Rutherford’s Model: Conclusion

1. Rutherford’s Model: Conclusion Massive nucleus of diameter 10-14 m and combined proton mass equal to half of the nuclear mass Planetary model: Electrons revolve around the positive cores planets revolve around the sun Questions: Q1: If there are only Z protons in the nucleus then what composes the other half of the mass Ans1: The difference of mass could be to grouping of neutral particles each consisting of electron-proton pair (fundamental particles). Q2: What provides the cohesive force that keep many protons confined is small distance (10-14). Ans2: The nucleus is a very complex system consisting of positively and negatively charged bodies bound closely together by electrical forces Q3: How do the electrons move together to form a stable atom, and how does their motion account for the observed spectra.

2. Spectral Lines

3. Spectral Lines For gas spectra, the wavelengths contained in a given line spectrum are characteristic of the particular element emitting it. Kirchhoff was able to discover two new elements (Rb,Cs) by observing new sequences of spectral lines. (foundation of absorption spectroscopy) He correctly deduced that all of Fraunhofer’s dark lines should be attributed to absorption of different elements present in the sun. He opened a way of determining the elemental composition of the starts trillion miles away. Absorption spectroscopy is done by passing a light from a continuous source through a gas of the element to be studied. The spectrum consist of a series of dark lines superimposed on the continuous spectrum of the source light. Each line of the absorption spectrum coincides to a line in the emission spectrum. But not all the emission lines are present in the absorption spectrum.

4. Bohr’s Quantum Model of the Atom In April 1913, Neils Bohr published a paper that shook the work of physics at its foundation. He gave the first successful theory of atomic line spectra and overthrow some of the most principles of Maxwell’s theory. Both Thompson and Rutherford realized that the electrons must revolve in order to avoid falling into the nucleus. But according to Maxwell’s theory, centripetally accelerated charges revolving with orbital frequency f, should radiate light waves with frequency f. Classically, as the electron radiates energy, its orbits radius decreases and its frequency of revolution increases, which leads to collapse of the atom. Bohr postulated that the classical radiation theory confirmed by Hertz’ experiment using large circuit does not hold for atomic sized systems. He applied Planck’s ideas of quantized energy levels to orbiting electrons. He also used the ideas of Einstein.

5. Bohr’s Model of Hydrogen • The electron moves in a circular orbits about the proton under the influence of Coulomb force • Only certain orbits are stable. These are the ones in which the electron does not radiate. The energy is fixed, and classical mechanics can be sued to describe the motion of the electron • Radiation is emitted by the atom when the electron jumps from a more energetic initial state to a lower state. The frequency of the photon emitted is independent of the frequency of revolution of electron. It is related to the change in atom’s energy as given by Planck formula. • The size of the allowed electron orbits is determined by an additional quantum condition imposed on the electron’s orbital angular momentum. Namely the allowed orbits are those for which the electron’s orbital angular momentum about the nucleus is quantized.

6. Success of Bohr’s theory Evaluated the size of n=1 orbit for the hydrogen atom correctly (Bohr’s radius) Evaluated the ionization energy of Hydrogen atom The agreement of his theory with Balmer’s equation. He showed that all observed spectral lines have interpretation in his theory He extended his theory to all one-electron ions He explained the difference between absorption and emission lines. He explained the emission of x-rays from atoms He explained the nuclear origin of beta particles. He explained the chemical properties of atoms in terms of electronic shell model He explained how atoms associate to form molecules Electrons of elements with higher atomic numbers form stable concentric rings with definite numbers of electrons allowed for each ring or shell The number of electrons in the outermost ring determines the valency

7. Correspondence Principle Predictions of quantum theory must correspond to the predictions of the classical physics in the region of sizes where classical theory is known to hold. The classical sizes for length, mass and time are on the order of cm, gram, and seconds, and typically involve large quantum numbers, as if we calculate n for hydrogen atom with radius 1 cm. Bohr showed that the quantization of angular momentum is a consequence of the smooth and gradual emergence of classical results from quantum theory in the limit of large quantum number.

8. Direct Confirmation of Atomic Energy Levels: Franck-Hertz Experiment (1914) Electrons emitted by the filament are accelerated over a relatively long region (1 cm) by the positive potential on the grid. The electrons are collected and registered on the electrometer if they have enough energy to overcome the retarding potential which is set 1 mm from the grid. At low electrons energy or accelerating voltages, electrons will collide elastically with the Hg atoms and transfer very little KE to the massive Hg, so the electron reaches the grid with KE = e V. As the accelerating voltage is increased to a threshold value, inelastic collisions will occur. Electrons can transfer almost all their energies to the atom raising it to the first excited state. Electrons will not be able to overcome the retarding potential and consequently I will drop. First Peak. When V is increased again, electrons could make two inelastic collisions. Look at I-V curve. If the adjacent maxima (or minima) are averaged a value of 4.9 V is found corresponding to the ground to first excited state transition Conclusion: Atoms can only accept discrete values amounts of energy, corresponding to discrete energy levels. The excited atom return to its ground state by emitting a photon of energy 4.9 eV.