Bohr's Model of the Hydrogen Atom
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Bohr's Model of the Hydrogen Atom

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Questions and Answers

What does a more negative energy value indicate about the energy level of an electron in a hydrogen atom?

  • Lower energy level (correct)
  • Stable energy level
  • Higher energy level
  • Increased electron activity

    • Using the formula $E = -\frac{kZ^2}{n^2}$, what would the energy of an electron be in the n=6 orbit of a hydrogen atom?

  • $-6.063 \times 10^{-19} J$
  • $-6.042 \times 10^{-20} J$ (correct)
  • $-2.419 \times 10^{-19} J$
  • $-4.864 \times 10^{-20} J$

    • What is the principal quantum number for the energy calculation provided in Example 5.3?

  • 3 (correct)
  • 4
  • 1
  • 2

    • Which constant is used in the energy equation for a hydrogen atom in the provided content?

    <p>$2.179 \times 10^{-18} J$</p> Signup and view all the answers

    What does the graph mentioned (Figure 5.4) illustrate about the hydrogen atom?

    <p>Energy levels and electron transitions</p> Signup and view all the answers

    What is the energy difference when an electron transitions from the n=4 orbit to the n=6 orbit in hydrogen?

    <p>$7.566 imes 10^{-20} ext{ J}$</p> Signup and view all the answers

    Which equation is used to calculate the wavelength of a photon based on its energy?

    <p>$E = rac{hc}{ u}$</p> Signup and view all the answers

    In which part of the electromagnetic spectrum does the transition from n=4 to n=6 fall?

    <p>Infrared</p> Signup and view all the answers

    What does a positive $ ext{ΔE}$ value indicate about the electron transition?

    <p>The electron gains energy</p> Signup and view all the answers

    Which of the following statements about Bohr's model is correct?

    <p>It highlights that electron energies increase with distance from the nucleus.</p> Signup and view all the answers

    How is the difference in energy calculated for an electron transition between two states?

    <p>$E_{1} - E_{2}$</p> Signup and view all the answers

    When an electron falls from n=5 to n=3 in He+, what is primarily being emitted?

    <p>An ultraviolet photon</p> Signup and view all the answers

    What does the quantum number n represent in Bohr's model?

    <p>The distance of the electron from the nucleus</p> Signup and view all the answers

    What does the ground state of an electron in a hydrogen atom represent?

    <p>The most stable configuration with the lowest energy</p> Signup and view all the answers

    When an electron transitions from an excited state to a lower energy level, what occurs?

    <p>A photon is emitted</p> Signup and view all the answers

    In Bohr's model, which factor influences the energy levels of hydrogen-like atoms?

    <p>The nuclear charge, Z</p> Signup and view all the answers

    What is the relationship between the principal quantum number (n) and the radii of electron orbits in hydrogen-like atoms?

    <p>The radius increases with the square of n</p> Signup and view all the answers

    Which statement about ionization energy in Bohr's model is correct?

    <p>Ionization energy increases as Z increases</p> Signup and view all the answers

    What happens to the energy levels ($E_n$) as the principal quantum number (n) approaches infinity?

    <p>They approach zero</p> Signup and view all the answers

    Which constant value is used in the energy expression for hydrogen-like atoms?

    <p>$2.179 imes 10^{-18}$ J</p> Signup and view all the answers

    Bohr's model applies to which type of atoms?

    <p>Hydrogen-like atoms with one electron and a nuclear charge</p> Signup and view all the answers

    What is the primary issue with the classical model of the atom that Bohr addressed?

    <p>Atoms emit electromagnetic radiation continuously.</p> Signup and view all the answers

    In Bohr's model, when is radiation emitted or absorbed by an electron?

    <p>Only during the transition between energy levels.</p> Signup and view all the answers

    Which equation relates the energy change of an electron to the properties of emitted or absorbed photons?

    <p>$ riangle E = h u$</p> Signup and view all the answers

    What does the variable $k$ represent in the energy level equation $E_n = - rac{k}{n^2}$?

    <p>A constant that includes fundamental constants.</p> Signup and view all the answers

    How does the energy of the emitted photon relate to the energy levels in an atom according to Bohr's model?

    <p>It is proportional to the energy difference between levels.</p> Signup and view all the answers

    What happens to the orbital energy values as the principal quantum number $n$ increases?

    <p>Orbital energy becomes less negative.</p> Signup and view all the answers

    Which conclusion about the Rydberg constant is true in context of Bohr's model?

    <p>It matched the theoretical values obtained from Bohr's equations.</p> Signup and view all the answers

    What did Bohr's model contribute to the understanding of atomic stability?

    <p>It introduced quantized energy levels for electron orbits.</p> Signup and view all the answers

    Study Notes

    Bohr's Model of the Hydrogen Atom

    • Bohr's model explains the stability of atoms by introducing quantized energy levels for electrons.
    • Electrons occupy specific orbits around the nucleus, defined by the principal quantum number (n).
    • The ground state, n=1, represents the lowest energy level.
    • Electrons can absorb energy and transition to higher energy levels (excited states).
    • When electrons return to lower energy levels, they emit photons with specific energies.
    • Bohr's model can be applied to hydrogen-like atoms (He+, Li2+, etc.) by incorporating the nuclear charge (Z).
    • The energy of an electron in a hydrogen-like atom is given by:
    • $E_n = -\frac{kZ^2}{n^2}$
    • Where:
    • $E_n$ is the energy of the electron in the nth orbit.
    • k is a constant ($2.179 \times 10^{-18}$ J).
    • Z is the nuclear charge.
    • n is the principal quantum number.
    • The radius of the electron orbit in a hydrogen-like atom is:
    • $r = \frac{n^2}{Z}a_0$
    • Where:
    • r is the radius of the electron orbit.
    • $a_0$ is the Bohr radius ($5.292 \times 10^{-11}$ m).
    • As the principal quantum number increases, the electron's energy increases, and the orbit moves further from the nucleus.
    • At very high values of n, the energy levels ($E_n$) approach zero, representing ionization (the electron is completely removed from the nucleus).
    • The ionization energy can be calculated as:
    • $\Delta E = E_n - E_{\infty} = E_1 = 0 + k = k$
    • Bohr's model provided a significant advancement in understanding atomic structure but was eventually replaced by quantum mechanics.

    Bohr Model and Energy Levels in a Hydrogen Atom

    • The energy levels of a hydrogen atom are quantized, meaning electrons can only occupy specific discrete energy levels.
    • The more negative the energy value, the lower the energy level.

    Example 5.3: Calculating the Energy of an Electron in a Bohr Orbit

    • The formula used for calculating the energy of an electron in a Bohr orbit is: $E = -\frac{kZ^2}{n^2}$.
    • To calculate the energy of an electron in a specific orbit (n = 3) of a hydrogen atom, we use the given values for k, Z, and n.

    Calculating the Energy and Wavelength of Electron Transitions

    • Example 5.4 demonstrates calculating the energy and wavelength of a photon absorbed by an electron transitioning from n=4 to n=6 in a hydrogen atom.
    • The energy difference between the two states is calculated using the formula:
    • $\Delta E = E_{1} - E_{2} = 2.179 \times 10^{-18} \left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right)$.
    • The wavelength of the absorbed photon is then calculated using the relationship between energy, Planck's constant, and the speed of light, $\lambda = \frac{hc}{E}$.

    Bohr's Model of the Hydrogen Atom

    • Although useful for the hydrogen atom, Bohr's model was superseded by quantum mechanics.
    • Bohr model introduces key features of atomic structure:
    • Quantized energy levels for electrons, described by quantum numbers.
    • Energy increases with increasing distance from the nucleus.

    Bohr Model

    • Bohr's model addressed the limitations of the classical planetary model, which suggested atoms were unstable.
    • It proposed:
    • Electrons occupy specific, quantized energy levels (stationary states).
    • Electrons do not radiate energy continuously in these orbits.
    • Radiation is emitted or absorbed only during transitions between energy levels.
    • Bohr established the relationship between energy change ($\Delta E$) and the emitted or absorbed photon:
    • $ \Delta E = E_{f} - E_{i} = h\nu = \frac{hc}{\lambda} $
    • The energy levels of an electron are quantized:
    • $E_{n} = -\frac{k}{n^2}$, where n = 1, 2, 3...
    • This equation, when applied to calculate energy changes, matches the Rydberg equation, which describes the wavelengths of light emitted by hydrogen.

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    Description

    Explore Bohr's Model of the Hydrogen Atom and understand its principles, including quantized energy levels and electron transitions. This quiz covers key concepts such as the implications of principal quantum numbers and energy calculations for hydrogen-like atoms.

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