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preface to fifteenth edition

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7.40 SECTION 7<br />

where the term k has been introduced <strong>to</strong> handle instrumental artifacts and the geometry fac<strong>to</strong>r because<br />

fluorescence (and phosphorescence) is emitted in all directions but is viewed only through a limited<br />

aperture.<br />

The thickness of a transparent film or the path length of infrared absorption cells b, in centimeters,<br />

is given by<br />

1 n<br />

b <br />

2nv¯ v¯<br />

<br />

D 1 2<br />

where n is the number of fringes (peaks or troughs) between two wavenumbers v¯ 1 and v¯ 2,<br />

and n D is<br />

the refractive index of the sample material (unity for the air path of an empty cuvette). If measurements<br />

are made in wavelength, as micrometers, the expression is<br />

1 n 1 <br />

b <br />

2<br />

2n <br />

D 2 1<br />

7.4.1.3 Grating Equation. The light incident on each groove is diffracted or spread out over a<br />

range of angles, and in certain directions reinforcement or constructive interference occurs, as stated<br />

in the grating formula:<br />

m b(sin i sin r)<br />

where b is the distance between adjacent grooves, i is the angle of incidence, r is the angle of<br />

reflection (both angles relative <strong>to</strong> the grating normal), and m is the order number. A positive sign<br />

applies where incoming and emergent beams are on the same side of the grating normal.<br />

The blaze wavelength is that wavelength for which the angle of reflectance from the groove face<br />

and the angle of reflection (usually the angle of incidence) from the grating are identical.<br />

The Bragg equation<br />

m 2d sin <br />

states the condition for reinforcement of reflection from a crystal lattice, where d is the distance<br />

between each set of a<strong>to</strong>mic planes and is the angle of reflection.<br />

7.4.1.4 Ionization of Metals in a Plasma. A loss in spectrochemical sensitivity results when a<br />

free metal a<strong>to</strong>m is split in<strong>to</strong> a positive ion and an electron:<br />

The degree of ionization, i , is defined as<br />

M M<br />

i<br />

<br />

e<br />

<br />

[M ]<br />

<br />

<br />

[M ] [M]<br />

At equilibrium, when the ionization and recombination rates are balanced, the ionization constant<br />

K i (in atm) is given by<br />

2<br />

2 M<br />

[M ][e ] K <br />

i<br />

i p<br />

[M] 1 i<br />

where p M (in atm) is the <strong>to</strong>tal a<strong>to</strong>m concentration of metal in all forms in the plasma.

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