DOCSLIB.ORG

One Hundred Years of Bohr Model

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
One Hundred Years of Bohr Model GENERAL ARTICLE One Hundred Years of Bohr Model Avinash Khare In this article I shall present a brief review of the hundred-year young Bohr model of the atom. In particular, I will ¯rst introduce the Thomson and the Rutherford models of atoms, their shortcom- ings and then discuss in some detail the develop- ment of the atomic model by Niels Bohr. Fur- ther, I will mention its re¯nements at the hand of Sommerfeld and also its shortcomings. Finally, I Avinash Khare is Raja will discuss the implication of this model in the Ramanna Fellow at IISER, Pune. His current interests development of quantum mechanics. are in the areas of low The `Bohr atom' has just completed one hundred years dimensional field theory, nonlinear dynamics and and it is worth recalling how it emerged, its salient fea- supersymmetric quantum tures, its shortcomings as well as the role it played in mechanics. Besides, he is the development of quantum mechanics. passionate about teaching an well as popularizing Thomson Model of Atoms science at school and college level. Till 1896, the popular view was that the atom was the basic constituent of matter. The ¯rst important clue regarding the internal structure of atoms came with the discovery of spontaneous radiation, ¯rst identi¯ed by Becquerel in 1896. The very existence of atomic radia- tion strongly suggested that atoms were not indivisible. With the discovery of the electron in 1897, J J Thomson was convinced that electrons must be fundamental con- stituents of matter and this led to his corpuscular theory of matter. This model was popularly known as `Plum Pudding Model'. In this model, the positive charge of the atom was assumed to be spread throughout the atom forming a kind of pudding in which negatively charged Keywords electrons were suspended like plums. Thomson showed Plum pudding model, Rutherford atom, Balmer series, Rydberg that his model had an amazing explanatory power for formula, star Puppis, charac- the observed periodicity in the elements. Thomson later teristic X-rays, Bohr–Sommerfeld applied a modi¯ed version of this model to a variety of approach. RESONANCE October 2013 885 GENERAL ARTICLE phenomena such as dispersion of light by dilute gases and developed methods for estimating the actual num- ber of electrons in an atom. By 1910, experiments had con¯rmed many of its predictions for the absorption and scattering of electrons in matter. However, this model was not suitable for predicting spectral lines which had already been seen by spectroscopists. Figure 1. Thomson’s model Rutherford Model of Atoms of atom. In this ‘plum pud- ding’ model of atom devel- Rutherford wanted to test this Thomson picture of the oped byThomson and Kelvin atom. On his advice, Geiger and Marsden carried out in 1094, the electrons(plums) a series of experiments. Using their data, Rutherford are embedded in a sphere of in 1911 provided conclusive proof of the inadequacy of uniform positive charge (pud- the Thomson model. In these experiments, a collimated ding). 4 beam of alpha particles (i.e., He2 nucleus) from a ra- dium source strike a thin gold foil. To their surprise, they found that few alpha particles were even scattered at large angles. This would not be expected if the alpha particle had hit a much lighter particle like the elec- tron. Rutherford argued that these experiments clearly showed that instead of being spread throughout the atom, the positive charge is in fact concentrated in a very small region at the center of the atom. This was one of the most important developments in atomic physics and was Figure 2. Rutherford’smodel the foundation of the subject of Nuclear Physics. We go of atom. In this model, the through the Rutherford argument here. atom consisted of a positively charged nucleus surrounded Let us suppose that a particle of mass M and velocity by negatively charged elec- v, hits a particle of mass m which is at rest. After the trons. collision, let us suppose that the particle of mass M continues along the same line with velocity v0, giving the target particle (with mass m) a velocity u (note, we are using the notation in which positive velocity is in the same direction as the incident particle of mass M, while a negative velocity will be in the opposite direction). Then the energy and momentum conservation equations are 1 2 1 2 2 Mv = mu + Mv0 ; Mv = (Mv0 + mu ) : (1) 2 2 886 RESONANCE October 2013 GENERAL ARTICLE On eliminating u, we have a quadratic equation for v0 in terms of v 2 2 2 m(v v0 ) = M(v v0) ; (2) ¡ ¡ which has two solutions: either v0 = v or m M v0 = v ¡ : (3) ¡ µm + M ¶ The ¯rst solution v0 = v; u = 0 is a trivial solution. The interesting solution is the second one given by (3). It says that v0 can be negative (i.e., scattered particle recoils backwards) only if m > M (similarly, somewhat weaker limits on m can be inferred from scattering at any large angle). Thus it was clear to Rutherford that the experimental results of Geiger and Marsden could not be explained in terms of multiple encounters with a positively charged sphere of atomic dimensions, as was Thomson's view. The fact that a few alpha particles were observed to be scattered at large angles clearly showed that the alpha particles must be hitting something in the gold atom which is much heavier than the electron. As Rutherford later explained, \it was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you ¯red a 15-inch shell at a piece of paper, and it comes back and hits you". Hence, Ruther- Rutherford ford concluded that the positive charge of the atom is concluded that the concentrated in a small heavy nucleus at the center of positive charge of the atom, around which the much lighter, negatively atom is concen- charged electrons circulate in orbits, like planets around trated in a small the sun. This is why the Rutherford nuclear model is heavy nucleus at often referred to as the planetary model of the atom. the centre of the This model, despite being successful, had one major atom, around which problem. It predicted that even light atoms like hy- the much lighter, drogen were unstable. The point was, according to the negatively charged classical electromagnetic theory, an electron revolving electrons circulate around a nucleus will radiate electromagnetic waves and in orbits. RESONANCE October 2013 887 GENERAL ARTICLE hence will deplete the electron's energy and it will even- tually spiral inwards towards the nucleus. Thus an atom would rapidly collapse to nuclear dimensions (the col- 12 lapse time can be computed to be of order 10¡ sec!). Further, the continuous spectrum of the radiation that would be emitted in this process was not in agreement with the observed line spectrum. Bohr Model In the autumn of 1911, Bohr went to England for his post-doctoral research. He had already done interest- ing work on the electron theory of metals during his PhD thesis { it was so advanced that no one in Den- mark could evaluate it fully. Bohr ¯rst went to Cam- bridge University and worked for about a year with J J Thomson before being invited by Rutherford to work with him at University of Manchester. Using the data from the absorption of alpha-rays, and using Ruther- ford's model, Bohr showed that the hydrogen atom has only one electron outside the positively charged nucleus while the helium atom has two electrons outside the pos- itively charged nucleus. It is worth noting here that till 1912, physicists were not sure about the number of elec- trons in the helium atom or even in the hydrogen atom. All this time, the problem which was really troubling Bohr was, however, the stability of the Rutherford atom and ¯nally he came up with a simple model of atomic structure. A key feature of this very successful model, proposed by Bohr in 1913, was the prediction of the line spectrum of radiation by atoms. So we shall digress here and describe what was known experimentally about A key feature of the atomic spectra at that time. Bohr model was the By 1900, the amount of information available about prediction of the atomic spectra was enormous. Spectroscopists had no- experimentally ticed that an atom can only absorb certain energies of observed line light (the absorption spectra) and once excited can only spectrum by atoms. release certain energies (the emission spectra), and these 888 RESONANCE October 2013 GENERAL ARTICLE energies happen to be the same. Further, the spectra coming from di®erent atoms showed that each atom has its own characteristic spectrum, i.e., a characteristic set of wavelengths at which the lines of the spectrum are found. Amongst all the atoms, the spectrum of hy- drogen is relatively simple. Since most of the universe consists of isolated hydrogen atoms, the hydrogen atom spectrum is of considerable importance. It was found that the hydrogen atom spectrum had a great regular- ity. This tempted several people to look for an empirical formula which would represent the wavelengths of the lines. Such a formula was discovered by Balmer, a Swiss school teacher, in 1885. He found the simple relation n2 ¸ = 3646 ; n = 3; 4; 5; ::: ; (4) n2 4 ¡ where ¸ is the wavelength. Using this formula, he was able to predict the wavelengths of the ¯rst nine lines of the series to better than one part in 1000. This discov- ery initiated a search for similar empirical formulas that would apply to other series.
Load more

Recommended publications
  • Schrödinger Equation)
    Lecture 37 (Schrödinger Equation) Physics 2310-01 Spring 2020 Douglas Fields Reduced Mass • OK, so the Bohr model of the atom gives energy levels: • But, this has one problem – it was developed assuming the acceleration of the electron was given as an object revolving around a fixed point. • In fact, the proton is also free to move. • The acceleration of the electron must then take this into account. • Since we know from Newton’s third law that: • If we want to relate the real acceleration of the electron to the force on the electron, we have to take into account the motion of the proton too. Reduced Mass • So, the relative acceleration of the electron to the proton is just: • Then, the force relation becomes: • And the energy levels become: Reduced Mass • The reduced mass is close to the electron mass, but the 0.0054% difference is measurable in hydrogen and important in the energy levels of muonium (a hydrogen atom with a muon instead of an electron) since the muon mass is 200 times heavier than the electron. • Or, in general: Hydrogen-like atoms • For single electron atoms with more than one proton in the nucleus, we can use the Bohr energy levels with a minor change: e4 → Z2e4. • For instance, for He+ , Uncertainty Revisited • Let’s go back to the wave function for a travelling plane wave: • Notice that we derived an uncertainty relationship between k and x that ended being an uncertainty relation between p and x (since p=ћk): Uncertainty Revisited • Well it turns out that the same relation holds for ω and t, and therefore for E and t: • We see this playing an important role in the lifetime of excited states.
    [Show full text]
  • Modern Physics: Problem Set #5
    Physics 320 Fall (12) 2017 Modern Physics: Problem Set #5 The Bohr Model ("This is all nonsense", von Laue on Bohr's model; "It is one of the greatest discoveries", Einstein on the same). 2 4 mek e 1 ⎛ 1 ⎞ hc L = mvr = n! ; E n = – 2 2 ≈ –13.6eV⎜ 2 ⎟ ; λn →m = 2! n ⎝ n ⎠ | E m – E n | Notes: Exam 1 is next Friday (9/29). This exam will cover material in chapters 2 through 4. The exam€ is closed book, closed notes but you may bring in one-half of an 8.5x11" sheet of paper with handwritten notes€ and equations. € Due: Friday Sept. 29 by 6 pm Reading assignment: for Monday, 5.1-5.4 (Wave function for matter & 1D-Schrodinger equation) for Wednesday, 5.5, 5.8 (Particle in a box & Expectation values) Problem assignment: Chapter 4 Problems: 54. Bohr model for hydrogen spectrum (identify the region of the spectrum for each λ) 57. Electron speed in the Bohr model for hydrogen [Result: ke 2 /n!] A1. Rotational Spectra: The figure shows a diatomic molecule with bond- length d rotating about its center of mass. According to quantum theory, the d m ! ! ! € angular momentum ( ) of this system is restricted to a discrete set L = r × p m of values (including zero). Using the Bohr quantization condition (L=n!), determine the following: a) The allowed€ rotational energies of the molecule. [Result: n 2!2 /md 2 ] b) The wavelength of the photon needed to excite the molecule from the n to the n+1 rotational state.
    [Show full text]
  • Bohr Model of Hydrogen
    Chapter 3 Bohr model of hydrogen Figure 3.1: Democritus The atomic theory of matter has a long history, in some ways all the way back to the ancient Greeks (Democritus - ca. 400 BCE - suggested that all things are composed of indivisible \atoms"). From what we can observe, atoms have certain properties and behaviors, which can be summarized as follows: Atoms are small, with diameters on the order of 0:1 nm. Atoms are stable, they do not spontaneously break apart into smaller pieces or collapse. Atoms contain negatively charged electrons, but are electrically neutral. Atoms emit and absorb electromagnetic radiation. Any successful model of atoms must be capable of describing these observed properties. 1 (a) Isaac Newton (b) Joseph von Fraunhofer (c) Gustav Robert Kirch- hoff 3.1 Atomic spectra Even though the spectral nature of light is present in a rainbow, it was not until 1666 that Isaac Newton showed that white light from the sun is com- posed of a continuum of colors (frequencies). Newton introduced the term \spectrum" to describe this phenomenon. His method to measure the spec- trum of light consisted of a small aperture to define a point source of light, a lens to collimate this into a beam of light, a glass spectrum to disperse the colors and a screen on which to observe the resulting spectrum. This is indeed quite close to a modern spectrometer! Newton's analysis was the beginning of the science of spectroscopy (the study of the frequency distri- bution of light from different sources). The first observation of the discrete nature of emission and absorption from atomic systems was made by Joseph Fraunhofer in 1814.
    [Show full text]
  • Bohr's 1913 Molecular Model Revisited
    Bohr’s 1913 molecular model revisited Anatoly A. Svidzinsky*†‡, Marlan O. Scully*†§, and Dudley R. Herschbach¶ *Departments of Chemistry and Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544; †Departments of Physics and Chemical and Electrical Engineering, Texas A&M University, College Station, TX 77843-4242; §Max-Planck-Institut fu¨r Quantenoptik, D-85748 Garching, Germany; and ¶Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138 Contributed by Marlan O. Scully, July 10, 2005 It is generally believed that the old quantum theory, as presented by Niels Bohr in 1913, fails when applied to few electron systems, such as the H2 molecule. Here, we find previously undescribed solutions within the Bohr theory that describe the potential energy curve for the lowest singlet and triplet states of H2 about as well as the early wave mechanical treatment of Heitler and London. We also develop an interpolation scheme that substantially improves the agreement with the exact ground-state potential curve of H2 and provides a good description of more complicated molecules such as LiH, Li2, BeH, and He2. Bohr model ͉ chemical bond ͉ molecules he Bohr model (1–3) for a one-electron atom played a major Thistorical role and still offers pedagogical appeal. However, when applied to the simple H2 molecule, the ‘‘old quantum theory’’ proved unsatisfactory (4, 5). Here we show that a simple extension of the original Bohr model describes the potential energy curves E(R) for the lowest singlet and triplet states about Fig. 1. Molecular configurations as sketched by Niels Bohr; [from an unpub- as well as the first wave mechanical treatment by Heitler and lished manuscript (7), intended as an appendix to his 1913 papers].
    [Show full text]
  • Bohr's Model and Physics of the Atom
    CHAPTER 43 BOHR'S MODEL AND PHYSICS OF THE ATOM 43.1 EARLY ATOMIC MODELS Lenard's Suggestion Lenard had noted that cathode rays could pass The idea that all matter is made of very small through materials of small thickness almost indivisible particles is very old. It has taken a long undeviated. If the atoms were solid spheres, most of time, intelligent reasoning and classic experiments to the electrons in the cathode rays would hit them and cover the journey from this idea to the present day would not be able to go ahead in the forward direction. atomic models. Lenard, therefore, suggested in 1903 that the atom We can start our discussion with the mention of must have a lot of empty space in it. He proposed that English scientist Robert Boyle (1627-1691) who the atom is made of electrons and similar tiny particles studied the expansion and compression of air. The fact carrying positive charge. But then, the question was, that air can be compressed or expanded, tells that air why on heating a metal, these tiny positively charged is made of tiny particles with lot of empty space particles were not ejected ? between the particles. When air is compressed, these 1 Rutherford's Model of the Atom particles get closer to each other, reducing the empty space. We mention Robert Boyle here, because, with Thomson's model and Lenard's model, both had him atomism entered a new phase, from mere certain advantages and disadvantages. Thomson's reasoning to experimental observations. The smallest model made the positive charge immovable by unit of an element, which carries all the properties of assuming it-to be spread over the total volume of the the element is called an atom.
    [Show full text]
  • Ab Initio Calculation of Energy Levels for Phosphorus Donors in Silicon
    Ab initio calculation of energy levels for phosphorus donors in silicon J. S. Smith,1 A. Budi,2 M. C. Per,3 N. Vogt,1 D. W. Drumm,1, 4 L. C. L. Hollenberg,5 J. H. Cole,1 and S. P. Russo1 1Chemical and Quantum Physics, School of Science, RMIT University, Melbourne VIC 3001, Australia 2Materials Chemistry, Nano-Science Center, Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 København Ø, Denmark 3Data 61 CSIRO, Door 34 Goods Shed, Village Street, Docklands VIC 3008, Australia 4Australian Research Council Centre of Excellence for Nanoscale BioPhotonics, School of Science, RMIT University, Melbourne, VIC 3001, Australia 5Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Parkville, 3010 Victoria, Australia The s manifold energy levels for phosphorus donors in silicon are important input parameters for the design and modelling of electronic devices on the nanoscale. In this paper we calculate these energy levels from first principles using density functional theory. The wavefunction of the donor electron's ground state is found to have a form that is similar to an atomic s orbital, with an effective Bohr radius of 1.8 nm. The corresponding binding energy of this state is found to be 41 meV, which is in good agreement with the currently accepted value of 45.59 meV. We also calculate the energies of the excited 1s(T2) and 1s(E) states, finding them to be 32 and 31 meV respectively. These results constitute the first ab initio confirmation of the s manifold energy levels for phosphorus donors in silicon.
    [Show full text]
  • Niels Bohr and the Atomic Structure
    GENERAL ¨ ARTICLE Niels Bohr and the Atomic Structure M Durga Prasad Niels Bohr developed his model of the atomic structure in 1913 that succeeded in explaining the spectral features of hydrogen atom. In the process, he incorporated some non-classical features such as discrete energy levels for the bound electrons, and quantization of their angular momenta. Introduction MDurgaPrasadisa Professor of Chemistry An atom consists of two interacting subsystems. The first sub- at the University of system is the atomic nucleus, consisting of Z protons and A–Z Hyderabad. His research neutrons, where Z and A are the atomic number and atomic weight interests lie in theoretical respectively, of the concerned atom. The electrons that are part of chemistry. the second subsystem occupy (to zeroth order approximation) discrete energy levels, called the orbitals, according to the Aufbau principle with the restriction that no more than two electrons occupy a given orbital. Such paired electrons must have their spins in opposite direction (Pauli’s exclusion principle). The two subsystems interact through Coulomb attraction that binds the electrons to the nucleus. The nucleons in turn are trapped in the nucleus due to strong interactions. The two forces operate on significantly different scales of length and energy. Consequently, there is a clear-cut demarcation between the nuclear processes such as radioactivity or fission, and atomic processes involving the electrons such as optical spectroscopy or chemical reactivity. This picture of the atom was developed in the period between 1890 and 1928 (see the timeline in Box 1). One of the major figures in this development was Niels Bohr, who introduced most of the terminology that is still in use.
    [Show full text]
  • Module P11.3 Schrödinger's Model of the Hydrogen Atom
    FLEXIBLE LEARNING APPROACH TO PHYSICS Module P11.3 Schrödinger’s model of the hydrogen atom 1 Opening items 3.4 Ionization and degeneracy 1.1 Module introduction 3.5 Comparison of the Bohr and the Schrödinger 1.2 Fast track questions models of the hydrogen atom 1.3 Ready to study? 3.6 The classical limit 2 The early quantum models for hydrogen 4 Closing items 2.1 Review of the Bohr model 4.1 Module summary 2.2 The wave-like properties of the electron 4.2 Achievements 3 The Schrödinger model for hydrogen 4.3 Exit test 3.1 The potential energy function and the Exit module Schrödinger equation 3.2 Qualitative solutions for wavefunctions1 —1the quantum numbers 3.3 Qualitative solutions of the Schrödinger equation1—1the electron distribution patterns FLAP P11.3 Schrödinger’s model of the hydrogen atom COPYRIGHT © 1998 THE OPEN UNIVERSITY S570 V1.1 1 Opening items 1.1 Module introduction The hydrogen atom is the simplest atom. It has only one electron and the nucleus is a proton. It is therefore not surprising that it has been the test-bed for new theories. In this module, we will look at the attempts that have been made to understand the structure of the hydrogen atom1—1a structure that leads to a typical line spectrum. Nineteenth century physicists, starting with Balmer, had found simple formulae that gave the wavelengths of the observed spectral lines from hydrogen. This was before the discovery of the electron, so no theory could be put forward to explain the simple formulae.
    [Show full text]
  • Photon Model of Light Bohr Model of Hydrogen Application
    Energy Quantization Objective: To calculate the energy of a hydrogen atom; to describe the Bohr model; to describe the photon model of light; to know the range of energies for visible light; to describe what produces an absorption spectrum and an emission spectrum; to apply conservation of energy to determine the energy of a photon emitted or a photon absorbed by a hydrogen atom. Photon model of light There are two models of light that are useful to explain various experiments. One model of light describes it as an electromagnetic wave made up of a propagating wave made up of an oscillating electric field and oscillating magnetic field (in a plane perpendicular to the electric field). The color of light depends on its wavelength (or frequency where λf = c in a vacuum). Light can be made up of many electromagnetic waves of various colors giving you what is called a spectrum. White light is made up of equal amounts of all of the colors of the visible spectrum. Another model of light describes it as a collection of particles called photons. These photons have no rest mass but do have energy (kinetic energy). The energy of a photon is E = hf where h is Planck’s constant and f is the frequency of the light. Thus the “color” of a photon depends on its energy. Visible light is a small region of the entire range of possible energies of photons. The entire range is called the electromagnetic spectrum which ranges from gamma rays with very high energy to radio with very low energy.
    [Show full text]
  • Bohr Model of Hydrogen Atom
    Bohr Model of Hydrogen Atom 1 Postulates of Bohr Model The electron revolves in discrete orbits around the nucleus without radiating any energy, contrary to what classical electromagnetism principle. In these orbits, the electron's acceleration does not result in radiation and energy loss. These discrete orbits are called stationary orbits. The electron cannot have any other orbit in between the discrete ones. The angular momentum of electrons in these orbits is an integral multiple of the reduced Planck's constant. mvr = nħ 2 Electron loses energy only when it jumps from one allowed energy level to another allowed energy level. It radiates energy in the form of electromagnetic radiation with a frequency ν determined by the energy difference of the levels according to the Planck relation: E2 -E1 = hν Bohr assumed that during a jump a discrete or quantum of energy was radiated. Bohr explained the quantization of the radiation emitted by the discreteness of the atomic energy levels. Bohr did not believe in the existence of photons. 3 According to the Maxwell theory the frequency ν of classical radiation is equal to the rotation frequency ν of the electron in its orbit, with harmonics as integer multiples of this frequency. This result is obtained from the Bohr model for jumps between energy levels En and En−k when k is much smaller than n. These jumps reproduce the frequency of the kth harmonic of orbit n. For sufficiently large values of n the two orbits involved in the emission process have nearly the same rotation frequency, thus giving credence to the classical orbital frequency.
    [Show full text]
  • Chapter 6 Electronic Structure of Atoms Ch6
    101 F02 Chapter 6 Electronic structure of atoms Ch6 • light • photons • spectra • Heisenberg’s uncertainty principle • atomic orbitals • electron configurations • the periodic table 6.1 The wave nature of light Visible light is a form of electromagnetic radiation, or radiant energy. Radiation carries energy through space 1 101 F02 Electromagnetic radiation can be imagined as a self-propagating Ch6 transverse oscillating wave of electric and magnetic fields. The number of waves passing a given point per unit of time is the frequency For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency. All electromagnetic radiation travels at the same velocity The wavelength and frequency of light is therefore related in a straightforward way: Blackboard examples 1. what is the wavelength of UV light with ν = 5.5 x 1015 s-1? 2. what is the frequency of electromagnetic radiation that has a wavelength of 0.53 m? Wave nature of light successfully explains a range of different phenomena. 2 101 F02 Ch6 Thomas Young’s sketch of two-slit diffraction of light (1803) 6.2 Quantized Energy and Photons Some phenomena cannot be explained using a wave model of light. 1. Blackbody radiation 2. The photoelectric effect 3. Emission spectra Hot Objects and the Quantization of Energy Heated solids emit radiation (blackbody radiation) In 1900, Max Planck investigated black body radiation, and he proposed that energy can only be absorbed or released from atoms in certain amounts, called “quanta” The relationship between energy, E, and frequency is: The Photoelectric Effect and Photons The photoelectric effect provides evidence for the particle nature of light and for quantization.
    [Show full text]
  • Section 28-2: Models of the Atom
    Answer to Essential Question 28.1: (a) In general, four energy levels give six photon energies. One way to count these is to start with the highest level, –12 eV. An electron starting in the –12 eV level can drop to any of the other three levels, giving three different photon energies. An electron starting at the –15 eV level can drop to either of the two lower levels, giving two more photon energies. Finally, an electron can drop from the –21 eV level to the –31 eV level, giving one more photon energy (for a total of six). (b) The minimum photon energy corresponds to the 3 eV difference between the –12 eV level and the –15 eV level. The maximum photon energy corresponds to the 19 eV difference between the –12 eV level and the –31 eV level. 28-2 Models of the Atom It is amazing to think about how far we have come, in terms of our understanding of the physical world, in the last century or so. A good example of our progress is how much our model of the atom has evolved. Let’s spend some time discussing the evolution of atomic models. Ernest Rutherford probes the plum-pudding model J. J. Thomson, who discovered the electron in 1897, proposed a plum-pudding model of the atom. In this model, electrons were thought to be embedded in a ball of positive charge, like raisins are embedded in a plum pudding. Ernest Rutherford (1871 - 1937) put this model to the test by designing an experiment that involved firing alpha particles (helium nuclei) at a very thin film of gold.
    [Show full text]