ground state

Examples of ground state in the following topics:

• The Third Law of Thermodynamics and Absolute Energy

  • The entropy of a system at absolute zero is typically zero, and in all cases is determined only by the number of different ground states it has.
  • Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times Boltzmann's constant kB.
  • The entropy of a perfect crystal lattice is zero, provided that its ground state is unique (only one), because ln(1) = 0.
  • An example of a system which does not have a unique ground state is one containing half-integer spins, for which there are two degenerate ground states.
  • Materials that remain paramagnetic at absolute zero, by contrast, may have many nearly-degenerate ground states, as in a spin glass, or may retain dynamic disorder, as is the case in a spin liquid.

• Glow of Space Shuttles

  • The glow observed as a space shuttle re-enters the atmosphere is due to excited NO2 releasing light to return to its ground state.
  • where NO2* represents the excited state of electrons in NO2.
  • It is the relaxation of these electrons from the excited state back to the ground state that produces the glow that is visible around the space shuttle (see the concept about the emission spectra for more information).
  • When atomic oxygen from the high atmosphere combines with nitric oxide on the surface of the space shuttle, the resulting excited nitrogen dioxide returns to the ground state emitting an apparent glow.
  • Recall that excited-state nitrogen dioxide is responsible for the glow observed as space shuttles re-enter Earth's atmosphere.

• Alkene Isomerization

  • A photochemical reaction occurs when internal conversion and relaxation of an excited state leads to a ground state isomer of the initial substrate molecule, or when an excited state undergoes an intermolecular addition to another reactant molecule in the ground state.
  • Non-radiative internal conversion of this S1 twisted state leads to the transition state region of S0, which decays equally to the ground states of the cis and trans isomers.
  • Molecules occupying this new excited state then relax to either DHP or cis-stilbene ground states.
  • This energetic state then serves to activate a substrate molecule to a lower energy triplet state by collisional exothermic energy and spin exchange, returning the sensitizer to its ground state.
  • These competing excitations and subsequent decay to cis and trans ground states lead to remarkable variations in isomer ratios.

• 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

• Mechanistic Background

  • Overall bonding in an excited state is usually lower than in the ground state.
  • At normal temperatures essentially all molecules will exist in the ground vibrational state (zero level).
  • The excited state may return to the ground state by emitting a photon (light blue line).
  • Molecular oxygen is a rare example of a triplet ground electronic state.
  • Alternatively, an excited state may return to the ground state by emitting a photon (radiative decay).

• Red States vs. Blue States

  • The terms "red state" (Republican-voting) and "blue state" (Democratic-voting) were standardized during the 2000 US presidential election.
  • During the 2000 US presidential election, the term "red states" was coined to mean those states whose residents primarily vote for the Republican Party and "blue states" as those states whose residents primarily vote for the Democratic Party .
  • Such a situation can lead a state to favor one party in state and local elections and another party in presidential elections.
  • Another criticism of the red state-blue state paradigm is that it has not been entirely predictive of how states will vote.
  • News media frequently display maps in blue, red, and purple to indicate primarily Democratic-voting states, Republican-voting states, and middle ground states.

• Privacy Rights and Sexuality

  • Family and anti-discrimination laws vary by state.
  • The right to sexuality incorporates the right to express one's sexuality, and to be free from discrimination on the grounds of sexual orientation.
  • The right to sexuality, and to freedom from discrimination on the grounds of sexual orientation, is based on the universality of human rights belonging to every person by virtue of being human.
  • Lesbian, gay, bisexual, and transgender rights in the United States have evolved over time and vary on a state-by-state basis.
  • Identify the legal cases and national legislation that protects people on the grounds of sexual orientation