Radiation Physics and Chemistry 71 (2004) 659–660

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Molar extinction coefficients for describing gamma-rayattenuation in solutions

Kulwant Singha, Leif Gerwardb,*aPhysics Department, Guru Nanak Dev University, Amritsar 143005, India

bDepartment of Physics, Technical University of Denmark, Building 307, DK-2800 Kongens Lyngby, Denmark

1. Introduction

Most studies of gamma-ray attenuation in matter

have been carried out with solid absorbers. In a

pioneering work, Teli et al. (1994) measured 123 keV

gamma-ray attenuation coefficients for aqueous solu-

tions of sodium chloride. Subsequently, Gerward (1996)

developed the theory of gamma-ray attenuation in

solutions and elaborated the ‘‘mixture rule’’ for dilute

solutions. The molar extinction coefficient is commonly

used by spectroscopists when dealing with the attenua-

tion of a beam of light (ultraviolet, visible or infrared)

passing through a solution. As once remarked by one of

the present authors, ‘‘if measurements of [gamma-ray]

attenuation coefficients of solutions become common

practice, it might be useful to quote the atomic

cross sections in units of cm2/mol instead of the

presently accepted units of b/atom or b/molecule’’

(Gerward, 1996).

2. Theory

In a homogeneous medium, a parallel beam of

monoenergetic gamma-rays is attenuated according to

Lambert’s law

I ¼ I0 expð�ml lÞ; ð1Þ

where I0 and I are the incident and transmitted

intensities, l is the length of the sample, and ml is the

linear attenuation coefficient. In physical chemistry it is

common practice to recast Eq. (1) in the following form

ing author. Tel.: +45-45-25-31-46; fax: +45-45-

ess: gerward@fysik.dtu.dk (L. Gerward).

ee front matter r 2004 Elsevier Ltd. All rights reserv

dphyschem.2004.04.043

(e.g. Atkins, 1995), known as Beer’s law:

logI0

I¼ ecl; ð2Þ

where c is the molar concentration of the absorbing

species, and e is the molar extinction coefficient. Note

that the logarithm has been converted to base 10. The

dimensionless product ecl is called the absorbance or

optical density of the solution. The molar extinction

coefficient is usually expressed in lmol–1 cm–1. However,

the alternative units cm2mol�1 emphasize the point that

e is a molar cross-section. It can be shown that e is

closely related to the mass attenuation coefficient,

mm=ml/r, where r is the density of mass:

e ¼Mmmln10

¼ 0:4343Mmm; ð3Þ

where M is the molar mass.

Thus, the molar extinction coefficient can readily be

calculated from existing compilations of mass attenua-

tion coefficients (e.g. Berger and Hubbell, 1987/99 or

Gerward et al., 2001). The total molar extinction

coefficient, e, for a chemical compound AxBy is given

by the simple expression

e ¼ xeA þ yeB; ð4Þ

where eA and eB are the molar extinction coefficients for

the elements A and B. Eq. (4) can easily be extended to

more than two components. When the absorption of the

solvent is appreciable, Eq. (2) should be replaced by the

more general expression

logI0

I¼ ðescs þ ewcwÞl; ð5Þ

where index s indicates the solute (e.g. a salt), and index

w indicates the solvent (e.g. water).

ed.

ARTICLE IN PRESS

Fig. 1. Energy dependence of the molar extinction coefficient

(epsilon) of formic acid, CH2O2 (Sandhu et al., 2002, data

points ). The full curve has been calculated using WinXCom

(Gerward et al., 2001).

K. Singh, L. Gerward / Radiation Physics and Chemistry 71 (2004) 659–660660

3. Applications

Singh and Gerward (2002) have summarized the

existing information on attenuation of gamma rays in

solutions. Sandhu et al. (2002) have measured molar

extinction coefficients of some fatty acids for gamma-

rays in the 81–1332 keV energy range, an example being

shown in Fig. 1. In the energy range considered, the

curve essentially represents the energy dependence of the

Compton scattering cross-section. It is seen that there is

good agreement between experiment and theory. Also

solid solutions, e.g. glasses, can be studied (Singh et al.,

2003a, b).

References

Atkins, P.W., 1995. Physical Chemistry 5th Edition. Oxford

University Press, Oxford (Chapter 16).

Berger, M.J., Hubbell, J.H. 1987/99. XCOM: Photon Cross

Sections Database. [National Institute of Standards and

Technology, Gaithersburg, MD, USA (originally published

as NBSIR 87-3597 ‘‘XCOM: Photon Cross Sections on a

Personal Computer’’). Web Version 1.2, available at http://

physics.nist.gov/xcom.

Gerward, L., 1996. On the attenuation of X-rays and gamma-

rays in dilute solutions. Radiat. Phys. Chem. 48, 697–699.

Gerward, L., Guilbert, N., Jensen, K.B., Levring, H., 2001.

X-ray absorption in matter. Reengineering XCOM. Radiat.

Phys. Chem. 60, 23–24.

Sandhu, G.K., Singh, K., Lark, B.S., Gerward, L., 2002. Molar

extinction coefficients of some fatty acids. Radiat. Phys.

Chem. 65, 211–215.

Singh, H., Singh, K., Gerward, L., Singh, K., Sahota, K.S.,

Nathuram, R., 2003a. ZnO–PbO–B2O3 glasses as gamma-

ray shielding materials. Nucl. Instrum. Methods B 207,

257–262.

Singh, H., Singh, K., Sharma, G., Gerward, L., Nathuram, R.,

Lark, B.S., Sahota, H.S., Khanna, A., 2003b. Barium and

calcium borate glasses as shielding materials for X-rays and

gamma-rays. Phys. Chem. Glasses 44, 5–8.

Singh, K., Gerward, L., 2002. Summary of existing information

on gamma-ray and X-ray attenuation coefficients of

solutions. Indian J. Pure Appl. Phys. 40, 643–649 and

references therein.

Teli, M.T., Chaudhary, L.M., Malode, S.S., 1994. Attenuation

coefficient of 123 keV gamma radiation by dilute solutions

of sodium chloride. Appl. Radiat. Isot. 45, 987–990.