Photon interaction studies in solutions of some alkali metal chlorides—I

Photon interaction studies in solutions of some alkali metalchloridesÐI

Gagandeep Kaura, Kulwant Singha,*, B.S. Larkb, H.S. Sahotac

aDepartment of Physics, Guru Nanak Dev University, Amritsar, IndiabDepartment of Chemistry, Guru Nanak Dev University, Amritsar, India

cDepartment of Physics, Punjabi University, Patiala, India

Received 27 July 1999; accepted 23 November 1999

Abstract

Attenuation coe�cients of aqueous solutions of alkali metal chlorides viz. LiCl, NaCl and KCl having di�erentconcentrations have been determined at 81, 356, 511, 662, 1173 and 1332 keV gamma photons using narrow beamtransmission method. The experimental results are analysed in terms of total cross sections, e�ective atomicnumbers and electron density values of these solutions. In addition, molar extinction coe�cients, interaction cross-

sections and interaction radii for the solid solutes in aqueous solutions have also been calculated at these energiesand concentrations. The mixture rule is applied to examine the compatibility of the results. 7 2000 Elsevier ScienceLtd. All rights reserved.

1. Introduction

Reliable values of attenuation coe�cients for

gamma rays are required in a variety of applications,

such as computerised tomography, dosimetry, radi-

ography etc. The study of these coe�cients is poten-

tially useful in the development of semi-empirical

formulations of high accuracy, for example along the

lines detailed by Jackson and Hawkes (1981). In order

to make use of the fact that scattering and absorption

of gamma radiations are related to the density and

e�ective atomic number of the material, a knowledge

of the mass attenuation coe�cient, m=r, is of prime im-

portance. Hubbell (1982) and Hubbell and Seltzer

(1995) have compiled the mass attenuation coe�cients

for a large number of compounds and mixtures ofdosimetric and biological importance.

Most of the previously determined coe�cients havebeen concerned with crystalline samples in the solidform. In their pioneering work, Teli et al. (1994a,

1994b, 1994c, 1996), and Teli and Chaudhary (1995a,1995b, 1996) have determined the gamma-ray attenu-ation coe�cients in dilute solutions of some salts. Den-

sities of the solutions, however, were estimated bytaking volumes of the solutions as the sum of thevolumes of solutes and solvents, which in the light ofprevalence of strong solute±solvent interactions is

untenable. The density of a solution should thus bemeasured experimentally.Gerward (1996) has elaborated the mixture rules for

linear and mass attenuation coe�cients in the generalcase as well as in the limit of extreme dilution and thushas developed the theory of X-ray and gamma-ray at-

tenuation in solutions.It was pointed out by Hine (1952) that the e�ective

Radiation Physics and Chemistry 58 (2000) 315±323

0969-806X/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved.

PII: S0969-806X(99 )00524-1

www.elsevier.com/locate/radphyschem

* Corresponding author. Fax.: +91-183-258819.

E-mail address: [email protected] (K. Singh).

atomic numbers in materials composed of several el-ements can not be represented uniquely and the num-

ber for each partial process has to be determinedseparately. El-Kateb and Abdul Hamid (1991) pointedout the e�ective atomic numbers in case of hydro-

carbon materials tend to be constant as a function ofenergy when contributions from photoelectric e�ectand pair production are not signi®cant. Certain par-

ameters such as e�ective atomic number and electrondensity of a medium are essential for the determinationof energy absorption in a given medium. Seltzer (1993)

reported new calculations of the mass energy-transfercoe�cient and the mass energy-absorption coe�cientfor photon energies from 1 keV to 100 MeV based ona re-examination of the processes involved after the in-

itial photon interaction. These coe�cients are used torelate the photon energy ¯uence in an irradiated med-ium to quantities approximating the absorbed dose.

The present study covers the energy regions in whichthe in¯uence of all photon processes can be seen andthe investigation is expected to yield valuable infor-

mation.As a sequel to our previous study (Singh et al.,

1998, 1999; Kaur et al., 2000) of the absorption prop-

erties of some solutes in water at di�erent concen-trations, the attenuation coe�cients of LiCl, NaCl andKCl at six di�erent gamma ray energies in aqueousmedium as a function of concentration are reported in

this paper. Densities required for their estimationshave been measured experimentally. However, in thispaper we have also reported a quantity which is more

practically used when we want to determine the inter-action of photons for solutions in terms of molar con-centration and that is molar decadic extinction

coe�cient e which is dependent upon the photonenergy and nature of the dissolved substance. Theenergy absorbed from radiation may produce a chemi-cal change in the absorbing medium and the amount

of this may be used to measure dose. The values ofmolar extinction coe�cients for the solid solutes inaqueous solutions have also been reported for the ®rst

time for these compounds in aqueous medium.

2. Theory

2.1. Attenuation coe�cients:

A material of thickness x, placed in the path of a

beam of gamma radiation will e�ect the transmittedintensity according to `Lambert±Beer' law, whichstates that a beam of monoenergetic gamma rays is

attenuated according to the equation:

I � I0eÿmrrx �1�

where I0 and I are the incident and transmitted intensi-ties, respectively, m=r (cm2/g) is the mass attenuation

coe�cient; r (g/cm3) is the density of the solution andx (cm) is the thickness of the sample. If the absorbingmaterial under experimentation is a binary solution, its

mass absorption coe�cient is given by the mixture ruleas:

mr��mr

�S

wS ��mr

�W

�1ÿ wS � �2a�

mr��mr

�W

�"�m

r

�S

ÿ�mr

�W

#wS, �2b�

where �m=r�S and �m=r�W are the mass attenuation

coe�cients of the solute and water, respectively, andwS is the weight fraction of the solute. Eq. (2a) can berewritten in the following form:

mr� mS

rS

�M1

M1 �M2

�� mW

rW

�M2

M1 �M2

��3a�

where M1 and M2 are the masses of solute and waterand mS and mW are their linear attenuation coe�cients,respectively. If rS, rW (=1 g/cm3) are the densities and

V1��M1=rS� and V2��M2=rW� are the volumes of thesolute and water, respectively, a � V1=V2 and c��M1=V2 � arS� is the concentration of the solution,

then Eq. (3a) becomes:

mr� mSa� mW

arS � rW

�4�

Neglecting the change in volume of the solution andmultiplying Eq. (4) by

r � M1 �M2

V1 � V2� arS � rW

1� a�5�

we get

m � �mS ÿ mW �a

1� a� mW �6�

A plot of m versus a=�1� a� yields a straight line with

the intercept being mW and the slope `m' equal to thedi�erence �mS ÿ mW� of linear attenuation coe�cientsof solute and water. From the slope and mW, mS thus

can be calculated. Knowing the experimental value of`m' and density of the solute its corresponding mass at-tenuation coe�cient �mS=rS� can be determined.

2.2. E�ective atomic numbers

Values of mass attenuation coe�cients can be usedto determine the total molecular cross-section st, m, bythe following relation.

G. Kaur et al. / Radiation Physics and Chemistry 58 (2000) 315±323316

st, m ��mr

�At

NA

�7�

where At �P

i niAi is the molecular weight, NA is theAvogadro's number and ni is the total number ofatoms (with respect to mass number) in the molecule.

The total atomic cross-section st, a can be easily deter-mined from Eq. (7) as:

st, a � st, m

1Xi

ni

�8�

Also the total electronic cross-section st, el for the indi-vidual element is expressed by the following formula:

st, el � 1

NA

Xi

fiAi

Zi

�mr

�i

�9�

where fi is the number of atoms of element i relative to

the total number of atoms of all elements in the mix-ture. The total atomic and electronic cross-sections arerelated to the e�ective atomic number �Zeff� throughthe following relation:

Zeff � st, a

st, el

�10�

The attenuation cross section in barns/atom can also

be obtained by dividing the mass attenuation coe�-cient m=r (cm2/g) by the total number of atoms presentin one unit of mass (1 g) of the material. Thus, one

has

s � m=r

NA

Xi

wi

Ai

�11�

where wi is the weight fraction of element i, and Ai isthe atomic weight (g/mol) of element i. Another physi-

cal quantity the electronic density NE (electrons/g) isgiven by:

NE ��Zeff

Ai

�NA

Xi

ni �12�

Also the number NE of electrons per gram is deter-mined by the measure of mass attenuation coe�cientat a given energy by the following relation:

NE � m=res

KN �13�

where esKN

is the Klein±Nishina cross-section. Theabove Eq. (13) is valid for energies where the mass at-tenuation coe�cient is mainly due to Compton scatter-

ing, and thus described by the Klein±Nishina formula.Except for 81 keV energy, this condition is very wellful®lled for the energies used in the present work.

2.3. Molar extinction coe�cients

The absorbance A or optical density of a solution is

de®ned by the equation:

A � logI0I

�14�

where I0 is the intensity of the incident beam imping-ing on a cell containing the solution and I that of thetransmitted beam. Since the optical density is pro-

portional to the amount of material in a solution, itmay be expressed as:

A � exMc �15�

where x (cm) is the path length of the cell, Mc (moles/l) is the molar concentration (number of moles of thesolute dissolved per litre of the solution) of the absorb-

ing species in the solution and e is a constant of pro-portionality called the molar extinction coe�cient.Since A is dimensionless, e has dimensions of area/mol.It is normally convenient to express e in l molÿ1 cmÿ1,but alternative units are cm2/mol. This change of unitsemphasizes the point that e is a molar attenuationcoe�cient, analogous to the mass attenuation coe�-

cient m=r: The latter has dimensions of area/mass andis typically reported in cm2/g. If e is known, the con-centration may be determined from a measurement of

A using Eq. (15).The change in the radiation intensity dI due to inter-

actions occurring during the passage is given by:

ÿdI � sIN dx �16�

where N is the number of interaction centres per unitvolume and s is the interaction cross section having

the dimensions of area (m2) called the probability ofinteraction and may be visualised as the area, whichhas to be hit by the photons in order to cause inter-

action. Eq. (16) may be written in terms of molar con-centration by using N � NAMc, where NA is theAvogadro's constant.

ÿdI � sINAMc dx �17�

Integration leads to

I � I0eÿsNAMcx �18�

This expression is essentially identical to the so-called`Lambert±Beer law' which is used to describe radiation

attenuation in homogeneous solutions. For practicalpurposes, the following form is preferred:

I � I0 � 10ÿeMcx �19�

Comparing Eqs. (18) and (19), we have

G. Kaur et al. / Radiation Physics and Chemistry 58 (2000) 315±323 317

e � sNAlog10 e �20�or numerically

sm2� 3:82� 10ÿ25

emolÿ1 dm3 cmÿ1

�21�

The values of interaction cross sections can then beused to calculate the interaction radii of the solutes in

solution, using s � pr2: The mixture rule can be incor-porated for the molar extinction coe�cients de®ned bythe following relation:

logI0I� e1Mc1x� e2Mc2x �22�

where e1, e2 are the molar extinction coe�cients of the

solid solute and pure water and Mc1, Mc2 are theirmolar concentrations, respectively.

3. Experimental details

The details of the experimental arrangement aregiven in our previous paper (Singh et al., 1998). A 1.50� 1.50 NaI(Tl) crystal having energy resolution of 12%

at 662 keV was used for the measurement of attenu-ation coe�cients. The 137Cs, 133Ba, 22Na and 60Co

sources of strength 5 mci were obtained from Bhabha

Atomic Research Centre, Trombay, Bombay, India.The signal from the detector after suitable ampli®ca-tion was recorded in an EG & G ORTEC Plug-in-card

coupled to a PC/AT. The stability and reproducibilityof the arrangement was tested before and after eachset of runs in the usual manner. The experimental pro-cedure records the intensity of gamma radiation pas-

sing through each sample of known thickness. Theintensity of the transmitted radiation was measured bygating the channels at the FWHM position of the

photo peak to minimise the contributions of bothsmall angle and multiple scattering events to themeasured intensity. A su�cient number of counts were

collected under the photo peak to limit the statisticalerror to less than 1%. The samples contained in per-spex boxes of di�erent thicknesses were placed one by

one between the source and detector.The intensity of the gamma radiation, passing

through a standard material can be written as:

lnISTD

I0� ÿ

�mrrx�

STD

�23�

where `STD' stands for the standard material which inthe present case is an aluminium slab of known thick-

ness. Intensity of the radiation passing through perspex(the material used for the solution container) is givenas:

lnI

I0� ÿ

�mrrx�

P

�24�

where `P' stands for perspex material.Subtracting Eq. (23) from Eq. (24) for eliminating

the need for measuring radiation intensity passing

through air I0, we have

lnI

ISTD

� ÿ�mrrx�

P

��mrrx�

STD

�25�

Similarly, the intensity of the radiation passing

through the solution can be written as:

lnI

ISTD

� ÿ�mrrx�

SOL

�"�m

rrx�

STD

ÿ�mrrx�

P

#�26�

A plot of `ÿln�I=ISTD�' versus �rx�SOL gives a straightline with the slope being the mass attenuation coe�-cient m=r of the solution. The terms in the bracket givethe intercept. The following procedure was used to

determine the value of m=r for solutions of di�erentconcentrations.(i) The perspex containers of di�erent path lengths

were ®lled with solutions under study. (ii) Each samplewas placed one by one between the source and thedetector and the corresponding spectra were recorded.

(iii) The solution sample was replaced with the alu-minium standard to determine the ISTD:For the determination of molar extinction coe�-

Fig. 1. Plot of linear attenuation coe�cient of the solution

(LiCl) as a function of a=�1� a�:


cients of solutes, the intensity of radiation passingthrough the container (®xed size) containing only dis-

tilled water was taken as I0, whereas that passingthrough a solution as I.

4. Results and discussion

4.1. Attenuation coe�cients

For the determination of attenuation coe�cients,

several measurements were carried out for the givensolutions of lithium chloride, sodium chloride and pot-assium chloride by putting them in perspex containers.

The experimental values of linear attenuation coe�-cients were calculated by using Eq. (26) for aqueoussolutions of these compounds in the concentration

range of 0.5 to 0.25 g/cm3. A plot of the linear attenu-ation coe�cient m as a function of a=�1� a� is shownin Fig. 1. It is clear from this plot that the values oflinear attenuation coe�cients vary linearly with the

concentration of the solution and increase with theincrease in concentration of the solution. The sensi-tivity of m against a=�1� a� and concentration at

di�erent photon energies is correlated with the slopesof the curves which are positive. From the slope ofthis plot, the linear attenuation coe�cient of the corre-

sponding solute mS was obtained. The mS values for thevarious solid solutes so arrived are shown in Table 1.The mS values were also calculated by using the weight

fractions of the solid solutes and a very accurate com-puter programme and data base named XCOM pho-ton cross-sections on a personal computer was

prepared by Berger and Hubbell (1987). The corre-sponding standard deviations in the attenuation coe�-

cients of the solutes are also been listed in Table 1.From the precisely measured densities of these sol-

utions at 258C (Singh et al., 1998), mass attenuation

coe�cients of the solutions were then obtained and aresummarised in Table 2. For a given salt, the graphbetween m=r and wS did give perfectly linear plots (a

typical plot for LiCl has been shown as an illustrationin Fig. 2). Also from the slope �m=r�S ÿ �m=r�W, (Eq.(2b)) the mass attenuation coe�cient of the corre-

sponding solute was obtained. These �m=r�S values forthe three solid solutes so arrived have been comparedin Table 3 with those calculated from XCOM calcu-lations of the solutes in their solid form. The di�erence

lies between 0.2 and 0.5% which is much within theexperimental uncertainty of measurement of the �m=r�Svalues. Thus, this method gives us an alternative

method for the direct determination of attenuationcoe�cients of solutes without preparing them in purecrystalline form.

4.2. E�ective atomic number and electron densities

By taking the experimental data of �m=r� for Li, Naand K at di�erent energies from El-Kateb and AbdulHamid (1991) the e�ective atomic numbers of solutions

were determined with the help of piece-wise interp-olation computer programme. The theoretical valuesof e�ective atomic numbers were also obtained from

calculated cross-sections. The e�ective atomic numbersalmost tend to be a constant function of energy whichis in line with the view point of El-Kateb and Abdul

Table 1

Linear attenuation coe�cients mS (cmÿ1) of the solutes in solid form

Solute Energy (keV) XCOM value Experimental value Slope

LiCl 81 0.5037 0.5193 Slope = 0.5467

356 0.1985 0.2608

511 0.1700 0.1798 Intercept = 0.4096

662 0.1515 0.1623

1173 0.1150 0.1220 Standard Deviation = 0.0009

1332 0.1078 0.1139

NaCl 81 0.4994 0.5057 Slope = 0.5340

356 0.2104 0.2119

511 0.1804 0.1859 Intercept = 0.3722

662 0.1608 0.1657

1173 0.1221 0.1262 Standard Deviation = 0 0004

1332 0.1078 0.1183

KCl 81 0.5824 0.6032 Slope = 0.6030

356 0.1967 0.2013

511 0.1679 0.1766 Intercept = 0.5844

662 0.1494 0.1576

1173 0.1132 0.1198 Standard Deviation = 0.0024

1332 0.1062 0.1127


Hamid (1991) in case of materials containing hydro-

gen, carbon and oxygen. The signi®cant variations inZeff were found with concentration of the solution

which is due to the variations in weight fractions ofNa and Cl in the solutions. The behaviour of all sol-

utions is identical with energy and concentration of the

solution. These values of e�ective atomic numberswere used to calculate the electron densities of sol-

utions at di�erent concentrations. The electron densityvalues determined from Eqs. (12) and (13) are shown

in Table 4. A very good linear relationship wasachieved between measured and theoretical electron

density values. These results clearly reveal the analyti-cal capability of our method and support the mixture

rule. The average values of molar extinction coe�-

cients obtained for the solutes in solution are shown in

Table 5. For a given solute and at a ®xed energy thesecoe�cients remain constant with change in concen-

tration of the solution as the molar extinction coe�-cient is a characteristic of the solute and depends on

the nature of the dissolved substance and not upon itsamount. However, the e values decrease with increas-

ing energy as e depends upon wavelength.

The values of interaction radii determined from thecalculated interaction cross-sections for solutes in sol-

ution are shown in Table 6. It is observed that the in-teraction radii of a particular alkali halide remain

constant with the increase in concentration and

decrease with energy and as we are taking the higheralkali halide the interaction radii values show an

Table 2

Mass attenuation coe�cients m=p (cm2/g) of solutions of alkali chlorides

Solution Density of the solution

(g/cm3Concentration

(g/cm3)

Mass attenuation coe�cient m=r (cm2/g)a

81

keV

356

keV

511

keV

662

keV

1173

keV

1332

keV

Lithium chloride

(LiCl)

1.0275698 0.05 a 0.1850 0.1100 0.09529 0.08514 0.06473 0.06069

b 0.1857 0.1104 0.09532 0.08510 0.06485 0.06075

1.0546711 0.10 a 0.1879 0.1092 0.09469 0.08453 0.06439 0.06027

b 0.1884 0.1097 0.09473 0.08460 0.06443 0.06036

1.0815910 0.15 a 0.1899 0.1087 0.09407 0.08404 0.06397 0.05999

b 0.1908 0.1091 0.09418 0.08411 0.06404 0.06009

1.1069374 0.20 a 0.1924 0.1080 0.09359 0.08357 0.06357 0.05960

b 0.1930 0.1086 0.09368 0.08365 0.06369 0.05967

1.1267312 0.25 a 0.1946 0.1075 0.09319 0.08336 0.06329 0.05931

b 0.1950 0.1080 0.09322 0.08342 0.06337 0.05937

Sodium chloride

(NaCl)

1.0273692 0.05 a 0.1847 0.1100 0.09529 0.08513 0.06481 0.06070

b 0.1851 0.1104 0.09538 0.08520 0.06489 0.06079

1.0543111 0.10 a 0.1863 0.1091 0.09475 0.08465 0.06443 0.06038

b 0.1872 0.1098 0.09483 0.08470 0.06450 0.06043

1.0794619 0.15 a 0.1899 0.1089 0.09428 0.08419 0.06409 0.06006

b 0.1893 0.1093 0.09434 0.08425 0.06415 0.06010

1.1065312 0.20 a 0.1899 0.1080 0.09377 0.08378 0.06378 0.05971

b 0.1908 0.1088 0.09388 0.08383 0.06383 0.05980

1.1263340 0.25 a 0.1917 0.1076 0.09339 0.08339 0.06349 0.05947

b 0.1924 0.1083 0.09346 0.08345 0.06354 0.05953

Potassium chloride

(KCl)

1.0259239 0.05 a 0.1873 0.1102 0.09537 0.08519 0.06484 0.06072

b 0.1881 0.1105 0.09543 0.08523 0.06491 0.06081

1.0525964 0.10 a 0.1923 0.1097 0.09483 0.08469 0.06447 0.06039

b 0.1929 0.1102 0.09493 0.08478 0.06455 0.06048

1.0779160 0.15 a 0.1969 0.1091 0.09439 0.08427 0.06413 0.06011

b 0.1972 0.1095 0.09448 0.08436 0.06422 0.06017

1.1037360 0.20 a 0.2066 0.1084 0.09397 0.08388 0.06378 0.05980

b 0.2012 0.1091 0.09406 0.08397 0.06392 0.05989

1.1210717 0.25 a 0.2041 0.1079 0.09359 0.08357 0.06359 0.05959

b 0.2049 0.1086 0.09367 0.08362 0.06364 0.05963

a Values in rows `a' and `b' stand for experimental and theoretical values, respectively.


Table 3

Mass attenuation coe�cients m=r (cm2/g) of the solutes in solid form

Solute Density of the salt (g/cm3) Energy (keV) Experimental value XCOM value

LiCl 81 0.2456 0.2436

356 0.0947 0.0959

2.068 511 0.0822 0.0822

662 0.0743 0.0733

1173 0.0558 0.0556

1332 0.0521 0.0522

NaCl 81 0.2286 0.2308

356 0.0954 0.0972

2.164 511 0.0835 0.0834

662 0.0743 0.0743

1173 0.0566 0.0564

1332 0.0531 0.0529

KCl 81 0.2928 0.2930

356 0.0960 0.0989

1.988 511 0.0843 0.0844

662 0.0751 0.0751

1173 0.0571 0.0569

1332 0.0537 0.0534

Fig. 2. Plot of mass attenuation coe�cient of the solution (LiCl) as a function of weight fraction of the solute.


Table 4

Electron densities of solutions of alkali chlorides

Sample Concentration (g/cm3) Electron density NE � �1023� (electrons/g)a

81 keV 356 keV 511 keV 662 keV 1173 1332 keV

Lithium chloride (LiCl) 0.05 a 3.600 3.332 3.328 3.325 3.326 3.326

b 3.587 3.320 3.327 3.323 3.320 3.323

0.10 a 3.653 3.311 3.307 3.304 3.304 3.305

b 3.643 3.296 3.306 3.301 3.302 3.300

0.15 a 3.699 3.293 3.288 3.285 3.284 3.290

b 3.682 3.281 3.284 3.282 3.281 3.285

0.20 a 3.742 3.278 3.270 3.267 3.268 3.267

b 3.730 3.260 3.267 3.264 3.260 3.263

0.25 a 3.780 3.260 3.254 3.258 3.250 3.251

b 3.773 3.245 3.253 3.253 3.246 3.247

Sodium chloride (NaCl) 0.05 a 3.589 3.332 3.330 3.327 3.328 3.328

b 3.581 3.320 3.327 3.325 3.324 3.323

0.10 a 3.629 3.314 3.311 3.308 3.308 3.309

b 3.612 3.293 3.308 3.306 3.304 3.306

0.15 a 3.670 3.299 3.293 3.290 3.290 3.291

b 3.662 3.287 3.291 3.288 3.287 3.288

0.20 a 3.699 3.284 3.277 3.273 3.273 3.274

b 3.682 3.260 3.274 3.272 3.271 3.269

0.25 a 3.730 3.269 3.263 3.259 3.259 3.259

b 3.716 3.248 3.260 3.257 3.256 3.256

Potassium chloride (KCl) 0.05 a 3.647 3.335 3.331 3.329 3.329 3.329

b 3.631 3.326 3.329 3.327 3.325 3.324

0.10 a 3.740 3.326 3.314 3.311 3.310 3.311

b 3.728 3.311 3.311 3.307 3.306 3.306

0.15 a 3.823 3.305 3.298 3.295 3.293 3.294

b 3.817 3.293 3.295 3.291 3.289 3.291

0.20 a 3.901 3.293 3.284 3.279 3.278 3.279

b 3.889 3.272 3.280 3.276 3.275 3.274

0.25 a 3.972 3.278 3.270 3.266 3.264 3.265

b 3.957 3.257 3.267 3.264 3.261 3.263

a Values in rows `a' and `b' stand for experimental and theoretical values, respectively.

Table 5

Molar extinction coe�cients e1 (molÿ1 l cmÿ1) of solid solutes in aqueous solutions of some alkali chlorides

Solute Concentration (mol/l) Energy (keV)

81 356 511 662 1173 1332

Lithium chloride (LiCl) 1.157±5.328 0.00293 0.00080 0.00075 0.00067 0.00049 0.00046

Standard deviation 0.00068 0.00099 0.00010 0.00092 0.00063 0.00063

Sodium chloride (NaCl) 1.838±3.860 0.00368 0.00107 0.00103 0.00093 0.00068 0.00064


Potasium chloride (KCl) 0.503±2.305 0.00861 0.00186 0.00171 0.00151 0.00113 0.00014



increase. This behaviour may be due to the chemicalbinding of the solute with solvent. At high concen-trations, the average distance between the species re-

sponsible for absorption is diminished to the pointwhere the charge distribution of the neighbours isa�ected. This interaction, in turn, can alter the species

ability to absorb a given wavelength of radiationbecause the extent of interaction depends upon concen-tration, the occurrence of this phenomenon causes de-viations from the linear relationships between

absorbance and concentration. The close proximity ofions to the absorber alters the molar absorptivity ofthe latter by electrostatic interactions; the e�ect is les-

sened by dilution. Deviations from Lambert±Beer lawalso arise because e is dependent upon the refractiveindex of the solution which is a function of concen-

tration of the solution.

Acknowledgements

The authors are thankful to U.G.C. for providing®nancial assistance to carry out the research project.

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Table 6

Average values of interaction radii of solutes in aqueous solutions of alkali chlorides

Solute Concentration range (mol/l) Interaction radii (m)� 10ÿ15

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

Lithium chloride (LiCl) 1.157±5.328 18.88 9.849 9.517 9.009 7.736 7.507


Sodium chloride (NaCl) 0.838±3.860 21.17 11.51 11.19 10.60 9.118 8.790


Potasium chloride (KCl) 0.503±2.305 132.35 15.02 14.42 13.54 11.70 11.26



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Photon interaction studies in solutions of some alkali metal chlorides—I