Bohr 2

Jul 25, 2008Download as PPT, PDF4 likes3,593 views

The document summarizes Niels Bohr's model of the atom from 1913. Bohr proposed that electrons orbit the nucleus in discrete, quantized energy levels. Electrons can jump between these energy levels, absorbing or emitting photons of light. The energy of the photons depends on the energy difference between the initial and final orbit. Bohr's model could only explain the hydrogen atom and failed to account for effects like the Zeeman and Stark effects seen in other atoms. Later developments in quantum mechanics disproved Bohr's idea of electrons having definite orbits.

Bohr’s Model Nucleus Electron Orbit Energy Levels Nucleus Electron Orbit Energy Levels

The Bohr Model In 1913 Bohr provided an explanation of atomic spectra His model includes both classical and non-classical ideas His model included an attempt to explain why the atom was stable

Bohr said classical view is wrong. Need a new theory — now called QUANTUM or WAVE MECHANICS . Bohr Model

Bohr’s Assumptions The electron moves in circular orbits around the proton under the influence of the Coulomb force of attraction The Coulomb force produces the centripetal acceleration

Bohr’s Quantum Conditions I. There are discrete stable “tracks” for the electrons. Along these tracks, the electrons move without energy loss (Stationery State). II. The electrons are able to “jump” between the tracks. In the Bohr model, a photon is emitted when the electron drops from a higher orbit (E i ) to a lower energy orbit (E f ). E i - E f = hf

Bohr Model: Orbit Radius Bohr assumed that the angular momentum of the electron was quantized and could have only discrete values that were integral multiples of h /2  , where h is Plank’s constant m e vr = nh /(2  ); n =1, 2, 3,… v = nh /(2  m e r )

Bohr Model: Energy of electron in orbit In each orbit, the energy of the electron is restricted to a certain value - E = - R H /n 2 R H is a constant in energy units: = 2.179 X 10 -18 J/atom = 13.6eV/atom = 1312 KJ/mole Number of orbit = n = 1, 2, 3, etc.

When an electron changes orbits it changes energies .

Energy is emitted in the form of light (electromagnetic radiation as the electron moves from a higher orbit to a lower one (from a higher energy level to a lower one). Energy is absorbed as electricity or heat as the electron moves from a lower to a higher orbit (energy level).

Specific Energy Levels The lowest energy state is called the ground state This corresponds to n = 1 Energy is –13.6 eV The next energy level has an energy of –3.40 eV The energies can be compiled in an energy level diagram The ionization energy is the energy needed to completely remove the electron from the atom The ionization energy for hydrogen is 13.6 eV

Energy Level Diagram The value of R H from Bohr’s analysis is in excellent agreement with the experimental value A more generalized equation can be used to find the wavelengths of any spectral lines

Orbit Radii and Energies r n =0.0529  n 2 (nm) E n =-13.6/ n 2 (eV) Energy difference between the levels  E =13.6(1/ n f 2 -1/ n i 2 ) For example, between n =1 and n =2 (as drawn in the picture)  E =13.6(1/ n f 2 -1/ n i 2 )=13.6(1/1 2 -1/2 2 )=10.2 eV  E= 10.2 eV Final state, n f Initial State, n i

PROBLEMS WITH THE BOHR ATOM A) It is only successful with the Hydrogen atom B) It could not account for extra lines in the H emission spectrum when a magnetic field was applied to the gas: Zeeman Effect : Splitting of Spectral lines under the external magnetic fields Stark Effect : Splitting of Spectral lines under the external electric field

C) PARTICLE-WAVE DUALISM 1923-24 - The French physicist de Broglie says that if light waves exhibit particle properties, under certain circumstances, then particles of matter should show wave characteristics under certain circumstances. h = 6.63 X 10-34 kg m2/sec if m is large and the speed is small, then  is so small as to be meaningless- 10 -34 m.

D) The idea of circular orbits and knowing where the electron is located is impossible: In 1927 Werner Heisenberg showed from quantum mechanics that it is impossible to know simultaneously, with absolute precision, both the position and the momentum of a particle such as an electron. The Heisenberg Uncertainty Principle! ▲ x * m ▲ v ≥ h/4 

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Compare and contrast the ideas that led to the Bohr model of the atom to the ideas that led to the quantum mecchanical theory that gave rise to the hydrogen atom wave functions. Solution The difficulty with the planetary picture provided before the Bohr model is that it is inconsistent with a well established fact of classical electrodynamics which says that an accelerated electric charge must continually radiate energy. If electrons actually followed such a trajectory, all atoms would act as source of radiation. The radiated energy would come from the kinetic energy of the orbiting electron; as this energy gets radiated away, As a result the electron would quickly fall into the nucleus. According to classical physics, no atom based on this model could exist for more than a brief fraction of a second. In contrary The Bohr model is a mixture of classical physics and quantum physics. The main postulated of Bohr\'s orbit are as follows: 1.) The electron in the atom moves in a circular orbit centred on its nucleus. Its motion in the orbit is governed by the Coulomb electric force between the negatively charged electron and the positively charged proton.The radius of orbit can be given as [r = nh/(2*pi*m*v), where n is principal quantum number.Emission spectrum of hydrogen is nicely explained by Bohr model. However, one serious difficulty with the Bohr model was that it was unable to explain the spectrum of any atom more complicated than hydrogen. 2.) An electron in a Bohr orbit does not continuously radiate electromagnetic radiation. Its energy is therefore constant. The orbit is referred to as a stationary orbit. 3.) Electromagnetic radiation isonlyemitted when the electron changes from one orbit to another of a lower total energy. (The electron is said to undergo atransition.) In such a case, the energy lost, E, is emitted asonequantum of radiation of frequencyfas given by thePlanck–Einstein formula: E = hf Although the Bohr model hypothesis for the quantization of angular momentum can be justified in terms of electron wave ideas, the Bohr model remains profoundly unsatisfactory as a wave model for the atom and also was not able to answer that why it doesn\'t fall into the nucleus. The main failures of Bohr\'s model are: - a mixture of classical and quantum ideas (electrons move classically on orbits, but their possible energy states are quantified) - postulates that on the allowed orbits electrons do not radiate (conflict with Maxwell’s theory) - could not account for the maximal electron numbers on one shell - could not explain splitting of the spectral lines in magnetic fields - it is a non-relativistic theory although the speed of the electrons is close to c In the Quantum Mechanical Model, the electron is treated mathematically as a wave. The electron has properties of both particles and waves. The advantage of Quantum Mechanical model over Bohr model is that it was successful to give explaination of the fact that electron does not fall in.

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The document discusses the history and development of models of the hydrogen atom. It begins by mentioning early observations of hydrogen. It then covers Thomson's "plum pudding" model, Rutherford's planetary model, Bohr's theory that electrons orbit the nucleus in distinct energy levels, and Schrodinger's wave equation solution that provides a more complete quantum mechanical description. The energy levels predicted by Bohr's theory and Schrodinger's equation match, both giving the ground state energy of the hydrogen atom as 13.6 electron volts.

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This document discusses electromagnetic radiation and atomic structure. It begins by explaining the wave characteristics of electromagnetic radiation like wavelength, frequency, and speed. It then discusses Planck's discovery that energy is quantized and Einstein's proposal that electromagnetic radiation consists of photons. The photoelectric effect is explained, providing evidence that light behaves as particles. The development of quantum mechanics and concepts like wave-particle duality, the Heisenberg uncertainty principle, and quantum numbers are summarized. The shapes and energies of atomic orbitals are described, along with how the periodic table developed based on patterns in elements' properties.

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The document summarizes atomic emission spectra and the origin of spectral lines. It discusses how atoms emit electromagnetic radiation when excited by an energy source. The emitted light is separated into spectral lines using a prism. Gases at low pressure emit discrete spectral lines, forming an atomic emission spectrum unique to each element. The Bohr model explained hydrogen's spectrum by proposing electron orbits of discrete energy levels. Later quantum theory described electron distributions as wave functions and orbitals rather than physical orbits. Spectral lines correspond to electron transitions between energy levels.

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Bohr 2

1. Bohr’s Model Nucleus Electron Orbit Energy Levels Nucleus Electron Orbit Energy Levels

2. The Bohr Model In 1913 Bohr provided an explanation of atomic spectra His model includes both classical and non-classical ideas His model included an attempt to explain why the atom was stable

3. Bohr said classical view is wrong. Need a new theory — now called QUANTUM or WAVE MECHANICS . Bohr Model

4. Bohr’s Assumptions The electron moves in circular orbits around the proton under the influence of the Coulomb force of attraction The Coulomb force produces the centripetal acceleration

5. Bohr’s Quantum Conditions I. There are discrete stable “tracks” for the electrons. Along these tracks, the electrons move without energy loss (Stationery State). II. The electrons are able to “jump” between the tracks. In the Bohr model, a photon is emitted when the electron drops from a higher orbit (E i ) to a lower energy orbit (E f ). E i - E f = hf

6. Bohr Model: Orbit Radius Bohr assumed that the angular momentum of the electron was quantized and could have only discrete values that were integral multiples of h /2  , where h is Plank’s constant m e vr = nh /(2  ); n =1, 2, 3,… v = nh /(2  m e r )

7. Bohr Model: Energy of electron in orbit In each orbit, the energy of the electron is restricted to a certain value - E = - R H /n 2 R H is a constant in energy units: = 2.179 X 10 -18 J/atom = 13.6eV/atom = 1312 KJ/mole Number of orbit = n = 1, 2, 3, etc.

8. When an electron changes orbits it changes energies .

9. Energy is emitted in the form of light (electromagnetic radiation as the electron moves from a higher orbit to a lower one (from a higher energy level to a lower one). Energy is absorbed as electricity or heat as the electron moves from a lower to a higher orbit (energy level).

10. Specific Energy Levels The lowest energy state is called the ground state This corresponds to n = 1 Energy is –13.6 eV The next energy level has an energy of –3.40 eV The energies can be compiled in an energy level diagram The ionization energy is the energy needed to completely remove the electron from the atom The ionization energy for hydrogen is 13.6 eV

11. Energy Level Diagram The value of R H from Bohr’s analysis is in excellent agreement with the experimental value A more generalized equation can be used to find the wavelengths of any spectral lines

12. Orbit Radii and Energies r n =0.0529  n 2 (nm) E n =-13.6/ n 2 (eV) Energy difference between the levels  E =13.6(1/ n f 2 -1/ n i 2 ) For example, between n =1 and n =2 (as drawn in the picture)  E =13.6(1/ n f 2 -1/ n i 2 )=13.6(1/1 2 -1/2 2 )=10.2 eV  E= 10.2 eV Final state, n f Initial State, n i

13. PROBLEMS WITH THE BOHR ATOM A) It is only successful with the Hydrogen atom B) It could not account for extra lines in the H emission spectrum when a magnetic field was applied to the gas: Zeeman Effect : Splitting of Spectral lines under the external magnetic fields Stark Effect : Splitting of Spectral lines under the external electric field

14. C) PARTICLE-WAVE DUALISM 1923-24 - The French physicist de Broglie says that if light waves exhibit particle properties, under certain circumstances, then particles of matter should show wave characteristics under certain circumstances. h = 6.63 X 10-34 kg m2/sec if m is large and the speed is small, then  is so small as to be meaningless- 10 -34 m.

15. D) The idea of circular orbits and knowing where the electron is located is impossible: In 1927 Werner Heisenberg showed from quantum mechanics that it is impossible to know simultaneously, with absolute precision, both the position and the momentum of a particle such as an electron. The Heisenberg Uncertainty Principle! ▲ x * m ▲ v ≥ h/4 

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