bohr's hydrogen atom model
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Speaker: Somenath ChakrabartySomenath ChakrabartyDepartment of Physics, VisvaBharatiDepartment of Physics, VisvaBharati
A Short Biography of Prof. BohrA Short Biography of Prof. Bohr●Niels Henrik David Bohr (October 08, 1885 Niels Henrik David Bohr (October 08, 1885 November 18, 1962). November 18, 1962). ●Master degree: Copenhagen University 1909.Master degree: Copenhagen University 1909.●Doctoral degree: Under Professor Christian Doctoral degree: Under Professor Christian Christiansen 1911.Christiansen 1911.●Fundamental Contribution to understanding of Fundamental Contribution to understanding of atomic structure and quantum physics.atomic structure and quantum physics.●His three papers in 1913, which later became His three papers in 1913, which later became famous as famous as The TrilogyThe Trilogy were published in were published in Philosophical Magazine in Philosophical Magazine in JulyJuly, , SeptemberSeptember and and NovemberNovember of that year leads to Nobel Award. of that year leads to Nobel Award.
●While still a student the Royal Denish Academy of While still a student the Royal Denish Academy of Sciences in Copenhagen awarded him a prize for Sciences in Copenhagen awarded him a prize for the solution of a certain scientific problem of the the solution of a certain scientific problem of the surface tension by means of oscillating fluid jets. surface tension by means of oscillating fluid jets. He received a gold medal and the work was He received a gold medal and the work was published in the Transactions of the Royal Society, published in the Transactions of the Royal Society, 1908. This problem was proposed by Lord 1908. This problem was proposed by Lord Rayleigh in 1879.Rayleigh in 1879.
●In 19131914 Bohr held the position of Lecture in In 19131914 Bohr held the position of Lecture in Physics at Copenhagen University. Physics at Copenhagen University. ●During 19141916 a similar appointment at the During 19141916 a similar appointment at the Victoria University in Manchester. Victoria University in Manchester. ●In 1916 he was appointed Professor of In 1916 he was appointed Professor of Theoretical Physics at Copenhagen University. Theoretical Physics at Copenhagen University. ●From 1920 to 1962, until his death, he was the From 1920 to 1962, until his death, he was the head of the Institute for Theoretical Physics at head of the Institute for Theoretical Physics at Copenhagen university. Copenhagen university. ●The Institute was named as Niels Bohr Institute The Institute was named as Niels Bohr Institute three years after his death (1965).three years after his death (1965).
Bohr's Contribution to the Bohr's Contribution to the Structure of Hydrogen Atom Structure of Hydrogen Atom
●Bohr was the first to apply the quantum theory to Bohr was the first to apply the quantum theory to atomic structure at the age of 28 years. atomic structure at the age of 28 years. ●The most impressive result of the socalled Bohr The most impressive result of the socalled Bohr theory. theory. ●The model explained the series of lines observed The model explained the series of lines observed in the spectrum of light emitted by atomic in the spectrum of light emitted by atomic hydrogen. hydrogen.
● Cathode rays are streams of electrons observed in vacuum tubes. ● If an evacuated glass tube is equipped with two If an evacuated glass tube is equipped with two electrodes and a high voltage is applied, the glass electrodes and a high voltage is applied, the glass opposite of the negative electrode is observed to opposite of the negative electrode is observed to glow, due to electrons emitted from and travelling glow, due to electrons emitted from and travelling perpendicular to the cathode. perpendicular to the cathode. ● They were first observed in 1869 by German physicist Johann Hittorf, and were named in 1876 by Eugen Goldstein.
● Electrons were first discovered as the constituents of cathode rays in 1897 by British physicist J.J.Thomson. ●He showed experimentally that the rays were composed of a previously unknown negatively charged particle, which was later named the electron.
The Problem was TwoFoldThe Problem was TwoFold1. Where and How to Accommodate Electrons
Inside the Atoms?2. (i) Why a gas at low pressure, under the action
of high electric potential (Voltage) in a closed tube emits light?(ii) Why lights of different color are emitted from (ii) Why lights of different color are emitted from
different gases under the same condition?different gases under the same condition?(iii) Why under spectrum analysis of these (iii) Why under spectrum analysis of these
emitted lights give line spectra (discrete type) but emitted lights give line spectra (discrete type) but not band spectra (continuous type) as is observed not band spectra (continuous type) as is observed in the case of white light?in the case of white light?
First Attempt: 1903First Attempt: 1903
Thomson's Atom Model: Thomson's Atom Model: ●Atoms are spherical in shape. ●Positive charges are uniformly distributed inside this sphere.●Negatively charged electrons are rigidly embedded inside positively charged environment. ●Total positive and negative charges are equal.●The atoms are therefore electrically charge neutral.
Limitation of the Model
Thomson's model could explain a small fractional part of spectral observation. Among so many lines, only one line in hydrogen spectrum could be reproduced.
From the natural structure of this model, it is known as Plum Pudding Model or Watermelon Model.
● Thomson's atom model is not really successful in explaining the spectral line emission.● A number of empirical formulae are then used to explain line spectra from various gases. ● As for example, the Rydberg formula with a universally fitted constant the Rydberg constant
Experiment with Alpha BeamExperiment with Alpha Beam
In the year 1909 H. Geiger a student of E. Rutherford and E. Marsden a friend of Rutherford performed an outstanding class of experiment:
Collision of a beam of alpha particles on a thin foil Collision of a beam of alpha particles on a thin foil of gold.of gold.
It was an Outstanding Piece of It was an Outstanding Piece of ExperimentExperiment
Observations:Observations:Among twenty thousand or more of incident alpha particles only one back scattered after collision with the gold foil.
Almost all of them pass through without scattering.Almost all of them pass through without scattering.
Conclusions by Prof. RutherfordConclusions by Prof. Rutherford
1. Almost the whole space inside the atom is void or empty.2. The actual mass is sitting at the center of the atom.3. Size of this massive part is negligibly small compared to the whole volume.4. The central massive object known as the nucleus of the atom is positively charged, causes the repulsive scattering of alpha or Heion beam.
Rutherford's ModelRutherford's ModelBased on these results Rutherford proposed a Based on these results Rutherford proposed a model for the atom with a heavy positively charged model for the atom with a heavy positively charged nucleus at the centre, surrounded by negatively nucleus at the centre, surrounded by negatively charged electrons, rotating like a small solar charged electrons, rotating like a small solar system. system. Unfortunately this model was in conflict with the Unfortunately this model was in conflict with the laws of classical physics. The laws predict that laws of classical physics. The laws predict that the electron will emit electromagnetic radiation the electron will emit electromagnetic radiation while orbiting a nucleus, would lose energy, while orbiting a nucleus, would lose energy, gradually spiral inwards, finally collapsed into the gradually spiral inwards, finally collapsed into the nucleus. Therefore atoms are unstable in this nucleus. Therefore atoms are unstable in this model.model.
Bohr's Atom ModelBohr's Atom Model
To overcome this difficulty, Niels Bohr proposed, To overcome this difficulty, Niels Bohr proposed, in 1913, what is now called the Bohr model of the in 1913, what is now called the Bohr model of the atom. He suggested that electrons could only atom. He suggested that electrons could only have certain classical motions:have certain classical motions:
According to Bohr's model, the electrons can only According to Bohr's model, the electrons can only travel in some special orbits: travel in some special orbits: (a) At a certain discrete set of distances from the nucleus with specific energies and angular momentum.(b) The electrons do not continuously lose energy as they travel. They can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency determined by the energy difference of the levels divided by the Planck constant.
The significance of the Bohr model is that the laws The significance of the Bohr model is that the laws of classical mechanics apply to the motion of the of classical mechanics apply to the motion of the electron about the nucleus only with some electron about the nucleus only with some restrictions by quantum rules. The angular restrictions by quantum rules. The angular momentum is restricted to be an integer multiple momentum is restricted to be an integer multiple of a fixed unit, which is again the Planck constant.of a fixed unit, which is again the Planck constant.
● One of the key success of Bohr model for One of the key success of Bohr model for hydrogen atom (1913) was to give an explanation hydrogen atom (1913) was to give an explanation of the Rydberg formula (1885) for the spectral of the Rydberg formula (1885) for the spectral emission lines of atomic hydrogen.emission lines of atomic hydrogen.● Not only did the Bohr model explain the reason for the structure of the Rydberg formula, it also provided a justification for its empirical results in terms of fundamental physical constants.
●Some features of Bohr's semiclassical model Some features of Bohr's semiclassical model were indeed very strange compared to the were indeed very strange compared to the principles of classical physics. It introduced an principles of classical physics. It introduced an element of discontinuity and indeterminism element of discontinuity and indeterminism unknown to classical mechanics. unknown to classical mechanics.
●Apparently not every point in space was Apparently not every point in space was accessible to an electron moving around a accessible to an electron moving around a hydrogen nucleus.hydrogen nucleus.●An electron moved in classical orbits, but during An electron moved in classical orbits, but during its transition from one orbit to another it was at no its transition from one orbit to another it was at no definite place between these orbits. definite place between these orbits. ●Thus, an electron could only be in its ground Thus, an electron could only be in its ground state (the orbit of lowest energy) or an excited state (the orbit of lowest energy) or an excited state.state.
Rutherford pointed out that if, as Bohr did, one Rutherford pointed out that if, as Bohr did, one postulates that the frequency of light, which an postulates that the frequency of light, which an electron emits in a transition, depends on the electron emits in a transition, depends on the difference between the initial energy level and the difference between the initial energy level and the final energy level, it appears as if the electron final energy level, it appears as if the electron must must knowknow to what final energy level it is heading to what final energy level it is heading in order to emit light with the right frequency. in order to emit light with the right frequency.
Limitations of Bohr's TheoryLimitations of Bohr's Theory
Bohr's biggest contribution in his model was to Bohr's biggest contribution in his model was to introduce quantum principles to classical physics, introduce quantum principles to classical physics, but his model had a few limitations:but his model had a few limitations:
● The Bohr model could only successfully explain the whole hydrogen spectrum.● It could not accurately calculate the spectral lines of larger atoms having more complex type electron distribution.● The model of course worked for hydrogenlike atoms, i.e., if the atom had only one electron in the outermost orbit.
● Bohr's model could not explain why the intensity of the spectral lines were not all equal. This suggests that some transitions are favoured more than others.● With better equipment and careful observation, it was found that there were previously undiscovered spectral lines. These lines were named as Fine structures. Bohr's model could not explain why this was the case.
● It was found that, when hydrogen discharge tube was placed in a magnetic field, the produced emission spectrum was split into a number of lines known as Zeeman splitting. Bohr's model could not account for this ● Although Bohr stated that electrons were in stationary states, he could not explain why.● Whether all the transitions are allowed or some of them are forbidden could not be explained.
Outcome of Bohr's Model
● Although Bohr's atom model is successful in Although Bohr's atom model is successful in explaining the line specta only from hydrogen or explaining the line specta only from hydrogen or hydrogen like atoms, but the basic postulates are hydrogen like atoms, but the basic postulates are applied to solve the structures of complex atoms applied to solve the structures of complex atoms and a collection of an enormous number of atoms and a collection of an enormous number of atoms in a solid, of course with some modifications and in a solid, of course with some modifications and also incorporating a number of new concepts.also incorporating a number of new concepts.
Stepping Stone for the Quantum Mechanics to Stepping Stone for the Quantum Mechanics to Enter into the IndustryEnter into the Industry
Personal Life of Bohr
● Niels was a passionate footballer as well, played several matches for the CopenhagenbasedAkademisk Boldklub, with Niels as goalkeeper.
In 1910, Bohr met Margrethe Nørlund, the sister of the mathematician Niels Erik Nørlund. Bohr resigned his membership in the Church of Denmark on 16 April 1912, and he and Margrethe were married in a civil ceremony at the town hall in Slagelse on 1 August.
● Niels had six sons. The oldest, Christian, died in a boating accident in 1934, and another, Harald, died from childhood meningitis. Aage Bohr became a successful physicist, and in 1975 was awarded the Nobel Prize in physics, like his father. Hans Henrik became a physician; Erik, a chemical engineer; and Ernest, a lawyer.
Bohr–van Leeuwen Theorem In his Ph.D. thesis Bohr extended Lorentz's classical model for electrons, but was unable to account for phenomena like the Hall effect, and concluded that classical electron theory could not fully explain the magnetic properties of metals. The thesis was accepted in April 1911. In 1921, the Dutch physicist Hendrika Johanna van Leeuwen independently derive a theorem from Bohr's thesis that is today known as the Bohr–van Leeuwen theorem Impossibility of classical diamagnetism.