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.

• sp2 Hybridization

  • Boron trifluoride (BF3) has a boron atom with three outer-shell electrons in its normal or ground state, as well as three fluorine atoms, each with seven outer electrons.
  • One of the three boron electrons is unpaired in the ground state.
  • One of the three boron electrons is unpaired in its ground state.

• 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).

• Aurora Borealis and the Aurora Australis

  • Clouds in the sky and any light (natural sunlight or man-made light) can prevent the possibility of seeing the aurora from the ground.
  • Auroras result from emissions of photons in the Earth's upper atmosphere (above 80 km, or 50 mi), from ionized nitrogen atoms regaining an electron, and from oxygen and nitrogen atoms returning from an excited state to ground state.
  • This energy serves to move the electrons in nitrogen and oxygen from their ground state up to an excited state, where they can then decay back to the ground state by emitting photons of visible light (see the concept on emission spectra for more information).
  • Nitrogen emissions are blue if the atom regains an electron after it has been ionized and red if the atom returns to ground state from an excited state.
  • Oxygen is unusual in terms of its return to ground state: it can take three-quarters of a second to emit green light and up to two minutes to emit red.

• Reactions of Coordination Compounds

  • Most substrates have a singlet ground-state; that is, they have lone electron pairs (e.g., water, amines, ethers).
  • Some substrates (e.g., molecular oxygen) have a triplet ground state.

• Planck's Quantum Theory

  • When an electric current is passed through a gas, some of the electrons in the gas molecules move from their ground energy state to an excited state that is further away from their nuclei.
  • When the electrons return to the ground state, they emit energy of various wavelengths.
  • This is because electrons release specific wavelengths of light when moving from an excited state to the ground state.

• Ionic Radius

  • The ionic radius is not a fixed property of a given ion; rather, it varies with coordination number, spin state, and other parameters.
  • For our purposes, we are considering the ions to be as close to their ground state as possible.

• Introduction

  • In the presence of an external magnetic field (B0), two spin states exist, +1/2 and -1/2.
  • The magnetic moment of the lower energy +1/2 state is aligned with the external field, but that of the higher energy -1/2 spin state is opposed to the external field.
  • The earth's magnetic field is not constant, but is approximately 10-4 T at ground level.
  • Irradiation of a sample with radio frequency (rf) energy corresponding exactly to the spin state separation of a specific set of nuclei will cause excitation of those nuclei in the +1/2 state to the higher -1/2 spin state.
  • The following diagram displays energy differences for the proton spin states (as frequencies).