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Journal of Radioanalytical and Nuclear Chemistry, Vol. 253, No. 3 (2002) 369–373

Molar extinction coefficients in aqueous solutions of some amino acids

Kulwant Singh,1* G. K. Sandhu,1 Gagandeep Kaur,1 B. S. Lark2

1 Department of Physics, Guru Nanak Dev University, Amritsar-143005, India2 Department of Chemistry, Guru Nanak Dev University, Amritsar-143005, India

(Received June 26, 2001)

Mass attenuation coefficients of amino acids viz. glycine (C2H5NO2), l-Serine (C3H7NO3), l-Theronine (C4H9NO3), l-Proline (C5H9NO2), l-Valine(C5H11NO2) and l-Phenylalanine (C9H11NO2) in aqueous solutions have been determined at 81, 356, 511, 662, 1173 and 1332 keV by the gamma-ray transmission method in a narrow beam good geometry setup. Precisely measured densities of these solutions were used for the determination ofthese coefficients which varied systematically with the corresponding changes in the concentrations (g/cm3) of the solutions. Molar extinctioncoefficients of amino acids were then obtained at these energies and were found to be in good agreement with the theoretical results. In addition,total interaction cross sections of amino acids in aqueous solutions were also calculated.

Introduction The present study of molar extinction coefficients ofglycine (C2H5NO2), l-Serine (C3H7NO3), l-Theronine(C4H9NO3), l-Proline (C5H9NO2), l-Valine (C5H11NO2)and l-Phenylalanine (C9H11NO2) solutes in solutionscovers the energy regions in which the influence of allphoton interaction processes can be seen. Theinvestigation is expected to yield a valuable informationabout the interaction of photons with hydrated ratherthan bare ions.

Since radioactive sources are increasingly used inbiological studies, radiation sterilization, and industry,1,2

a thorough knowledge of the interaction of photons withbiologically important substances is desirable. The studyof attenuation coefficients is potentially useful in thedevelopment of semi-empirical formulations of highaccuracy, possibly along the lines detailed by JACKSON

and HAWKES.1 Mass attenuation coefficients of gamma-rays in some compounds and mixtures of dosimetric andbiological importance have been compiled by HUBBEL3

in the energy range 1 keV to 20 MeV. An updatedversion of the attenuation coefficients for elementshaving atomic numbers from 1 to 92 and for 48additional substances has also been compiled byHUBBEL and SELTZER.4 GOPINATHAN et al.5–8 havestudied the total attenuation cross sections for severalamino acids and sugars in the solid form for limitedenergies.

Theory

LAMBERT developed the equation for attenuation of aphoton beam as a function of the thickness of ahomogeneous medium. BEER developed the equation forthe effect of concentration. According to Beer-Lambertlaw, the probability that a photon will be absorbed in amedium is directly proportional to the concentration ofthe absorbing molecule and to the thickness of thesample.

Most of the previous studies for the determination ofthese coefficients have been concerned with crystallinesamples in the solid form. TELI and co-workers9–11 havedetermined gamma-ray attenuation coefficients in dilutesolutions of some salts. GERWARD12 determined linearand mass attenuation coefficients in the general case aswell as in the limit of extreme dilution and developed thetheory of X-ray and γ-ray attenuation in solutions.Recently SINGH et al.13 determined attenuationcoefficients of some solutes in water at differentconcentrations. Densities were determinedexperimentally as these are required for the estimation ofmass attenuation coefficients. KAUR et al.14 in a recentpublication reported the molar extinction coefficient ε, amore useful quantity for alkali metal chlorides inaqueous solutions. This coefficient depends upon theoptical-region photon wavelength and nature of thedissolved substance.

The absorbance or radiation density (RD) of asolution is defined by:

RDI

I= log 0 (1)

where I0 is the intensity of the incident beam impingingon a cell containing the solution and I that of thetransmitted beam. The radiation density is related to theconcentration of the solution as:

RD x c= G (2)

where x is the path length of the cell (cm) and c is themolar concentration (number of moles of the solutedissolved per litre of the solution) of the absorbingspecies in the solution. Molar extinction coefficient ε,depends upon the wavelength of the incident radiationand is greatest where the absorption is most intense.

* E-mail: [email protected]

0236–5731/2002/USD 17.00 Akadémiai Kiadó, Budapest© 2002 Akadémiai Kiadó, Budapest Kluwer Academic Publishers, Dordrecht

KULWANT SINGH et al.: MOLAR EXTINCTION COEFFICIENTS IN AQUEOUS SOLUTIONS OF SOME AMINO ACIDS

Its dimensions are 1/(concentration × path length) and itis normally convenient to express it in litres per mole percentimetre (l.mol–1.cm–1). Alternative units arecm2.mol–1. This change in units emphasizes the pointthat ε is a molar cross section for absorption analogousto the mass attenuation coefficient µ/ρ and, the greaterthe cross section of the molecule for absorption, thegreater its ability to block the passage of the incidentradiation.

Experimental

The narrow beam transmission set-up are discussedin our previous paper.13 The radioactive sources wereobtained from Bhabha Atomic Research Centre,Bombay, India. The stability and reproducibility of thearrangement was tested before and after each set of runsin the usual manner. The samples contained in Perspexboxes of different thicknesses were placed one by onebetween the source and detector. The intensity of thetransmitted radiation was measured by gating thechannels at FWHM position of the photo peak tominimize the contributions of both small angle andmultiple scattering events to the measured intensity. Asufficient number of counts were collected under thephotopeak to limit the statistical error to less than 1%.The experimental values of µ/ρ for solutions of differentconcentrations were determined by:

The change in the radiation intensity dI due to itsinteractions occurring during the passage throughmaterial is given by:

–dI = σINdx (3)

where N is the number of interaction centres per unitvolume and σ is the interaction cross section having thedimensions of area (m2) called the probability ofinteraction and may be visualised as the area, which hasto be hit by the photons in order to cause interaction.Equation (3) may be written in terms of molarconcentration by using N = NA.c, where NA is theAvogadro constant:

I I ex

=−

0

OT T (11)

The mass absorption coefficient of a binary solutionis given by the mixture rule as:

–dI = σINAcdx (4) OT

OT

OT=

�� +�� −

ss

wsw w( )1 (12a)

Integration leads to:

I I e N cx= −0

U A (5) or

OT

OT

OT

OT=

�� +�� −

�� ! "$##w s wsw (12b)This expression is essentially identical to the so-

called “Lambert-Beer law” which is used to describeradiation attenuation in homogeneous solutions. Forpractical purposes, the following form is preferred: where (µ/ρ)S and (µ/ρ)W are the mass attenuation

coefficients of the solute and water, respectively, and wSis the weight fraction of the solute.I I cx− ⋅ −

0 10 G (6)Values of mass attenuation coefficients (µ/ρ) of

solutions were also used to determine the total molecularcross section σt,m by:

Comparing Eqs (5) and (6), we get:

ε = σNAlog10e (7)

U OTt m

tA

N,�� A

(13)or numerically

U Gm2

251 1

3 82 10= ⋅⋅ ⋅

−− −.

mol dm cm3(8)

where At = Σ niAi is the molecular weight, NA is theAvogadro’s number and ni is the total number of atoms(with respect to mass number) of the ith element in themolecule. The total atomic cross section σt,a can beeasily determined from the Eq. (13) as:

Mixture rule can be incorporated for the molarextinction coefficients of mixtures defined by:

RDI

Ic x c xw w s s= = +log 0 G G (9)

U Ut a t mi

in, ,=

∑1

(14)where εw and εs are the molar extinction coefficients ofpure water and solid solute, cw and cs are their respectivemolar concentrations. The total atomic cross section is, in turn, related to

the total electronic cross section σt,el through therelation:

To determine the molar extinction coefficient of thesolute in the aqueous solution Eq. (9) can be rewritten:

G Gss

w wc xRD c x= −

1[ ] (10) Z

n z

neffi i t el

i t el= ∑

∑UU

,

,(15)

where Zeff is the effective atomic number of themolecule.

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Results and discussion have been compared with theoretical values of molarextinction coefficients of pure solutes Eqs (7) and (16):

The experimentally determined values of massattenuation coefficients for aqueous solutions of aminoacids in different concentrations are listed in Table 1.These values are compared with theoretical valuescalculated with XCOM developed by BERGER andHUBBELL.15 The agreement is excellent.

OT

U�� =s

s

s

N

MA (16)

where MS is the molar mass of the solute (amino acid).Excellent agreement is achieved between the

experimental and theoretical values. It is observed thatfor a particular solute, its molar extinction coefficientremains constant with concentration of the solution anddepends upon the wavelength of the incident radiation.Lambert Beer law in aqueous solutions is obeyed.

Molar extinction coefficients for the solutes inaqueous solutions of these amino acids determined bythe use of Eq. (10) are shown in Table 2. These values

Table 1. Mass attenuation coefficients (in cm2/g) of solutions of some amino acids

Solution Molar Density of the Concentration, Mass attenuation coefficients (µ/ρ), cm2/gweight solution, g/cm3 g/cm3

81 keV 356 keV 511 keV 662 keV 1173 keV 1332 keV

Glycine 75..07 0.12 a 1.08958 0.1819 0.1107 0.0956 0.0854 0.0650 0.0609C2H5NO2 b 0.1820 0.1110 0.0958 0.0855 0.0650 0.0610

0.24 a 1.09638 0.1811 0.1103 0.0953 0.0851 0.0648 0.0607b 0.1813 0.1101 0.0951 0.0851 0.0649 0.0608

Solid a 1.15880 0.1737 0.1067 0.0921 0.0823 0.0627 0.0587b 0.1738 0.1067 0.0922 0.0823 0.0629 0.0588

l-Serine 105..09 0.05 a 1.01892 0.1829 0.1111 0.0960 0.0857 0.0653 0.0612C3H7NO3 b 0.1830 0.1110 0.0959 0.0858 0.0653 0.0612

0.10 a 1.03837 0.1829 0.1111 0.0960 0.0857 0.0653 0.0612b 0.1836 0.1113 0.0964 0.0860 0.0654 0.0613

Solid a 1.03990 0.1738 0.1067 0.0921 0.0823 0.0627 0.0587b 0.1739 0.1065 0.0922 0.0822 0.0628 0.0586

l-Proline 115..13 0.01 a 0.99974 0.1828 0.1111 0.0960 0.0857 0.0653 0.0612C5H9NO2 b 0.1826 0.1111 0.0960 0.0856 0.0653 0.0611

0.03 a 1.00248 0.1826 0.1110 0.0959 0.0857 0.0653 0.0612b 0.1825 0.1111 0.0960 0.0857 0.0654 0.0613

Solid a 1.00380 0.1743 0.1078 0.0931 0.0832 0.0634 0.0594b 0.1741 0.1080 0.0931 0.0832 0.0634 0.0593

l-Valine 117..15 0.03 a 1.00124 0.1827 0.1111 0.0959 0.0857 0.0653 0.0612C5H11NO2 b 0.1826 0.1112 0.0961 0.0857 0.0653 0.0612

0.06 a 1.00730 0.1825 0.1110 0.0959 0.0857 0.0653 0.0611b 0.1820 0.1109 0.0959 0.0855 0.0651 0.0611

Solid a 1.00200 0.1766 0.1093 0.0944 0.0844 0.0643 0.0602b 0.1762 0.1090 0.0943 0.0844 0.0643 0.0602

l-Theronine 119..12 0.05 a 1.01340 0.1825 0.1110 0.0958 0.0856 0.0652 0.0611C4H9NO3 b 0.1813 0.1108 0.0957 0.0855 0.0651 0.0610

Solid a 1.04100 0.1747 0.1075 0.0929 0.0830 0.0632 0.0592b 0.1745 0.1074 0.0928 0.0830 0.0632 0.0592

l-Phenylalanine 165..19 0.01 a 0.99959 0.1828 0.1111 0.0960 0.0857 0.0653 0.0612C9H11NO2 b 0.1826 0.1109 0.0959 0.0856 0.0652 0.0611

0.03 a 1.00208 0.1825 0.1110 0.0959 0.0856 0.0652 0.0611b 0.1824 0.1111 0.0960 0.0857 0.0652 0.0611

Solid a 1.00200 0.1719 0.1066 0.0921 0.0823 0.0627 0.0587b 0.1721 0.1063 0.0922 0.0823 0.0627 0.0587

a: Stands for theoretical values, b: stands for experimental values.

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Table 2. Molar extinction coefficients ε (in l.mol–1.cm–1) of solid solutes in aqueous solutions of amino acids

Solute Molar Concentration, Density, 81 keV 356 keV 511 keV 662 keV 1173 keV 1332 keVweight g/cm3 g/cm3

Glycine 75.07 0.12 1.08958 0.0057 0.0036 0.0031 0.0027 0.0021 0.0019C2H5NO2 0.24 1.09638 0.0061 0.0038 0.0035 0.0032 0.0021 0.0019

solid 1.15880 0.0057 0.0035 0.0030 0.0027 0.0021 0.0019Avg. exp. 0.0058 0.0036 0.0032 0.0028 0.0021 0.0019Thr. Val. 0.0057 0.0035 0.0030 0.0027 0.0021 0.0019

1-serine 105.09 0.05 1.01892 0.0085 0.0051 0.0046 0.0040 0.0029 0.0027C3H7NO3 0.10 1.03837 0.0087 0.0053 0.0048 0.0041 0.0030 0.0028


l-Proline 115.13 0.01 0.99974 0.0085 0.0054 0.0046 0.0042 0.0035 0.0034C5H9NO2 0.03 1.00248 0.0088 0.0052 0.0047 0.0043 0.0036 0.0035


l-Valine 117.15 0.03 1.00124 0.0091 0.0057 0.0050 0.0044 0.0034 0.0032C5H11NO2 0.06 1.00730 0.0086 0.0054 0.0048 0.0042 0.0033 0.0031

solid 1.00200 0.0090 0.0056 0.0048 0.0043 0.0033 0.0031Avg. exp 0.0089 0.0056 0.0049 0.0043 0.0033 0.0031Thr. Val. 0.0090 0.0055 0.0048 0.0043 0.0033 0.0031

l-Theronine 119.12 0.05 1.01340 0.0089 0.0053 0.0046 0.0041 0.0031 0.0031C4H9NO3 solid 1.04100 0.0090 0.0056 0.0048 0.0043 0.0033 0.0031

Avg. exp. 0.0090 0.0055 0.0047 0.0042 0.0032 0.0031Thr. Val. 0.0090 0.0056 0.0048 0.0043 0.0032 0.0031

l-Phenylalanine 165.19 0.01 0.99959 0.0120 0.0076 0.0067 0.0058 0.0045 0.0043C9H11NO2 0.06 1.00208 0.0124 0.0078 0.0067 0.0060 0.0047 0.0044


The values of total interaction cross sectionsdetermined from Eq. (8) lie in the range of7.0–47.7.10–28 m2 (or correspond to a circle of radiusabout 1.8–3.8.10–14 m). Corresponding values for leadat 1 MeV energy are σ = 24.0.10–28 m2 (a circle ofradius about 2.8.10–14 m). From Table 3 it is clear thatthere is a good agreement between the values of totalinteraction cross sections calculated from the molarextinction coefficients (present work), from massattenuation coefficients6 and the theoretical values ofHUBBELL.3 It is to be noted here that at 511, 662, 1173and 1332 keV energies, the main contribution to theinteraction cross sections of amino acids under study isalmost entirely from incoherent scattering. This isbecause of the presence of low atomic number elementssuch as H, C, N and O. For these elements the competingprocesses, e.g., photoelectric and coherent scatteringcross sections are negligible in comparison to the total

cross-sections. The values of interaction cross sections at81 keV are higher due to the dominance of photoelectriceffect at this energy.

It is observed that the interaction cross sectionsalmost remain constant with concentration and dependupon energy of incident photons. This behavior may bedue to the chemical binding of the solute with solvent.By using the experimental values of mass attenuationcoefficients of H, C, O and N at these energies from EL-KATEB and ABDUL HAMID,16 the effective atomicnumbers of solutions were determined from Eq. (17) andwere compared with the theoretical values calculatedwith the help of the piece-wise interpolation computerprogram. For all the amino acids under study, values ofeffective atomic numbers were found to be constant withconcentration of the solution and energy and were of theorder of 3.26±0.58.These findings are in line with theview-point of EL-KATEB and ABDUL HAMID16 in case ofmaterials containing hydrogen, carbon and oxygen.

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Table 3. Interaction cross sections (in barn/molecule) of solutes in aqueous solutions of amino acids

Solute Molecular 81 keV 356 keV 511 keV 662 keV 1173 keV 1332 keVweight

Glycine 75.07 Avg. exp. 22.2 13.8 12.2 10.9 7.8 7.3C2H5NO2 Thr. Val. 21.7 13.3 11.5 10.3 7.8 7.3

Ref. 6 21.7 13.1 10.2 7.8 7.3

l-serine 105.09 Avg. exp. 32.0 19.4 17.3 15.1 11.2 10.4C3H7NO3 Thr. Val. 30.3 18.6 16.1 14.3 11.0 10.2

Ref. 6 30.4 18.4 14.3 11.2 10.5

l-Proline 115.13 Avg. exp. 33.1 20.4 17.8 16.1 13.0 12.5C5H9NO2 Thr. Val. 33.3 20.6 17.8 15.9 12.1 11.3

Ref. 6

l-Valine 117.15 Avg. exp. 33.9 21.2 18.5 16.4 12.6 12.0C5H11NO2 Thr. Val. 34.3 21.2 18.3 16.4 12.5 11.7

Ref. 6 33.8 20.7 16.2 12.4 11.7

l-Theronine 119.12 Avg. exp. 34.3 20.8 18.0 16.1 12.1 11.7C4H9NO3 Thr. Val. 34.5 21.2 18.4 16.4 12.3 11.7

Ref. 6 34.4 20.8 16.2 12.6 11.9

l-Phenylalanine 165.19 Avg. exp. 46.8 29.3 25.4 22.6 17.5 16.5C9H11NO2 Thr. Val. 47.2 29.2 25.3 22.6 17.2 16.1

Ref. 6 47.7 28.9 22.6 17.5 16.6

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