Lecture 5: Discrete Spectra of Atoms

Chapter 5: 8th Ed. pages 108 - 123 or 3rd Ed. pages 108 - 123

Structure of an Atom

  • A typical atom has a diameter close to 10-10 m.
  • Most of the mass of an atom is concentrated in a tiny nucleus which has a diameter close to 10-14 m.
  • The nucleus is composed of two types of particles: protons and neutrons.
  • Electrons move in the region outside of the nucleus.
  • We don't know exactly where an electron is, but we can describe the probability that the electron is in a certain region called an orbital.

Quantum Mechanics and Atoms

Bohr Model of Hydrogen

  • Electrons can only "orbit" the atom's nucleus at special locations.
  • Each special location corresponds to a particular amount of energy called an energy level.
  • Energy levels are discrete . We enumerate them with integers n .
  • Bohr's model assumes that the orbitals are circular orbits.
  • This is not what really happens, because orbital is determined by two quantities -- energy and angular momentum of the electron.
  • But Bohr's model is still a useful model if we are interested only in energy
  • The lowest energy state is called the "ground state" . It corresponds to innermost n=1 orbit on the diagram.
  • If the electron is in the n=1 energy level, then we say that the atom is in its ground state.
  • If the electron is in a higher energy level, n > 1, then we call the atom "excited" .
  • E1 is the energy of the ground state, En is the energy of the nth energy level,     En > E1.

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Transitions between energy levels

  • In order for an atom to become excited, it must absorb enough energy to allow the electron to make a quantum jump to a higher energy level.
  • for the electron to make the jump from the ground level to level n, the atom must be supplied with Energy = En - E1.
  • There are must be enough energy to excite the atom at least to the next level. Smaller amounts of energy cannot be absorbed nor stored.
  • Energy for excitation can come in the form of a photon of light (photo-excitation)
  • or it can come from atom collisions (collisional excitation)
  • To de-excite, the atom must release energy. Energy is released in discrete amounts.
  • Given time, the excited atom will spontaneously de-excite by emitting a photon. It tries to get to the lowest energy state if left to itself !

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Absorption of a photon

  • Remember, the energy of a photon is Energy = h f where f = frequency and h = Planck's constant = 6.626 x 10-34Js.
  • The electron can make the jump from the ground level if the photon has the frequency

    f = (En - E1)/h
  • If the atom is already excited and is in, say, the N'th level it can jump to the n'th level if the photon has frequency

    f = (En - EN)/h
  • This process is called absorption since the atom absorbs a photon.
  • Only photons with specific frequencies can be absorbed.

Emission of a photon

  • The opposite process is called emission
  • Emission of a photon occurs when an electron in a high energy state jumps down to a lower energy state.
  • If the electron jumps from the n'th energy level to the ground state, a photon emitted with frequency
    f = (En - E1)/h
  • Frequencies of the emitted photons are discrete.
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Example: Hydrogen atom

  • The chemical element is determined by the number of protons in the nucleus.
  • Number of electrons is equal number of protons when atom is not ionized.
  • Hydrogen H has one proton and one electron orbiting it.
  • Energy levels of Hydrogen atom are given by the formula
  • electron-volt:
    1 eV = 1.60218 x 10-19 Joules.
    This is a useful unit for atomic energy measurements

Energy between two levels of the Hydrogen atom

Wavelength of the photon absorbed or emitted in transition between two levels of the Hydrogen atom


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Ionization and recombination

  • If atom is supplied with too much energy, an electron can be pulled away completely. This process is called ionization
  • What is left when electron is pulled away is ion - an atom with less electrons than protons. Ions are electrically charged.
  • Minimal energy that needed to ionize an atom can be found by considering transition to n=infinity level. It is called ionization energy
  • Ionization energy for Hydrogen from the ground state is 13.6 eV.
  • If the environment is hot, most of the atoms are ionized by collisions between them.
  • In the opposite process an ion captures the electron. Such process is called recombination

Back Next lecture: Atomic Spectra
Continuing with Chapter 5