Transcript Bohr model
Ch2 Bohr’s atomic model • Four puzzles – – – – Blackbody radiation The photoelectric effect Compton effect Atomic spectra • Balmer formula • Bohr’s model • Frank-Hertz experiment Blackbody • Absorptivity (absorptance): the ratio of the radiation absorbed by a body to that incident on the body. • Blackbody: A body with a surface having an absorptivity equal to unity. • A realistic blackbody: For a cavity kept at a constant temperature with the interior wall blackened, a small hole in the wall behaves like a blackbody. Some observations • Stefan's Law states that the power radiated by a body is proportional to the 4th power of the absolute temperature. R T 4 • For a given temperature, the radiation forms a continuous spectrum with respect to the frequency. Wein's Displacement Law Reyleigh-Jeans law Ultraviolet catastrophe Puzzles in blackbody radiation • Two puzzles: – Why were not radiation above the ultraviolet region present? – Why was there a non-uniform distribution of electromagnetic radiation being emitted? Plank’s theory • Planck made an assumption that the energy of an oscillator must be an integral multiple of the product of the constant h and the frequency of the electromagnetic radiation it emitted. E0 nhf • His assumption resulted in a formula for the blackbody radiation that was in excellent agreement with experiment at all frequencies. Two puzzles to be explained • Radiation in the high frequency region were not emitted from the blackbodies because this required large energy changes which could not occur in the atoms. • Certain energy states were more probable in the atoms and therefore frequencies associated with these energy states were more likely to be emitted. The photoelectric effect • When light of a high frequency was incident on a metallic surface, electrons were emitted from the surface. Actual observation • Intensity: The high intensity of light would not cause electrons to have high KE. The actual reaction time is very short (10-9s). • Frequency: At a certain frequency called threshold frequency, electrons were emitted. A frequency beyond it will cause the electrons to have a greater KE. • Stopping voltage: The energy of the ejected electrons was proportional to the frequency of the illuminating light & had nothing to do with intensity. Einstein’s explanation • For a photoelectron, E=hf . • The minimum energy required to pull electrons from inside to outside the metal is called the work function W. W=hf0 • If an electron is given an energy E larger than W, it can escape the metal and will have a maximum KE: 1 2 mvmax E W hf hf 0 2 The Compton effect (Compton scattering) 2h 2 f i sin me c 2 This could be explained when X rays are regards as particles (photons). The collision between a photon and an electron is regarded as an elastic collision. Discrete spectra • Atoms emit and absorb light only at specific frequencies. – Emission lines, – Absorption lines, • Balmer found that the wavelengths of visible and near ultraviolet line spectra of hydrogen obey a simple formula exactly: 1 1 1 RH ( 2 2 ) 2 n • RH=1.097x107m-1 is called the Rydberg (里德伯) constant. Bohr model • There are three postulates used in Bohr’s model: – The electron moved in a certain set of stable orbits in which classical mechanics can be used to describe motion of the electron. – Moving electrons in stable states do not radiate. An electron can make a sudden quantum jump between the orbits. – The orbital angular momenta of the electrons are quantized. Quanta in the atom • The total energy of the electron is inversely 1 E proportional to the square of n, i.e. where n n is called quantum number. • The total energy is also found to be negative, indicating a “bound” state. The most negative state, the most tightly bound electron, occurs for n=1, referred to as the ground state of the atom, n>=2, excited states. L nin • The angular momentum of the electron moving a circular orbit can only take discrete values: n 2 Line spectra of the H atom 1 2 e2 m e2 1 2 En mv 2 2 40 r 2 40 n • Energy levels: • Lyman series: n=1; Balmer series: n=2; Paschen series: n=3; Brackett series: n=4 Improvement on the Bohr model • Finite nuclear mass (motion of nucleus): When taking the nuclear mass into account, the reduced mass should replace the electron mass. • Relativistic correction: The effect of the relativistic mass change m(v) should be considered. Fastermassivedecrease in energy. • Sommerfeld’s extension: Electrons should have elliptical orbits with the same energies as that in circular orbits. The second quantum number should be introduced. Frank-Hertz experiment • Frank & Hertz in 1913 showed the existence of discrete energy levels in atoms. Frank-Hertz experiment results Explanation • With the increase of grid potential, more electrons move to the plate and the current rises accordingly. • For mercury atoms, when V=4.9V, the electrons make inelastic collision and leave the atom jump to a high orbit (n=2). The original electrons move off with little energy and could not reach the plate and thus reduce the current. • As V is increased further, the current rises again and would drop at V=9.8V. This would make more atoms to jump to n=2 state. Limitations of Bohr model • It can not be generalised to deal with systems with two more electrons as the force between the electrons can not be easily added. • It can not explain the closely spaced lines. • It can not be used to calculate the rate of transitions between different energy levels. • The Bohr model was eventually superseded by the quantum mechanics developed by E Schrodinger, W Heisenberg and others, following the ideas of L de Broglie.