History of the Atomic Model. Bohr s Model of the Atom

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1 Bohr s Model of the Atom Niels Bohr (93) was the first to propose that the periodicity in the properties of the elements might be explained by the electronic structure of the atom Democritus (400 B.C.) Believed that matter was composed of invisible particles of matter he called atoms. Antoine Lavoisier (700 s) Law of Conservation of Mass Matter is not created or destroyed. Joseph Proust (700 s) Law of constant composition compounds are composed of atoms in definite ratios. John Dalton (Late 700 s) First atomic theory explaining chemical reactions Henri Bacquerel (896) While studying the effect of x-rays on photographic film, he discovered some chemicals spontaneously decompose and give off very penetrating rays. J.J. Thomson (897) Discovered the electron using cathode ray tubes Marie Curie (898) Studied uranium and thorium and called their spontaneous decay process "radioactivity, leading Rutherford to discover the alpha particle. Hantaro Nagaok (903) Postulated a "Saturnian" model of the atom with flat rings of electrons revolving around a positively charged particle. Robert Millikan (909) Found the charge and mass of the electron in his famous oil-can experiment. Ernest Rutherford (9) Discovered the nucleus in his famous gold foil experiment. Data from his experiments led Rutherford to propose a planetary model in which a cloud of electrons surrounded a small, compact nucleus of positive charge. Only such a concentration of charge could produce the electric field strong enough to cause the heavy deflection of alpha particles observed. Rutherford's Problems. according to the Larmor Formula in classical electromagnetism; an orbiting charge should steadily lose energy and spiral toward the nucleus, colliding with it in a small fraction of a second.. the planetary model could not explain emission and absorption spectra of atoms that were observed.

2 Niels Bohr (93) Solidified Rutherford s Planetary atomic model by using the work of Max Plank and Albert Einstein on the nature of Electromagnetic Radiation to predict the spectral lines of hydrogen described by the work of Johann Balmer and Johhanes Rydberg. The Emission Spectra of Elements One property of the elements that really captured the attention of scientists is that one does not observe a continuous spectrum for hydrogen, as one gets from a white light source. Only a line spectrum of discrete wavelengths is observed. To develop an understanding of Bohr s Planetary Model, we must investigate the nature of Electromagnetic Waves and the work of a few important scientists. Johann Balmer (885) Showed that the wavelengths of the four visible lines of hydrogen fit a simple formula relationship. λ = hm /(m - n ) λ Johannes Rydberg (888) Expanded Balmer s relationship to a more general equation that could be used to calculate all spectral lines of hydrogen, not only the visible, known as the Rydberg equation: (R ) H n n R H = Rydberg constant = x0 7 m - n = principle Quantum Number Electromagnetic Waves Electromagnetic Radiation refers to energy that travels though space consisting of an energy wave and a perpendicular magnetic wave. Waves The distance between corresponding points on adjacent waves is the wavelength ( ).

3 Waves The number of waves passing a given point per unit of time is the frequency ( ). All transverse waves fit the inverse proportion: νλ = k Describes all wavelengths of electromagnetic radiation. Visible light only makes up a small portion of the electromagnetic spectrum cycles : sec sec Hertz (Hz) Max Plank (900) Quanta = minimal amount of energy that can be emitted or absorbed by electromagnetic radiation. Studying energy absorbed and emitted by hot glowing matter, He noted that energy is only released or absorbed in chunks of some minimal size he called quanta. Plank s Quantization of EMR E = hν E = energy h = Planck s constant = 6.66 x 0-34 J. s ν= frequency So, energy is absorbed or emitted in packets, or quanta, of: hν, h ν, 3h ν, 4hν... Equation sheet Albert Einstein (905) By observing the Photoelectric effect, Einstein proposed that a beam of light is not a wave propagating through space, but rather a collection of discrete wave packets(photons), each with energy hf. This shed light on the previous discovery of the Planck relation (E = hν) linking energy (E) and frequency (ν) as arising from quantization of energy. The factor h is known as the Planck constant. The Photoelectric Effect In opposition to Maxwell's theory that EMR energy is proportional to intensity, Einstein concluded that EMR energy is proportional to wave frequency: E photon = h where h is Planck s constant ( J-s.)

4 Einstein's Wave-Particle Duality of Light Albert Einstein determined that E.M.R. is composed of packets of quantized energy called photons; each having its own characteristic wavelength and traveling at a constant speed, the speed of light (c), 3.00 X 0 8 m/s. Therefore, if one knows the wavelength of light, one can calculate the energy of one photon-wave, or quanta, of that light: c = E = h Reminder J kg m s So: Short wavelength --> high frequency high energy Long wavelength --> small frequency low energy Bohr s Model Bohr solidified Rutherford s planetary model of the atom by explaining how electrons maintain specific energy levels orbiting the nucleus in particular circular orbits with fixed energy, its distance from the nucleus being proportional to its energy. Under this model an electron could not spiral into the nucleus because it could not lose energy in a continuous manner; instead, it could only make instantaneous "quantum leaps" between the fixed energy levels. When this occurred, light was emitted or absorbed at a frequency proportional to the change in energy (hence the absorption and emission of light in discrete spectra). Bohr s Model. Electrons in an atom can only occupy certain orbits (corresponding to certain energies).. Electrons in permitted orbits have specific, allowed energies; these energies will not be radiated from the atom. These allowed energy levels (E n or n) can have quantized values from to infinity ( ) According to Bohr, the energy of these quantized states can be determined by: E n = - hcr H /n Or: -.8 x 0-8 J E E n = - k /n n = E n = Energy in a main energy level R H = Rydberg constant = x0 7 m - k = hcr H =.79 x 0-8 J n = principle Quantum Number Or by rearranging: n Lower the Energy (more +), the more stable and visa versa.

5 Bohr s Model 3. Energy is only absorbed or emitted in such a way as to move an electron from one allowed energy state to another; the energy is defined by: E photon = hν. Electrons exist in the lowest energy level possible, their ground state.. As Energy is absorbed by the atom, electrons are ejected to outer electron orbits of higher energies known as excited states 3. Excited states are unstable, therefore, electrons will fall back to their ground states, releasing quantum(s) of energy called photons. For the transition of an e - from an initial energy level (E i ) to a final energy level (E f ), we can write: ΔE = E nf E ni = E photon The absorbed energy is equal to the change in energy states for an electron; which is equal to the energy of an absorbed or released photon. Where: ΔE electron = E photon = h = c / Substituting into the equation: And rearranging, we get: ΔEelectron remember: ΔE = E nf E ni = E photon Ephoton ΔE = h = c / k nf ni Know These!! Using the Bohr model, we can calculate the wavelengths absorbed or emitted from a Hydrogen atom. Likewise, we can calculate the energy level jumps of a Hydrogen electron that has absorbed energy..calculate the energy required to excite the hydrogen electron from level n= to level n=. Also, calculate the wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach this excited state.

6 .Calculate the energy required to remove the electron from a hydrogen atom in its ground state. Bohr s Model Bohr s theory was a great accomplishment and he Received the Nobel Prize in 9. However, Bohr's model was not perfect. It could only predict the spectral lines of hydrogen; it couldn't predict those of multielectron atoms. Worse still, as spectrographic technology improved, additional spectral lines in hydrogen were observed which Bohr's model couldn't explain. Henri Mosely (95) Determined the charges on the nuclei of most atoms resulting in a reorganization of the periodic table based upon atomic number instead of atomic mass. Ernest Rutherford (97) concluded that hydrogen nuclei were singular particles and a basic constituent of all atomic nuclei. He named such particles protons. Bohr s quantized energy state was then corrected to take into the account the effect of multiple proton nuclei: where: E hcr H z = nuclear charge k = hcr H = +.79 x 0-8 joule z n Remembering that for Hydrogen, z =.

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