ground state

Examples of ground state in the following topics:

• The Third Law

  • The third law of thermodynamics is sometimes stated as follows: The entropy of a perfect crystal at absolute zero is exactly equal to zero.
  • At zero kelvin the system must be in a state with the minimum possible energy, thus this statement of the third law holds true if the perfect crystal has only one minimum energy state.
  • Instead of being 0, entropy at absolute zero could be a nonzero constant, due to the fact that a system may have degeneracy (having several ground states at the same energy).
  • In simple terms, the third law states that the entropy of a perfect crystal approaches zero as the absolute temperature approaches zero.
  • Provided that the ground state is unique (or W=1), the entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because log(1) = 0.

• Absolute Zero

  • More simply put, absolute zero refers to a state in which all the energy of a system is extracted (by definition, the lowest energy state the system can have).
  • Absolute zero is universal in the sense that all matteris in ground state at this temperature .
  • To be precise, a system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state.
  • The uncertainty principle states that the position of a particle cannot be determined with absolute precision; therefore a particle is in motion even if it is at absolute zero, and a ground state still carries a minimal amount of kinetic energy.

• Ionization Equilibrium - the Saha Equation

  • Let's consider a electron and ions in the ground state in equilibrium with neutral atoms also in the ground state
  • We know that the ratio of the number of atoms in any state to those in the ground states is simply $g_0/U(T)$, so we can get Saha's equation

• Thermal Distributions of Atoms

  • In thermal equilibrium the number of atoms in a particular state is proportional to $ge^{-\beta E}$ where $\beta=1/kT$ and $g$ is the statistical weight or degeneracy of the state (for $L-S-$ coupling $g=2(2J+1)$), so we find that
  • Atoms generally have a certain ionization energy (for example, hydrogen has 13.6~eV) but there are an infinite number of states between the ground state and the ionization level so $e^{-\beta E_i}$ approaches a constant for large $i$ and $g_i$ typically increases so $U$ will diverge.
  • First, for temperatures less than $10^4$~K only the ground state is typically populated so it is okay to take $U=g_0$.
  • The size of the highly excited states of atoms increases as $n^2$ so we only have to sum over the states until we reach

• Fluorescence and Phosphorescence

  • Fluorescence occurs when an orbital electron of a molecule or atom relaxes to its ground state by emitting a photon of light after being excited to a higher quantum state by some type of energy.
  • Excitation of electrons to a higher state is accompanied with the change of a spin state .
  • Once in a different spin state, electrons cannot relax into the ground state quickly because the re-emission involves quantum mechanically forbidden energy state transitions.

• Time

  • The second is now operationally defined as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom."
  • It follows that the hyperfine splitting in the ground state of the cesium 133 atom is exactly 9,192,631,770 hertz .

• Problems

  • Assume that the electron is in the ground state.

• Gamma Decay

  • When a nucleus emits an α or β particle, the daughter nucleus is usually left in an excited state.
  • It can then move to a lower energy state by emitting a gamma ray, in much the same way that an atomic electron can jump to a lower energy state by emitting a photon.
  • Next, the excited nickel-60 drops down to the ground state by emitting two gamma rays in succession (1.17 MeV, then 1.33 MeV), as shown in .
  • In certain cases, the excited nuclear state following the emission of a beta particle may be more stable than average; in these cases it is termed a metastable excited state if its decay is 100 to 1000 times longer than the average $10^{-12}$ seconds.
  • Excited levels for Ni-60 that drop to ground state via emission of gamma rays are indicated

• Lasers

  • An electron in an excited state may decay to an unoccupied lower-energy state according to a particular time constant characterizing that transition.
  • A material with many atoms in an excited state may thus result in radiation that is very monochromatic, but the individual photons would have no common phase relationship and would emanate in random directions.
  • However, an external photon at a frequency associated with the atomic transition can affect the quantum mechanical state of the atom .
  • The result is an atom in the ground state with two outgoing photons.

• Safety Precautions in the Household

  • There are three connections to the earth or ground (earth/ground, ).
  • The third earth/ground connection involves the case of the appliance, through the green earth/ground wire, forcing the case to be at zero volts.
  • Grounding the case solves more than one problem, however.
  • If grounded, the case voltage is kept near zero, but if the case is not grounded, a shock can occur.
  • The case of the appliance is also grounded to zero volts.