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Questions and Answers
What is the cause of molecular spectra emission?
How many types of molecular spectra are there?
What is the energy range required for electronic excitation?
What is the difference between rotational and translational motion?
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What is the order of energy required for excitation?
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What is associated with each vibrational energy sublevel?
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What is the result of molecules absorbing energy?
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What type of motion has a comparable energy difference between successive states in many systems?
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What is the value of the permittivity of free space (𝜀°)?
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What is the formula for the centripetal force (𝐹𝑐)?
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What is the formula for the energy of an electron in a hydrogen atom?
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What is the value of the speed of light (𝑉) in terms of the angular momentum (𝑛²ℎ²)?
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What is the formula for the radius (𝑟) of an electron in a hydrogen atom?
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What is the value of the Planck constant (ℎ)?
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What is the main postulate of Bohr's theory regarding the energy of an electron in an atom?
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What is the condition for an electron to exist in a certain energy level (orbits) according to Bohr's theory?
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What is the relationship between the energy of the system and the radius of the orbit according to Bohr's theory?
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What is the equation that relates the wavelength of an electron to its velocity and mass?
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What is the significance of the equation λ = h / (mV) in Bohr's theory?
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What is the angular momentum of an electron in an orbit according to Bohr's theory?
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What is the condition for an electron to move from one orbit to another according to Bohr's theory?
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What are the two opposite forces that keep the electron in its orbit according to Bohr's theory?
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What is the total energy of an electron in a hydrogen atom?
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What is the unit of energy level?
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What is the relationship between the energy level and the radius of an electron in a hydrogen atom?
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What is the value of the total energy of an electron in the ground state of a hydrogen atom?
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What is the formula for the energy of an electron in a hydrogen atom?
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What is the type of spectrum emitted by an atomic system?
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What is the formula for the frequency of a photon emitted by an electron in a hydrogen atom?
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What is the value of the energy difference between two energy levels of an electron in a hydrogen atom?
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What is the wavelength of a photon emitted by an electron in a hydrogen atom?
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What is the direction of the electron in a hydrogen atom when its energy is 0 eV?
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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
