Bohr Model of the Atom

by Ryan Moorcroft

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Team Bohr Model of the Atom Teachers

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    Atoms are incomprehensibly small. You could line up over 300,000 Carbon atoms and they could still be hidden behind a single strand of human hair. In the past 200 years, incredible advances have been made in the realm of atomic physics. We have even learned that atoms are made up of even smaller subatomic particles and how they are structured within the atom.

    The Bohr Model of the Atom Diagram of the Bohr's model of the atom StudySmarterIn the Bohr model of the atom, electrons orbit around a positive nucleus. Wikimedia Commons

    In the Bohr model of the atom, electrons can only exist in clearly defined levels called shells, which have a set size and energy, They 'orbit' around a positively-charged nucleus. Electrons can move between these shells by absorbing or emitting photons with specific energies.

    Development leading to the Bohr Model of the Atom

    Our understanding of the atom went through several distinct models throughout the last two centuries, improving with accuracy as new evidence was obtained and more fundamental physical principles were revealed.

    Plum Pudding Model

    Before the 20th century, we had no idea what the subatomic structure of the atom was like. In 1803 John Dalton theorized that the atom was indivisible and could not be broken down into anything smaller. However, when the electron was discovered in 1897 by J. J. Thomson, this all changed. After much deliberation and research, he proposed the plum pudding model or the Thomson Model.

    The model attempted to explain how an atom had no net electric charge, yet individual electrons possessed negative charges. Thomson proposed that negatively charged "plums" (electrons) were surrounded by a positively charged "pudding," as an atom must contain some positive charge to cancel out the negative charge of the electrons.

    Rutherford Model

    In 1905, Thomson’s student Ernst Rutherford tested the plum pudding model by directing a beam of alpha particles at a strip of gold foil. Alpha particles are a form of radiation with a large positive charge. He expected the alpha particles to pass through the gold with no deflection as the positively charged "pudding" should be evenly spread out. However, a very small number of the alpha particles were deflected, sometimes being reflected completely.

    The Bohr Model of the Atom comparison of two diagrams showing the interaction with the atom and the alpha particles, at the left, the Thomson model with no deviation, and at the right, the Rutherford model with few particles getting deflected StudySmarterIn the experiment with alpha particles, the expectation was for the alpha particles to go through without any deviation, in accordance with Thomson's model. However, a small number of the particles were deflected, which can be explained by Rutherford's Model, Wikimedia Commons CC-BY-SA-3.0

    It took several years for Rutherford to correctly interpret the results of his experiment. He proposed that the atom actually consisted of a small, compact, and positively charged nucleus surrounded by a cloud of electrons, called the Rutherford model. The proton and the neutron (the subatomic particles that make up the nucleus) were discovered later, in 1917 and 1932, respectively.

    Bohr Model

    Unfortunately, the Rutherford model was still flawed. The leading theory at the time was that the electrons revolved around the nucleus in arbitrary circular orbits, like how a planet orbits a star. However, electrons lose energy when they are accelerated, and therefore they should collapse into the nucleus under the Rutherford model. In 1913, Niels Bohr proposed his own structure of the atom to explain this.

    The Bohr Model of the Atom Development leading to the Bohr Model of the Atom StudySmarterSubatomic structure of a Hydrogen atom. An electron absorbs and emits energy to move between energy levels, Wikimedia Commons CC-BY-SA-3.0

    In Bohr's model of the atom, electrons orbit around the nucleus in fixed energy levels called shells. Electrons can only exist in these shells and they move between them by gaining and losing certain amounts of energy corresponding to the energy difference between the energy levels. This is how Niels Bohr was able to explain why the atom does not collapse. His conclusions are based on quantum physics, which you won't have to worry too much about at this level.

    Atomic Structure of the Bohr Model

    Energy and Color

    Almost all light in the universe comes from atoms. When scientists study a pure element, they observe that only a few specific colors are ever emitted. Different elements emit different patterns of colors, called an emission spectrum. For example, hydrogen has an orange line, two blue lines, and a purple line. The colors and patterns of hydrogen are distinct, even from helium.

    The Bohr Model of the Atom Atomic Stucture of the Bohr Model StudySmarterEmission Spectrum comparison of Hydrogen and Helium, Wikimedia Commons CC-BY-SA-4.0

    Remember that light is pure energy in the form of an electromagnetic wave or photon. The energy of an EM wave determines its color. Redder light has lower energies, while bluer light has higher energies. As an atom can only absorb and emit certain colors of light, we know that something within the structure of the atom must have specific energy levels.

    The Bohr Model of the Atom Atomic Stucture of the Bohr Model StudySmarterAn electron absorbs and emits photons to move energy levels, Wikimedia Commons CC BY 3.0

    In Bohr’s model, electrons orbit the nucleus at discrete energy levels called shells. They cannot exist between energy levels unless they are passing from one level to another. The lowest level (E1) is the ground state, while all higher energy levels are excited states. It’s important to note that the energy of an electron in an atom is always negative. The negative symbol denotes that the electron must be given energy to be ejected from the atom entirely. This energy is defined as ionization energy or ionization state. Consider a hydrogen atom with a ground state of -13.6 eV, giving the electron ionization energy of 13.6 eV will force it to be ejected.

    One electron volt eV is a unit of energy equal to the amount of work done on an electron when accelerating it through a potential difference of one volt.

    When an electron moves from a higher energy level to a lower one a photon is emitted with an energy corresponding to the energy difference between the two shells. If an electron moves between two energy levels, the energy of the emitted photon can be calculated with the Planck equation:

    E = hf = E2 - E1

    WhereEis Energy,his Planck’s constant, andfis the frequency of light produced.

    Similarly, this equation can also be used when an electron absorbs energy from a photon and moves into a more excited state. Electrons in an atom can only absorb certain energies of light, which would move it to a more excited state. Electrons are able to move between multiple orbits in one transition, for example, betweenE4andE2.

    Question

    An electron moves from an excited state to its ground state. The excited state has an energy value of-3.4 eVand the ground state has an energy value of-13.6 eV. What is the frequency of the emitted photon?

    Answer

    E2 = -3.4 eV

    E1 = -13.6 eV

    E2 - E1 = E

    -3.4 eV +13.6 eV = 10.2 eV

    ConverteVinto Joules.

    1 eV = 1.602 × 10-19 J, therefore 10.2 eV = 1.634 × 10-18 J

    Re-arrange Planck's equation to make frequency the subject.

    E = hf f = Eh

    h = 6.67 × 10-34 m2kg/s

    1.634 × 10-18 J6.626 × 10-34 m2kg/s = 2.466 × 1015 kg m2/s2kg m2/s= 2.466 × 1015 1s= 2.466 × 1015 Hz

    How Electrons fill Energy Levels

    There is a limit to how many electrons can physically exist in any shell at a given point in time. The first shell can only hold two electrons, while shells 2 and 3 can contain 8 electrons each. The diagram below shows the electron configuration of ten elements on the periodic table, assuming no electron has been excited to a higher state.

    The Bohr Model of the Atom Atomic Stucture of the Bohr Model StudySmarterThe electron configuration of ten elements, Wikimedia Commons CC-BY-4.0

    As electrons are added to an atom, they will fill the lowest unfulfilled energy levels available. Each shell must be filled before the next starts to fill. The only exception is when an electron has been excited. However, excited electrons will very quickly undergo spontaneous emission of a photon to return to a lower energy level. This is because the negatively-charged electrons are attracted to the positively-charged nucleus, like how gravity attracts a skydiver to the ground.

    Limitations of the Bohr Atomic Model

    Bohr's model was essentially flawless, as long as the atom you were studying had only one electron. Unfortunately, every single atom on the periodic table, with the exception of hydrogen, has more than one electron. When Bohr attempted to use his atomic model to predict the spectral lines of other elements, his calculations drifted further and further from the actually observed emission spectrums as the number of electrons in a sample element increased.

    One problem is that multiple electrons in the 'orbit' of a nucleus will begin to interact with each other, complicating the energy structures of the electron shells. Erwin Schrödinger, in 1926, determined that electrons actually move around the nucleus in different clouds according to their energy level. The white regions on the image below show a higher probability of finding an electron in that space, while darker regions demonstrate the opposite.

    The Bohr Model of the Atom Limitations of the Bohr Atomic ModelIn Schrödinger's Quantum Model of the atom, electrons move around the nucleus in different clouds, Pixabay

    Niel's Bohr did not take wave-particle duality into account in his model. You are probably already aware that light can act as both a particle and a wave, but this holds true for electrons too. According to Heisenberg's uncertainty principle, the exact position and motion of an electron can never be precisely predicted. The probability of finding a particle at a particular location is related to the wave associated with the particle. This is why the electron shells are not just simple lines. They are instead "diffuse clouds of probability."

    Advantages and Disadvantages of Bohr's Atomic Model

    The main reason Bohr's model is useful is that it clearly demonstrates the underlying structure of the atom and how electrons can gain and lose energy through the absorption and emission of photons.

    Unfortunately, Bohr's model isn't completely correct due to quantum mechanical principles. Electrons do not "orbit" the nucleus at neat, distinct lines but instead in indistinct clouds. However, Bohr's model is relatively neat and accurate and is an important fundamental step at high school level to understanding the physics that governs the world.

    Bohr Model of the Atom - Key takeaways

    • Atoms are made up of sub-atomic particles. In the Bohr model of the atom, electrons "orbit" a positively charged nucleus at defined energy levels called shells.
    • The lowest energy level (E1) is called the ground state. Any higher energy levels are called excited states.
    • Electrons can move between energy levels by absorbing or emitting a photon of the specific corresponding energy between the two energy levels.
    • Different elements emit different colors of light, called an emission spectrum. The energy of the emitted photons from an atom determines the spectral lines seen on the emission spectrum.
    • The Planck equation helps determine the relationship between different energy levels and the frequency of light emitted or absorbed during electron transitionE = hf = E2 - E1.
    • There is a limit to the number of electrons that can exist in each electron shell. Electrons will fill the lowest unfulfilled energy levels first before the next begins to fill.
    • The development of our understanding of the atom has progressed significantly in the past 200 years. From Dalton's model to Thomson's model, to Rutherford's model, to Bohr's model, and finally to Schrödinger's quantum model.
    • Bohr's model is used as a foundation for understanding the atomic structure for students, but the quantum model is more accurate.

    Test your knowledge with multiple choice flashcards

    Which state would an electron atom be in if given 100 eV of energy by an incoming photon, when the ground state is -79 eV?

    Are electrons able to transition between more than one energy level at a time? 

    Which subatomic particle does not exist within the nucleus of an atom?

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