could not be extended successfully even to a two-electron system such as helium
- it was never able to explain the spectra that arise when a magnetic field is applied to the system
- it was not able to predict the intensities of the spectral lines
