Bohr's Theory of Hydrogen Atom
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Questions and Answers

What is the cause of molecular spectra emission?

  • Molecules when excited (correct)
  • Molecules absorbing energy
  • Molecules emitting energy
  • Molecules in their ground state

    • How many types of molecular spectra are there?

  • Five
  • Three (correct)
  • Four
  • Two

    • What is the energy range required for electronic excitation?

  • Microwave, far IR
  • Near IR
  • Visible, UV (correct)
  • X-ray, gamma ray

    • What is the difference between rotational and translational motion?

    <p>It is difficult to distinguish between the two</p> Signup and view all the answers

    What is the order of energy required for excitation?

    <p>Rotation &lt; Vibration &lt; Electronic</p> Signup and view all the answers

    What is associated with each vibrational energy sublevel?

    <p>A number of rotational quantum levels</p> Signup and view all the answers

    What is the result of molecules absorbing energy?

    <p>Molecules vibrate or rotate</p> Signup and view all the answers

    What type of motion has a comparable energy difference between successive states in many systems?

    <p>Rotational and translational motion</p> Signup and view all the answers

    What is the value of the permittivity of free space (𝜀°)?

    <p>8.85 × 10⁻¹² C²N⁻¹m⁻²</p> Signup and view all the answers

    What is the formula for the centripetal force (𝐹𝑐)?

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

    What is the formula for the energy of an electron in a hydrogen atom?

    <p>𝑘𝐸 + 𝐸𝑝𝑜𝑡</p> Signup and view all the answers

    What is the value of the speed of light (𝑉) in terms of the angular momentum (𝑛²ℎ²)?

    <p>√(𝑛²ℎ²/𝑚𝑟)</p> Signup and view all the answers

    What is the formula for the radius (𝑟) of an electron in a hydrogen atom?

    <p>𝑛²ℎ²/4𝜋𝑚𝑘𝑒²</p> Signup and view all the answers

    What is the value of the Planck constant (ℎ)?

    <p>6.626 × 10⁻³⁴ Js</p> Signup and view all the answers

    What is the main postulate of Bohr's theory regarding the energy of an electron in an atom?

    <p>The energy of the electron can only vary by a finite amount.</p> Signup and view all the answers

    What is the condition for an electron to exist in a certain energy level (orbits) according to Bohr's theory?

    <p>The electron must exist only in a certain energy level (orbits) and cannot exist between them.</p> Signup and view all the answers

    What is the relationship between the energy of the system and the radius of the orbit according to Bohr's theory?

    <p>The energy of the system increases as the radius of the orbit increases.</p> Signup and view all the answers

    What is the equation that relates the wavelength of an electron to its velocity and mass?

    <p>λ = h / (mv)</p> Signup and view all the answers

    What is the significance of the equation λ = h / (mV) in Bohr's theory?

    <p>It shows that the wavelength of an electron is inversely proportional to its velocity.</p> Signup and view all the answers

    What is the angular momentum of an electron in an orbit according to Bohr's theory?

    <p>mvr = nh/2π</p> Signup and view all the answers

    What is the condition for an electron to move from one orbit to another according to Bohr's theory?

    <p>The electron must absorb energy equal to the difference between the two orbits.</p> Signup and view all the answers

    What are the two opposite forces that keep the electron in its orbit according to Bohr's theory?

    <p>Attraction force and centripetal force.</p> Signup and view all the answers

    What is the total energy of an electron in a hydrogen atom?

    <p>Kinetic energy + Potential energy</p> Signup and view all the answers

    What is the unit of energy level?

    <p>Electron Volts</p> Signup and view all the answers

    What is the relationship between the energy level and the radius of an electron in a hydrogen atom?

    <p>Energy level is inversely proportional to the radius</p> Signup and view all the answers

    What is the value of the total energy of an electron in the ground state of a hydrogen atom?

    <p>-13.6 eV</p> Signup and view all the answers

    What is the formula for the energy of an electron in a hydrogen atom?

    <p>E = -2.17 x 10^-18 J / n^2</p> Signup and view all the answers

    What is the type of spectrum emitted by an atomic system?

    <p>Line spectrum</p> Signup and view all the answers

    What is the formula for the frequency of a photon emitted by an electron in a hydrogen atom?

    <p>ν = 3.3 x 10^15 Hz</p> Signup and view all the answers

    What is the value of the energy difference between two energy levels of an electron in a hydrogen atom?

    <p>2.17 x 10^-18 J</p> Signup and view all the answers

    What is the wavelength of a photon emitted by an electron in a hydrogen atom?

    <p>1.1 x 10^7 cm^-1</p> Signup and view all the answers

    What is the direction of the electron in a hydrogen atom when its energy is 0 eV?

    <p>The electron is at infinity</p> Signup and view all the answers

    Study Notes

    Bohr's Theory of the Hydrogen Atom

    • The energy of an electron in an atom cannot vary continuously, but only in finite amounts.
    • Electrons exist only in certain energy levels (orbits) and cannot exist between them.
    • The variation of electron energy occurs only when the electron moves from one orbit to another by absorbing energy equal to the difference between the two orbits.

    Postulations of Bohr's Theory

    • The energy of the system increases with increasing radius.
    • The only possible orbit for an electron in an atom is one that has angular momentum (mvr) equal to (nh/2π).
    • There are two opposite forces that keep the electron in its orbit: attraction force and centripetal force.

    Wave Nature of Electrons (De Broglie's Suggestion)

    • Dualism might exist for material particles and electrons.
    • The equation λ = h/mv relates the wavelength of an electron to its momentum.

    Application to Electron Orbits

    • The equation 2πr = nλ relates the circumference of an electron orbit to the number of wavelengths that fit in the orbit.
    • The equation mvr = n(h/2π) relates the angular momentum of an electron to its energy level.

    Forces Acting on the Electron

    • The attraction force between the electron and the nucleus is given by F = k(q+)(q-)/r^2.
    • The centripetal force acting on the electron is given by Fc = mv^2/r.

    Energy of the Electron

    • The total energy of the electron is given by Etot = kE + Epot, where kE is the kinetic energy and Epot is the potential energy.
    • The potential energy of the electron is given by Epot = -ke^2/r.

    Bohr's Energy Equation

    • The energy of the electron is given by Etot = -2.17 x 10^(-18) J / n^2, where n is the energy level.
    • The energy difference between two energy levels is given by ΔE = 2.17 x 10^(-18) J / (n1^2 - n2^2).

    Molecular Spectra

    • Atomic spectra are emitted as line spectra, while molecular spectra are emitted as band spectra.
    • Molecular spectra are related to the internal motion of molecules (electronic and atomic nuclei motion).
    • There are three types of molecular spectra: rotation spectra, vibration-rotation spectra, and electronic band spectra.

    Origin of Molecular Spectra

    • The energy required for excitation is in the order: rotation (microwave, far IR) < vibration (near IR) < electronic (visible, UV).
    • Each electronic level is subdivided into vibrational sublevels (v), and each vibrational energy sublevel is associated with a number of rotational quantum levels (J).

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    Description

    Understanding the postulations of Bohr's theory, including energy levels, electron orbits, and energy variation in the hydrogen atom

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