Indian Journal of Pure & A ppl ied Physics Vol. 39, December 200 L pp. R 1 6-824

Measurement of mass and linear attenuation coefficients of gamma­

rays for various elements through aqueous solution of salts

M T Tcl i , C S Mahajan & R Nathuram*

Nuclear Research Laboratory, Departmcnt of Physics, Dr Habasaheb Ambedkar Marathwada U n i versity, A urangahad 43 1 oo..! *Radiation Standard and Instrumentation D ivision, Bhabha Atomic Research Centre, M u mbai 400 OR5

Received 21 May 200 I ; accepted 6 August 200 I

Solution technique is developcd for the measurement of l i near and mass attenuation coefficients of salts for gamma­rays and from them elemental attenuation coefficients arc estimated. I mproved mixture rule (Radial Ph),,\' & ehl'l/I, 5:1 ( 1 998) 593), i s employed for the measurement for sal ts containing carbonates, sulphates and chlorides etc . for variolls Gamma energies M ass attenuation coeJ'licients for many clements are estimated. Their results show excellent agreemenl

with theory.

1 Introduction

With wide spread uti l i zation of radiation and radioisotopes in medicine, industry and basic sciences, the problem of radiation protection has become important aspect whi le hand l ing radiation sources and rad iation generating equipments. Selection of materials for radiation shielding and protection needs accurate assessment of i nteraction parameters. These parameters are of immense i mportance for photons being highly penetrating radiation as compared to particulate radiations. Although theoretical and experimental values for elements and sol i ds are avai lable i n l iterature, accurate values for i norgan ic salts used in several appl ications are scare. Katab & Hamid i have measured mass attenuation coefficients of organic compounds and estimated the coefficients for the elements H, C and O. Gagandeep ef a{Y, and S ingh et (/1.4 a lso have done work in gamma photon interaction with solutions of some compounds. A method of measuring attenuation coefficient of several inorganic salts i n water phase using mixture ru le has been developed and used by Tel i ef 0[5- 1 2 . The values arri ved at have been compared theoret ical ly l J . 14 and can be ut i l i zed i n accurate dosi metric app lications.

It i s i nconvenient to use elements d irectly in pure form for measurement of gamma attenuat ion coefficients and it is d i fficult to obtain them i n pure form too. The authors therefore use the elements i n the form of their organic or i norgan ic compounds

such as salts, which are readi ly avai l able also. Furthermore, l iquid or solution form is most su itable as its dens ity being very low, there is less poss ibi l ity of mult iple scattering and so a longer column of absorber can be used which wi l l reduce the error in the measurement of the length of the path traversed by the rad iation . The authors use water-soluble salts for their experiments. They have made measurements for s ix gamma energies for the salts contain ing carbonates, sulphates, chlorides, n itrates and oxides and from them estimated the gamma attenuation coefficients for the elements. Comparison of them with the values in Hubbel l Tables l J. l� shows good agreement.

2 Method

The method of measurement of l inear and mass attenuation coeffic ients of gamma-rays for salts by using their aqueous solutions has a l ready been developed by Tel i et aU-I� and they have measured l i near and mass attenuation coefficients of some salts also. The method is further improved by Tel i 1 5

by considering the fact that volume of solut ion is not equal to the sum of the volumes of salt ( solute ) and of water (solvent) 1 6. 1 7 . This improved method is employed in this work for measuring the mass attenuation coeffic ients of salts from their aqueous solution. Mixture rule is further employed for obtain ing the mass attenuation coefficients of elements. Brief theory i s given below to explain the technique.

TEll et of. : ATTENUATION COEFFICIENTS OF GAMMA RAYS

T(.:- Bttte tte C ap

! I • ........... �;.;.;;.;..;;.A. _ , _ ..... .;..;;.;.';:';';O ...... � • , ,

, ,

Glass Co ntainer

�==;';:";':';;';':';':';';':'::..:I - t - .to:.::.�o.::..;.:::..:.:.:..;;.;.;..� t I , I • I I , • I , ,

---�-- - + - .....,.,...,..,..,==...,.." �i��Jf:���i��:}}�l:���:���� ! - � - �:":':":':':'�':":":..:.:.I�--..

Scintilation COlwter

B urette

Fig. I - Experimental set-up for measurement of the gamma ray absorption coefticienls

8 1 7

3 Theory attenuation coefficients are given from the exponential law viz:

When I and 10 are the intensities of gamma radiation of energy E traversed through the container respectively with and without the absorber

of height h then the l inear (11) and mass (/l/p) as

. . . ( I )

8 1 8 INDIAN J PURE & APPL PHYS, VOL 39,DECEMBER 200 1

3 . .... .3.:2

.3 :2.a

--- Theoretical + + -+- + ExperiInental

:2.6 2 . .... 2.:2

---... 2 .J2!l ..... 1 .a S u 1 .6 -....-c.. 1 . ....

::t. 1 . 2

0.8 0.6 0 . .... 0.2

0 0 40 eo

Atoxnic · Number (Z) Fig. 2 - M ass attenuation coefficient versus atomic number for elements at gamma energy 0. 1 23 MeV. The continuous l ine is the

theoretical curve from Hubbel l & Sel tzer l4. Experimental values are shown by points

0 . 1 8

0 . 1 7

0 . 1 6

0 . 1 5

0 . 1 "'

0.1 3 ".-,.. bO .0.1 :2 --N ._ S 0.1 1 · 0 , - 0. 1 a..

::t.. 0.09

0.08

0 .07

0 ,06

0.06

0 .0"'

; " . .. ,

a

--- Theoretical (. + + + + Experimental

40

Atomic Number (Z)

o · s" JWC.'"

eo

Fig, 3 - Mass attenuation coefficient versus atomic number for elements in the gamma energy 0.5 1 1 - 1 .33 MeV. The continuous lines are the theoretical curves from Hubbel l & Seltzer l4, Experimental values are shown by points

and

E. _ _ d [ In(!!l )ll = _1 In(!!l )

p d(ph) I � ph I

. . . (2)

. . . (3)

For the container of the absorber in cyl i ndrical form of inner cross-section nr�, p = m/nrh where r is the inner radius of the container and In is the absorber mass of height h in the container.

Eg. (3) then simplifies to:

TELl et al.:ATIENUATION COEFFICIENTS OF GAMMA RAYS 8 1 9

Table I - Measured values of gamma mass attenuation coefficients (Wp) cm2/gm of various salts and compounds for six ganuna energies from 0. 1 23 to 1 .33 MeV and comparison of them with Hubbell

Tables14• Figures are given upto 5 decimals for exhibiting deviation

Salt Gamma energy (MeV)

0. 1 23 0.5 1 1 0.662 1 . 1 7 1 .28 1 .33

Acetone Expt 0. 1 57 1 7 0.09620 0.08527 0.06568 0.06275 0.06 1 1 9 . Theo 0. 1 5722 0.09522 0.08500 0.06484 0.06 1 97 0.0609 1

% devi 0.03 1 3 1 - 1 .02075 -0.3 1 646 - 1 .286 1 6 - 1 .27007 -0.46334 Ethanol Expt 0. 1 6 1 07 0.0982 1 0.08738 0.0670 1 0.06439 0.06 1 1 9

Theo 0. 1 6 1 88 0.0975 1 0.08724 0.0665 1 0.06339 . 0.06222 %devi 0.50330 -0.72097 -0. 1 6048 -0.74574 - 1 .56957 -0. 1 3500

I-propanol Expt 0. 1 6 1 2 1 0.09866 0.08768 0.0674 1 0.06429 0.06272 Theo 0. 1 6 1 40 0.09777 0.08728 0.06658 0.06367 0.06253 %devi 0. 1 1 648 -0.9072 1 -0.46288 - 1 .24360 -0.97402 -0.29 1 05

N,N-di-methyl Expt 0. 1 5742 0.09622 0.08520 0.06589 0.06246 0.06 1 42 acetamide. Theo 0 . 1 5723 0.09523 0.08494 0.06459 0.06 1 99 0.06087

%devi -0. 1 1 829 -0.03642 -0.3049 1 - 1 .59269 -0.75652 -0.9 1 0 1 8 Carbon tetra- Expt 0. 1 6653 0.083 1 4 0.07524 0.056 1 3 0.05465 0.05328 chloride Theo 0. 1 6485 0.08437 0.075 1 2 0.057 1 6 0.05448 0.05395

%devi - 1 .0 1 726 1 .45 1 96 -0. 1 5440 1 .96 1 43 -0.3 1 754 1 .23635 Lithium carbonate Expt 0.08538 0.07520 0.05809 0.05534 0.05458

Theo 0.08443 0.07530 0.05739 0.05486 0.05385 %devi - 1 . 1 2 1 6 1 0. 1 3678 - 1 .22848 -0.90785 - 1 .35928

Sodium carbonate Expt 0.08457 0.07452 0.05741 0.054 1 2 0.05321 Theo 0.08524 0.07508 0.05739 0.05450 0.05403 %devi 0.78833 0.075379 0. 1 5825 0.69725 1 .52668

Potassium Expt 0. 1 6948 0.0862 1 0.07626 0.05742 0.05635 0.05449 carbonate Theo 0. 1 7077 0.08567 0.07628 0.05802 0.05548 0.05448

%devi 0.75366 -0.622 1 1 0.01 704 1 .04 1 00 - 1 .56635 -0.04222 Ammonium Expt 0. 1 5765 0.09050 0.08056 0.06 1 96 0.05996 0.05732 sulphate Theo 0. 1 59 1 5 0.09 1 75 0.0824 1 0.062 1 2 0.05962 0.05849

%devi 0.94500 1 .36670 2.24499 0.25275 -0.5585 1 1 .99350 Sodium sulphate Expt 0. 1 508 1 0.0857 1 0.07659 0.05805 0.05660 0.05376

Theo 0. 1 5037 0.08542 0.07679 0.05808 0.05549 0.05442 %devi -0.29394 -0.33480 0.02474 0.05854 - 1 .98583 1 .22377

Copper sulphate Expt 0.08578 0.07584 0.0572 1 0.05561 0.05404 Theo 0.08634 0.07635 0.05764 0.055 1 3 0.054 1 3 %devi 0.64627 0.66664 0.758 1 3 -0.85792 0 . 1 6257

Zinc sulphate Expt 0.201 87 0.08986 0.07998 0.06048 0.05987 0.05573 Theo 0.20335 0.090 1 1 0.07989 0.06085 0.05797 0.05674 %devi 0.72880 0.27854 -0. 1 0764 0.60803 -3.27238 1 .78886

Magneisum Expt 0. 1 6454 0.09020 0.08078 0.06 1 1 0 0.06026 0.05705 chloride Theo 0. 1 6285 0.09036 0.08063 0.06 1 40 0.05869 0.05762

%devi - 1 .04208 0. 1 7928 -0. 1 9348 0.48695 -2.687 1 3 0.977 1 4 Alumnium Expt 0.08866 0.07990 0.05974 0.05895 0.05602 chloride Theo 0.089 1 4 0.07956 0.06053 0.05788 0.05682

%devi 0.54 1 84 -0.4 1 854 1 .29862 - 1 .8609 1 1 .4 1 145 Calcium chloride Expt 0. 1 7975 0.08774 . 0.07857 0.05922 0.05756 0.05526

Theo 0. 1 83 1 3 0.08787 0.07825 0.05940 0.0568 1 0.05578 %devi 1 .84785 0. 1 4 1 1 2 -0.4 1 0 1 4 0.3 1 3 1 3 - 1 .3 1 1 3 1 0.9305 1

. . . (Contd)

820 INDIAN J PURE & APPL PHYS, VOL 39, DECEMBER 200 1

Table 1 . . . (Contd) Salt Gamma energy (MeV)

0. 1 23 0.5 1 1 0.662 1 . 1 7 1 .28 1 .33

Cobaltus chloride Expt 0. 1 9 7 1 9 0.08837 0.07904 0.05922 0.05865 0.05552 Theo 0. 1 9692 0.0889 1 0.07903 0.06005 0.05743 0.05638 %devi -0. 1 3609 0.60626 -0.00632 1 .3855 1 -2. 1 2799 1 .5 1 824

Nickel chloride Expt 0.20478 0.08894 0.08023 0.06028 0.0593 1 0.05609 Theo 0.20402 0.08984 0.07983 0.06063 0.05798 0.05692 %devi -0.37496 1 .00842 -0.50360 0.57068 -2.30440 1 .45992

Strontuim chloride Expt 0.08848 0.0783 1 0.05866 0.05742 0.05462 Theo 0.08895 0.07806 0.05853 0.05588 0.05493 %devi 0.52726 -0.32026 -0.2 1 868 -2.76858 0.57 1 62

Barium chloride Expt 0.88 1 60 0.09 1 80 0.078 1 0 0.05497 0.05305 0.05209 Theo 0.89 1 1 2 0.09362 0.78322 0.05577 0.05297 0.05 1 95 %devi 1 .06955 1 .946 1 2 0.28 1 00 1 .44694 -0. 1 4348 -0.2772 1

Stannous chloride Expt 0.58 1 1 0 0.09079 0.077 1 0 0.05624 0.05400 0.0528 1 Theo 0.57978 0.09030 0.07687 0.056 1 3 0.05347 0.05475 %devi -0.22755 -0.42925 -0.29529 -0. 1 9242 -0.97808 3.53092

Caesium chloride Expt 0.09484 0.0777 1 0.05560 0.05208 0.04994 Theo 0.094 1 4 0.07740 0.05453 0.05 1 25 0.05027 %devi -0.736 1 1 -0.39665 - 1 .95 1 1 1 - 1 .60969 0.65839

Mercurius chloride Expt 2.32904 0. 1 3304 0.07559 0.06039 0.0564 1 0.05524

Theo 2.28 1 44 0. 1 3 1 39 0.09902 0.060 1 8 0.05623 0.05502

%devi -2.08635 - 1 .25963 0.07569 -0.35395 -0.3 1 476 -0.4 1 260

Titanium dioxide Expt 0. 1 9982 0.08368 0.04747 0.05522 0.054 1 6 0.05227 Theo 0.20038 0.08360 0.07420 0.05589 0.05344 0.05254

%devi 0.28246 -0. 1 0048 -0.36522 1 .20594 - 1 .34925 0.52527

Chromic oxide Expt 0. 1 9984 0.08303 0.07342 0.05633 0.05389 0.05306

Theo 0. 1 964 1 0.08344 0.07442 0.056 1 1 0.05359 0.05254

%devi - 1 .7463 1 0.49377 1 .34380 -0.38849 -0.55985 -0.99349

Zirconium dioxide Expt 0.46093 0.08601 0.07359 0.055 1 5 0.05274 0.05 1 29

Theo 0.47 1 37 0.086 1 5 0.074 1 0 0.05490 0.05230 0.05 1 2 1

%devi 2.2 1 588 0. 1 7062 0.69233 -0.4499 1 -0.83553 0.03905

Neodium oxide Expt 1 .2 1 876 0. 1 0400 0.08255 0.05476 0.05342 0.05 1 30

Theo 1 .22997 0. 1 0296 0.08 1 97 0.0554 1 0.05248 0.05 1 39

%devi 0.9 1 1 57 - 1 .0 1 208 -0.69902 1 . 1 695 1 - 1 .77959 0. 1 8874

Samarium oxide Expt 1 .38572 0. 1 0296 0.08347 0.0543 1 0.05202 0.05095

Theo 1 .39550 0. 1 0530 0.0833 1 0.0550 1 0.05258 0.05 1 57

%devi 0.70097 2.2 1 378 -0. 1 9085 1 .26709 1 .063 1 0 1 .206 1 3

Dysporsium oxide Expt 1 . 1 9246 0. 1 1 2 1 2 0.08545 0.05595 0.05379 0.05 1 2R

Theo 1 . 1 799 1 0. 1 1 1 42 0.08562 0.05587 0.05286 0.05 1 70

%devi - 1 .06330 -0.63277 0.20438 -0. 1 4 1 39 - 1 .76889 0.8 1 436

Bismuth nitrate Expt 1 .65009 0. 1 2274 0.09560 0.06 1 48 0.05993 0.05722

Theo 1 .6 1 4 1 8 0. 1 1 980 0.0938 1 0.06 1 75 0.0585 1 0.05725

%devi -2.22509 -2.45404 - 1 .9 1 563 0.4324 1 -2.44252 0.054 1 4

Silver nitrate Expt 0.6 1 8 1 3 0.09052 0.07682 0.05492 0.05429 0.05 1 36

Theo 0.60892 0.08975 0.0765 1 0.05573 0.05326 0.05226

%devi - 1 .5 1 234 -0.85458 -0.39993 1 .45877 - 1 .94532 1 .33750

Boric acid Expt 0.08628 0.07739 0.05839 0.05732 0.05428

Theo 0.0867 1 0.07729 0.05905 0.05644 0.05523

%devi 0.49704 0. 1 4084 1 . 1 1 602 - 1 .553 8 1 1 .70753

Ammonium meta- Expt 0.087 1 2 0.07742 0.05844 0.05672 0.05467

vanadium Theo 0.08652 0.077 1 1 0.05856 0.05594 0.05492

%devi -0.69467 -0.40463 0.20663 - 1 .39788 0.45701

Cadmium acetate Expt 0.09 1 86 0.07955 0.059 1 3 0.05685 0.05427

Theo 0.09 1 5 8 0.079 1 5 0.05856 0.05600 0.05495

%devi -0.3 1 23 1 -0.50663 -0.96646 - 1 .525 1 1 1 .23578

TELl et al. :A TTENUA nON COEFFICIENTS OF GAMMA RAYS 82 1

Table 2 - Measured values of gamma mass attenuation coefficients (Ilip) cm2/gm of various elements for six gamma energies from 0. 1 23 to 1 .33 Me V and comparison of them with Hubbell Tables 14.

Figures are given up to 5 decimals for exhibiting deviation

Element Gamma energy (MeV)

0. 1 23 0.5 1 1 0.662 1 . 1 7 1 .28 1 .33

Hydrogen Expt 0.27952 0. 1 707 1 0. 1 58 1 5 0. 1 1 805 0. 1 0942 0. 1 0755

( I ) Theo 0.27970 0. 1 7 1 30 0 . 1 5296 0. 1 1 680 0. 1 1 1 50 0. 1 0959

%devi 0.06435 0.34442 3 .39304 - 1 .0702 1 1 .86547 1 .86 1 48

Lithium Expt 0.07403 0.06722 0.04970 0.04777 0.0473 1

(3) Theo 0.07452 0.06666 0.05087 0.04856 0.04767

%devi 0.65 1 85 -0.842 1 1 2.29028 1 .6 1 954 0.76 1 2 1

Boron Expt 0.07882 0.07258 0.05495 0.04 1 56 0.05 1 27

(4) Theo 0.07995 0.07 1 34 0.05443 0.05 1 97 0.05099 %devi 1 .4 1 395 - 1 .74257 -0.95555 20.0292 -0.54529

Carbon Expt 0. 1 42 1 4 0.08845 0.077 1 4 0.06055 0.05643 0.05687

(6) Theo 0. 1 4349 0.08634 0.07707 0.05879 0.05625 0.05524 %devi 0.94083 -2.44383 -0.09083 -2.9937 1 -0.32000 -2.95076

Nitrogen Expt 0. 1 4387 0.08604 0.07535 0.05953 0.05578 0.05579

(7) Theo 0. 1 43 1 9 0.08648 0.07702 0.05895 0.056 1 5 0.05502 %devi -0.47252 0.50696 2. 1 7240 -0.98595 0.66364 - 1 .40760

Oxygen Expt 0. 1 4595 0.08622 0.07667 0.05793 0.0598 1 0.05386 (8) Theo 0. 1 4435 0.08647 0.077 1 8 0.05888 0.05630 0.05527

%devi - 1 . 10842 0.289 1 2 0.66079 1 .6 1 345 -6.23445 2.55 1 1 1

Sodium Expt 0. 1 4 1 1 2 0.08434 0.07558 0.05676 0.053 1 5 0.05325 ( 1 1 ) Theo 0. 1 4339 0.08287 0.074 1 4 0.05640 0.05388 0.05277

%devi 1 .58252 - 1 .76884 -0.94600 -0.63933 1 .33952 -0.90 1 43

Magnesium Expt 0. 1 5444 0.08457 0.07602 0.05809 0.05525 0.05593 ( 1 2) Theo 0. 1 5092 0.08558 0.07630 0.05827 0.05553 0.05445

%devi -2.33226 1 . 1 8440 0.36442 0.32779 0.494 1 9 -2.70589

Aluminium Expt 0.08466 0.07547 0.05620 0.05 1 02 0.05298 ( 1 3) Theo 0.08348 0.07467 0.05679 0.05429 0.05324

%devi - 1 .4 1 329 - 1 .06944 1 .03 1 85 6.01 650 0.49728

Sulphur Expt 0. 1 7444 0.08666 0.07790 0.060 1 4 0.055 1 1 0.05428 ( 1 6) Theo 0. 1 7230 0.08686 0.077 1 0 0.05895 0.05626 0.05505

%devi -0.24 1 93 0.2256 1 - 1 .04383 -2.02 1 40 2.04623 1 .39650

Chlorine Expt 0. 1 6928 0.08254 0.07503 0.05564 0.05445 0.05288 ( 17) Theo . 0. 1 7243 0.08370 0.07447 0.0566 1 0.054 1 5 0.053 1 7

%devi 1 .8243 1 1 .380 1 7 -0.75 1 54 1 .7 1 587 -0.56036 0.55 1 42

Potassium Expt 0. 1 88 1 2 0.08586 0.07589 0.05662 0.0542 1 0.05453 ( 19) Theo 0. 1 9 1 92 0.085 1 5 0.07564 0.0574 1 0.05489 0.0539 1

%devi 1 .97863 -0.83387 -0.3 1 993 1 .33767 1 .24 1 78 - 1 . 1 4270

Calcium Expt 0.20763 0.08762 0.07876 0.05874 0.05646 0.05484 (20) Theo 0.20576 0.08762 0.07777 0.05899 0.05644 0.05539

%devi -0.032 1 8 0.00376 1 .27223 0.4247 1 -0.03326 1 .00 1 96

Titanium Expt 0.23582 0.08 1 98 0.07300 0.05340 0.05038 0.05 1 20 (22) Theo 0.206 1 0 0.08 1 05 0.07 1 94 0.05387 0.05 1 52 0.05073

%devi - 14.4 1 95 - 1 . 1 505 1 - 1 .48001 0.86839 2.2 1 1 38 -0.93445

Vanadium Expt 0.08 1 64 0.07230 0.05390 0.0499 1 0.05094 (23) Theo 0.07986 0.07 1 06 0.05354 0.05 1 1 5 0.05024

%devi -2.2328 1 - 1 .75 1 89 -0.666 1 4 2.43250 - 1 .39898 Chromium Expt 0.22472 0.08 1 55 0.07 1 9 1 0.05559 0.05 1 1 5 0.05270

(24) Theo 0.22 1 40 0.08 1 98 0.07257 0.05478 0.05228 0.05 1 23 %devi - 1 .499 1 6 0.52055 0.90382 - 1 .48673 2. 1 58 1 1 -2.86278

Contd . . .

822 INDIAN J PURE & APPL PHYS, VOL 39, DECEMBER 2(0)

Table 2 . . . (Contd)

Element Gamma energy (MeV)

0. 1 23 0.5 1 1 0.662 1 . 1 7 1 .28 1 .33

Iron Expt 0.27628 0.08437 0.07493 0.05434 0.05 1 88 0.05 1 1 5 (26) Thoo 0.27707 0.08322 0.07336 0.05529 0.05289 0.05 1 9 1

%devi 0.284 1 9 - 1 .38544 -2. 1 4444 1 .72903 1 .90629 1 .44964 Cobalt Expt 0.2973 1 0.08 1 97 0.07 1 47 0.05355 0.05865 0.05074

(27) Thoo 0.29 1 09 0.08223 0.07236 0.05446 0.05 1 3 8 0.05 1 1 4 %devi -2. 1 3803 0.3 1 245 1 .22865 1 .67945 0.052 1 0 0.762 1 5

Nickel Expt 0.32847 0.08425 0.07627 0.05784 0.05404 0.05302 (28) Thoo 0.32393 0.08599 0.07555 0.05679 0.05432 0.05330

%devi - 1 .40 1 37 2.02620 -0.948 1 7 · - 1 .85 1 72 0.50007 0.537 17 Copper Expt 0.08338 0.07 1 1 1 0.05473 0.05 1 36 0.05204

(29) Thoo 0.08266 0.07259 0.05438 - 0.05201 0.05 104 %devi - 1 .37398 2.03743 -0.63286 1 .24889 - 1 .96039

Zinc Expt 0.34907 0.08379 0.07277 0.05509 0.05 1 66 0.05027 (30) Theo 0.35040 0.08380 0.07270 0.05504 0.05 1 77 0.050 1 4

%devi 0.38002 0.01 038 -0. 1 0280 -0.09944 0.2 1 566 -0.25684

Strontium Expt 0.54872 0.0834 1 0.07 1 94 0.05283 0.05023 0.04932 (38) Theo 0.52940 0.08335 0.07 1 65 0.05258 0.05009 0.049 1 8

%devi -3.64875 -0.086 1 1 -0.40264 -0.48024 -0.283 1 3 -0.30307

Zirconium Expt 0.57 1 4 1 0.08593 0.07250 0.054 1 7 0.05026 0.05025 (40) Thoo 0.56680 0.08555 0.07276 0.05345 0.05086 0.04975

%devi -0.8 1 346 -0.44684 0.35340 - 1 .34855 1 . 1 8228 - 1 .0 1 1 94

Silver Expt 0.8898 1 0.09301 0.07707 0.05298 0.05 1 64 0.04999 (47) Thoo 0.876 1 0 0.09 1 65 0.076 1 5 0.0539 1 0.05 1 52 0.05056

%devi - 1 .56585 - 1 .48590 - 1 .2 1 470 1 .72474 -0.24033 1 . 1 3686

Cadmium Expt 0.09097 0.07595 0.05424 0.04984 0.04872 (48) Theo 0.09097 0.07509 0.05299 0.05066 0.04965

%devi 0.00359 - 1 . 1 40 1 5 -2.36665 1 .6 1 6 1 0 1 .88236

Tin Expt 0.95214 0.09220 0.07536 0.05307 0.05002 0.04980 (50) Theo 0.92940 0.092 1 4 0.07535 0.05298 0.05029 0.04928

%devi -2.44620 -0.06087 -0.Dl' 6 1 1 -0. 1 6330 0.53653 - 1 .064 1 5

Antimony Expt 1 . 1 0898 0.09266 0.07549 0.05282 0.05014 0.04923 (5 1 ) Theo 1 .090 1 0 0.09276 0.07548 0.05288 0.05009 0.04909

%devi - 1 .73226 0. 1 1 050 -0.02070 0. 1 1 666 -0.0920 1 -0.27939

Cesium Expt 0.098 1 2 0.07842 0.05420 0.05 1 44 0.049 1 6

(55) Theo 0.09693 0.078 1 3 0.05298 0.05048 0.04950 %devi - 1 .22486 -0.37 1 05 -2.28799 - 1 .90983 0.69 1 6 1

Barium Expt 1 .384 1 9 0.09556 0.07767 0.05208 0,04909 0.04964

(56) Theo 1 .4 1 1 10 0.0972 1 0.0779 1 0.05273 0.04979 0.04878 %devi 1 .90007 1 .69490 0.30368 1 .23904 1 .4 1 1 89 - 1 .767 1 4

Neodymium Expt 1 .45026 0. 1 0695 0.08352 0.05423 0.05235 0.05087

(60) Theo 1 .49060 0. 1 0570 0.08277 0.05483 0.05 1 85 0.05075 %devi 2.70634 - 1 . 1 849 1 -0.90537 1 .09393 -0.96825 -0.23322

Samarium Expt 1 .58360 0. 1 0564 0.08456 0.05373 0.05078 0.05048

(62) Theo 1 .59520 0. 1 0830 0.08429 0.05439 0.05 1 99 0.05098 %devi 0.727 1 0 2.45925 -0.3 1 492 1 .207 1 4 2.325 1 5 0.97435

Dysporsium Expt 0. 1 1 595 0.08674 0.05566 0.05290 0.05089

(66) Theo 0. 1 1 5 1 0 0.08687 0.05543 0.05235 0.05 1 1 7

%devi -0.73433 0. 1 4448 -0.4 1 690 - 1 .05908 0.53853

Mercury Expt 3.09 1 0 1 0. 1 4970 0. 1 0730 0.06 1 50 0.056«;?5 0.05559

(80) Thoo 3.02370 0. 1 4960 0. 1 0780 0.06 1 44 0.05697 0.05567

%devi -2.2263 1 -0.06804 0.46369 -0.09402 0.02992 0. 1 4 1 68

Bismuth Expt 3 . 1 8482 0. 1 56 1 1 0. 1 1 1 25 0.06200 0.0582 1 0.05782

(83) Theo 3.2 1 700 0. 1 6020 0. 1 1 240 0.06280 0.05885 0.05737

%devi 1 .00026 2.55598 1 .02464 1 .27002 1 .08924 -0.78346

TELl et al.: ATTENUATION COEFFICIENTS OF GAMMA RAYS 823

Jl 2 d . m-2 . ' . ' , - = 1fr. -[In(lo l l)]= -In(lo I I) p . dm m

. . . (4)

In the formulae (2) to (4) derivatives involve s lopes of the curves of In (lell) against m or h. The graphs being ideally straight lines, the slopes can be replaced by the right hand sides of the respective equations . This avoids the use of the graphs.

When the absorber consists of a mixture of various elements with mass weight factors m/m, m/m etc, the ()1Ip) of the mixture or compound is given by the following mixture rule: .

Jl = L!!!ilJl l

P m� p . . . (5)

Using p = m/v, this reduces to:

Jlv = LJliV . . . . (6)

For a solution of binary compounds m = ml + m2 and Eq. (5) reduces to:

. . . (7)

This represents a straight line for the plot of �p versus (m/m). The intercept on the �p axis gives (�P)I while the slope gives [(�P)2-(�P) I ] . From these, (�P)I and (J1IP)2 are determined.

Similarly, if v = V I + V2 in Eq. (6) then for linear attenuation coefficient also we get a straight line equation:

. . . (8)

This determines JlI and 112 for the members of the solution mixture.

. .

For water solution, however, v. + Vw does not coincide with the solution volume and so Eq. (8) cannot be directly appliedI6• 17• In this case, the authors re-scale the linear attenuation coefficient as Teli15•

V Jl' = Jl- , v' = V1 + v2 v' . . . (9)

where V is the volume of the solution and Il is its experimentally measured value by using Eq. (2).

Dividing Eq. (6) by v' we again get a straight line now for Il'

as:

Jl' == Jl. + (P2 - Jl. ) [ :: ] . . . ( 1 0)

Here Jl' is computed from Eq. (9) by using

experimental Jl. The plot of Jl' against (vz/v' ) now

leads to the accurate determination of JlI and 112 i .e. of Jl. (for salt) and Jlw (for water).

4 Experimental Technique

The authors measured the mass attenuation coefficients of the compounds by performing vertical narrow beam geometry (Fig. 1 ) . The diameter of the collimator is 1 . 1 8 cm. A cylindrical glass container of internal diameter 2.9 cm was placed below the source at a distance of 1 2.3 cm and 9.0 cm above the detector. To prevent the evaporation of the chemicals, the burette was directly connected to the glass container. The burette and the glass container are sealed and interconnected through 1 .2 mm diameter polyethylene tube to bypass the air. The sodium Iodide detector [0.75" x 2") was connected to PC based 8k-MCA (4k-MCA was also used in another set-up). In their calculations, the intensities (counts) 1 and 10 are replaced in Eqs (2) to (4) by the gross area under the photo-peak in the accumulated gamma spectrum for 1 800 sec.

Using Eq. (7) the authors measured (J1Ip) for 33 salts containing (a) carbonates of lithium, potassium, sodium and barium, (b) sulphates of ammonia, sodium, ferric, copper and zinc, (c) chlorides of aluminium, calcium, cobalt, nickel, strontium, stannous, caesium and mercurius (d) nitrates of silver and bismuth (e) micro fined oxides of titanium, chromium, zirconium, neodium, samarium and dysporsium and boric acid, ammonium metavanadium, cadmium acetate dihydrate etc. Six standard gamma sources COS? (0. 1 23), Na22 (0.5 1 1 , 1 .28), Cs1J7 (0.662) and C06C1 ( 1 . 1 7, 1 .33) MeV are used. The results are shown in the Table 1 .

.

For the measurement of the mass attenuation coefficients of the elements, the authors first aimed to estimate the attenuation coefficients for the basic elements H, C and O. For this purpose, the authors measured the attenuation coefficients of acetone, ethanol and I -propanol and solved the three

824 INDIAN J PURE & APPL PHYS, VOL 39,DECEMBER 200 1

simultaneous equations given by their mixture rule and thus obtained the mass attenuation coefficients for the elements hydrogen, carbon and oxygen. Similar type of measurements for the elements H, C and 0 has been done by Kateb & Himid I but the authors' results show better accuracy Teli et a(1. Next, they measured the mass attenuation coefficient for carbon tetrachloride and using the mixture rule obtained the coefficients for chlorine by using the previously measured values for carbon. In this way, the mass attenuation coefficients for various elements are estimated by measuring the coefficients of the respective compounds one by one and a series of 34 elements H, Li, B , C, N, 0, Na, Mg, AI, S, CI, K, Ca, Ti, V, Cr, Fe, Co, Ni, Cu, Zn, Sr, Zr, Ag, Cd, Sn, Sb, Cs, Ba, Hg, Bi, Nd, Sm and Dy has been spanned. The results are shown in the Table 2.

The comparison of their measurements with the theoretical values (Figs 2 and 3) from Hubbell & Seltzerl4 Tables is done by calculating the percentage deviation as:

Ol d . . (%),heo -(%tp 1 00 -10 eVlatlOn = (%) x

P theo These are also presented in the Tables and the

authors found the deviations mostly below 1 % indicating thereby excellent agreement of the authors' measurements with theory. The linear attenuation coefficient is obtainable by multiplying the mass attenuation coefficient of the respective substance by its density.

5 Conclusions

The theoretical values of mass attenuation coefficients for elements are available from Hubbelll4 Tables and the authors carried out the work of their experimental measurement for the first time by devising a simple experimental method with excellent accuracy and by efficiently employing the mixture rule. The agreement of the authors' so measured values with theory confirms the theoretical considerations of the contribution of

various processes such as photoelectric effect, Compton effect and pair production to the total absorption cross section for low energy gamma radiation. The measured mass and linear attenuation coefficients of salts are useful for dosimetry purpose while those of the pure elements are important from theoretical points of view.

Acknowledgements

The authors are very much thankful to Department of Atomic Energy, for financial support under BRNS Major Research grant.

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