higher level are more probable than the reverse, which is why there is a net absorption of energy. The sensitivity of the EPR method (i.e., the minimal number of detectable spins ) depends on the photon frequency according to where is a constant, is the sample's volume, is the unloaded quality factor of the microwave cavity (sample chamber), is the cavity filling coefficient, and is the microwave power in the spectrometer cavity. With and being constants, ~ , i.e., ~ , where ≈ 1.5. In practice, can change varying from 0.5 to 4.5 depending on spectrometer characteristics, resonance conditions, and sample size. A great sensitivity is therefore obtained with a low detection limit and a large number of spins. Therefore, the required parameters are: A high spectrometer frequency to minimize the Eq. 2. Common frequencies are discussed below A low temperature to decrease the number of spin at the high level of energy as shown in Eq. 1. This condition explains why spectra are often recorded on sample at the boiling point of liquid nitrogen or liquid helium. Spectral parameters In real systems, electrons are normally not solitary, but are associated with one or more atoms. There are several important consequences of this: An unpaired electron can gain or lose angular momentum, which can change the value of its g-factor, causing it to differ from . This is especially significant for chemical systems with transition-metal ions. Systems with multiple unpaired electrons experience electron–electron interactions that give rise to "fine" structure. This is realized as zero field splitting and exchange coupling, and can be large in magnitude. The magnetic moment of a nucleus with a non-zero nuclear spin will affect any unpaired electrons associated with that atom. This leads to the phenomenon of hyperfine coupling, analogous to J-coupling in NMR, splitting the EPR resonance signal into doublets, triplets and so forth. Additional smaller splittings from nearby nuclei is sometimes termed "superhyperfine" coupling. Interactions of an unpaired electron with its environment influence the shape of an EPR spectral line. Line shapes can yield information about, for example, rates of chemical reactions. These effects (g-factor, hyperfine coupling, zero field splitting, exchange coupling) in an atom or molecule may not be the same for all orientations of an unpaired electron in an external magnetic field. This anisotropy depends upon the electronic structure of the atom or molecule (e.g., free radical) in question, and so