good and one ivould have to know soinctliing about liranching in the alcohol. Several other less conimercially important type.; of nonionic detergent stocks have been examined (Table 111). ;\I1 represent cases where a n absolute niolecular weight could be determined and in each case reasonable d u e s have I;eeii obtained. .\I1 of these types do have a base of reference such as is illcstrated by the mercaptan ethosylate in Figure 4. The +a1 from the S-CH2-C protons (7.5 tau) i j rather inconspicuous, but the integral can be used as a standard to determine I ~ o i rmany protons arc in the rest of the molecule. One muzt dccidc whether it is an
S-CH1-C or S-CH-C grouping, hut only one of these gives a reasonable result. The method, as one might expect, is suhject to interferences. K a t e r \vi11nornially not interfere (c.f. sample RWK1217-85 in Talile 11'). Poly(ethy1ene oxide) \vi11 interfere and would not be detected easily. Generally, we have had no trouble isolating the nonionic from commercial detergent formulations and have had little problem with interfering compounds. Since its introduction about 10 years ago, S l I R has made tremendow contributions to such fields as structure elucidation, conforinabional analysis, and kinetics of very rapid processes.
Recent improvenients in the price and ease of operation of commercial instruments have brought KXR to t'he point where n-e can apply it to some less exotic and inorc mundane prohleins. The time saved and the extra information provided by KMR in these prohlenis may soon rival in importance its more theoretical implications. LITERATURE CITED
(1) Sadtler, P., .kin. Soc. Testing 11:tterials, Bull. 190,51-3 (1953). ( 2 ) Siggia, S., Sonp Cheni. Specialties 34,
s o . 3, 51 (1958). (3) Siggia, P.,Starlse, A. C., Jr., Garis, J. J., Jr., Stahl, C. R., Asar,. CHEM. 30, 115 (1958). RECEIVEDfor review January 10, 1063. Accepted hpril 29, 1963.
Determination of Submicrogram Quantities of Manganese, Sodium, and Copper in Natural Diamonds by Neutron Activation Analysis E. C. LIGHTOWLERS Wheatstone Physics labclratory, King's College, University o f london, Strand, london, W. C. 2, England
manganese content of 18 natural diamonds, and the sodium and copper content of seven of these specimens, has been measured quantitatively by neutron activation analysis. Gamma-scintillation spectrometry has been used to detect the 0.85-m.e.v. gamma emission of Mnj4, the 1.37m.e.v. gamma emission of Na24, and the annihilation radiation due to the positron emission of Cuj4. The specimens examined weighed between 5 and 100 mg., and the levels of impurity found were 0.002 to 0.09 p.p.m. of manganese, 0.05 to 0.4 p.p.m. of sodium, and less than 0.0004 to 0.9 p.p.m. of copper. The precautions taken to avoid errors due to self-shielding and various forms of interference are discussed.
b The
T
liere is ])art of a program of research designed to te-t the corrclation b e t w e n some of the optical and electrical properties of natural diamonds and their chemical impurity content. The optical and electrical propertir.2 of diamond are seriously affected by prolonged pile irradiation, due to crystal damage produced by the high fait-neutron flux component in high thermal-flux irradiation positions. Lxten4ve nieawrements on these properties are, therefore, inade on the crystals prior to irradiation, and since each crystal ia unique, nondestructive HL; W O R K REPORTED
analysir hac been used in all the dctcrminations. The measurement of thc aluminum content of natural diamond5 by neutron activation analysis has been described in a prei ious account (6). During these analyses, where the irradiation times were only a few minutes, mangane-e, sodium, and copper were discernible as major impurities, and their identification and quantitative measurement by nondestructive neutron activation analysis will be reported here. INSTRUMENTATION
The relevant nuclear data for thc 401v neutron reactions of manganese, .odium, and copper are given in Table I (1, 6). The method of analysis n a s based on the detection of the 0.841n.e.v. gamma emission of the manganese, the 1.37-m.e.17. gamma emission of the sodium, and the 0.51-n1.e.v. annihilation radiation due to the positron emission of the copper. The manganese determinations were performed near the reactor because of the relatively short half life (2.576 hours). A 1 X l l / z inch SaI(T1) crystal, contained in an ,1.E.R.E. lead crystal housing, was used as detector, and an A. E.R .E .-type 1363 100-channel pulse height analyzer for recording the gamma 5pectra. The copper and sodium determinations were carried out together because of the similarity in the half lives of their reaction products--12.80 hours and 14.97 hours, respectively. A 1 3 / 4 X 2 inch SaI(T1) crystal con-
tained in a 1 X 2 foot cadmium and copper lined 2-inch lead castle ( 2 ) was used as detector, also a Marshall Instruments (Cambridge) 100-channel pulse height analyzer for recording gamma spectra. Both analyzers \rere equipped with automatic life-time integrators thus eliminating dead-t'ime corrections, and their print-out facilities were used to produce permanent records of the gamma spectra. 90 special precautioris were taken against instrumental drift, other than the use of a stabilized mains supply and the prevention of severe changes in room temperature. Sinall changes in the energy calibration of the spectrometer were overcome by recording standard sources every few hours throughout the measurements. EXPERIMENTAL
Diamond Specimens. Eighteen natural diamonds, weighing between 5 a n d 100 mg. and described elsexhere (6), have been analyzed for manganese, and seven of these for sodium and copper. &ill the crystals were cleaned before irradiation by reflux boiling in sodium hydroxide solution, nitric acid, and demineralized water to remove surface contamination. Comparison Samples. h coniparator method was employed in all the analyqes, and because of t h e relatively large thermal-neutron cross sections of manganese a n d copper, preliminary tests were made on self-shielding in these materials t o determine t h e most suitable form of the comparison sample. VOL. 35, NO. 9, A U G U S T 1963
0
1285
Table I.
Element Manganese Sodium Copper a
*
Stable isotopes
Nuclear Data for the Irradiation of Copper, Sodium, and Manganese
Abundance,
7%
Isotopic cross section for thermal neutrons (barns) 13.2
(n,Y ) product Mn56 NaZ4 cue4
100 0.52 Na23 100 4.4 Cue8 69.1 CUB6 30.9 2 .o CUB6 R indicates relative intensity, A indicates absolute intensity. The 0.51 m.e.v. is due to the annihilation of the 19% p f emission. Mn66
Plumb and Lewis ('7) have derived a n expression for the fractional flux depression f to be expected for a sphere of radius a of a material with thermalneutron cross section u and -1- atoms per unit volume. f = 3/4Nua Substitution of the relevant data for manganese gives f l u = 0.8 cm.-l, and for copper flu = 0.3 cm.-l, which sets a n upper limit on the particle size of about lo-* cm. for less than 1% self-shielding if powdered metals are used. It is difficult to adapt this formula for calculations on foils, but i t would be expected that the minimum foil thickness should be substantially less than these figures. It should perhaps also be noted that a close-packed fine powder would be almost equivalent to a solid piece of pure metal, and if powders are to be used, they should be dispersed over a fairly large area. This formula has also been applied to the crystalline sulfates of manganese and copper which can be obtained with better than 99% purity. The maximum particle sizes for MnSO4.4HzO and CuSOa.5Hz0 are 2 mm. and 5 mm., respectively, for less than 1% selfshielding. The following experiments were carried out to check the calculations given above. Three 10-mg. samples of 99.5%, 600-mesh, manganese powder sealed in X inch cylindrical polyethylene containers, were packed inside a nylon rabbit interspaced with two 10-mg. samples of finely powdered manganese sulfate, also sealed in polyethylene containers. These were irradiated for 5 rabbit irradiation minutes in the E position in the U.K.A.E..l. reactor BEPO. Ten-milligram samples were considered to be the minimum quantities which could be conveniently weighed to 1%. After irradiation, each sample was dissolved and diluted appropriately for the preparation of counting sources. Two sources were prepared from each solution and were measured under conditions of identical geometry on the same scintillation spectrometer, and the counting rates corrected for background and decay time and normalized to the same mass of manganese. Total counts in excess of lo4 were taken on each source with an expected relative standard deviation of 3=lyo. The relative standard deviation in the counting rates obtained was 1286
ANALYTICAL CHEMISTRY
Half life 2.576 hours 14.97 hours 12.80 hours 5.10 min.
=k2.53Y0 with no bias for any particular source and it was concluded that there was no measurable self-shielding or variation in neutron flux along the length of the rabbit. The experiment was repeated with two 10-mg. samples of manganese powder and two 10-mg. samples of manganese sulfate, sealed in 4-mm. bore, fused silica ampoules. The four containers were packed inside a standard irradiation can and irradiated, with the silica tubes in a vertical position, in the E belt-stringer irradiation facility in the U.K.A.E.A. reactor BEPO for 12 hours. Two counting sources were prepared from each irradiated sample, and after the appropriate corrections had been applied the counting rates for the manganese sulfate sources were found to be about 20% higher than those prepared from the manganese powder, indicating a flux depression of 20% in the manganese samples. T o ascertain whether there was any contribution because of preferential sticking of the radioactive manganese atoms to the walls of the silica tubes. these were crushed and boiled in manganese carrier solution and nitric acid. These solutions were added to the previously obtained solutions and further counting sources prepared. Small increases in counting rates were observed with the manganese powder sources of between 1 and 4%. These results indicate that manganese powder is unsuitable as a comparator when packed in small bore silica tubes, and that considerable care must be taken to recover the whole of the manganese activity. Similar experiments were carried out intercomparing copper sulfate and 0.005inch thick, 10-mg. copper foils. The self-shielding in these foils was found to be between 2 and 3%. Because of the high saturation activities of 10-mg. samples of manganese and copper, 39 and 7.6 mc., respectively, for the pure metals and 9.5 and 1.95 mc. for the crystalline sulfates, alternative comparators were considered. These included solid solutions, aqueous solutions, and evaporated layers. Only the latter were thought to be convenient, and have been investigated eyperimentally . An aqueous solution of manganese sulfate was prepared a t a concentration of 0.2 mg. of manganese per ml., and two 0.1-ml. aliquots evaporated to
Gamma energies (m.e.v.) and yo intensities" 0.845(100R) 1.81 (29R) 2 . 1 3 (l5R) 1.368(1004) 2.754 (1OOA) 1.34(1A)0.515 1.04(100R)0 83 ( 3 R )
dryness inside polyethylene containers. These were irradiated together with two IO-mg. samples of finely powdered manganese sulfate for 12 hours in the E 1/7 BEPO irradiation facility. The evaporated sources were redissolved by boiling the containers in manganese sulfate carrier solution. Two counting sources were prepared from each irradiated sample and the counting rates compared. A relative standard deviation of =t2.12% was obtained with the eight sources. Evaporated layers can, therefore, be considered reliable for short irradiations and are much more convenient to handle. However, for irradiations of several days, marked softening of the polyethylene containers is observed, which might hinder the dissolution of the evaporated layers. In all the early manganese determinations involving the DS. series diamonds, 10-mg. samples of 99.5%, 600-mesh manganese powder sealed in X '/* inch polyethylene containers were used as comparators. For the later determinations involving the BL. and R. series diamonds, IO-mg. samples of manganese sulfate were used, but in some of the repeated determinations evaporated layers were employed. For the copper determinations, the comparators were 10-mg. samples of copper sulfate in all cases. Since the cross section of sodium for thermal neutrons is only 0.52 barn and there are no marked resonances (S), self-shielding was not investigated and 10-mg. samples of anhydrous sodium carbonate were used as comparators. Irradiations. 911 the irradiations were carried out in the E l/, belt-stringer irradiation position in the U.K.A.E.A. reactor BEPO in a thermal flux of 1.2 X 1012 n cm.-2 second-'. For the manganese determinations, two diamonds were irradiated together with two comparison samples, each sealed in polyethylene containers and packed in close proximity in a standard aluminum can. The irradiation times were 12 hours, The copper and sodium determinations were carried out simultaneously and two diamonds were similarly packed with two sodium and two copper comparators. The irradiation times were 3 days. Manganese Determinations. After irradiation, 30 minutes was allowed for t h e activity of t h e aluminum can to die away. T h e diamonds were cleaned b y boiling for a few minutes
13
2 0
30
40
>C
bo
CHANNEL
70
PO
L_
90
a0
NUMBER
13
.O
5 0
70
60
C H A N N E L NUMBER
Figure 1 , Gamma spectrum of irradiated copper illustrating differences betweeri encapsulated and open source
Figure 2. Thirty-minute spectrum of diamond after removal from reactor
R2, 1
hour
0.51 -M.e v. peak areas normalized
in nitric* acid to rem01 e suiface contamination and count ed alternately on thin aluminum source trays placed directly on the crystal for periods u p t o 1 hour, depending o n t h e total activity present. The gamma-ray spectrometer was adjusted tc cover the range of 0.1 m.e.v. to 1.6 m.ev., and spectra were recorded for about three half lives. Spectra were also recorded about 15 hours later to check fo. possible interference, and to determine qualitatively the presence of other impurities. Four comparison sources were prepared to produce approximately 5000-perminute total counts, and were counted a t convenient periods under conditions of identical geometry. Copper and Sodium Determinations. T h e 0.51-m.e.7.. annihilation radiation due to the positron emission of Cue4 was used to measure the copper im1)urity. The maximum range of . positrons is about 260 mg cm.-* (i)-that is, about 200 em. in air, and 0.12 cm. in diamond. T h r counting rate from a uniform distribution of CuG4 throughout a diamond cannot, thercfore, be directly compared with that from a thin layer deposited on a source tray, since a much larger proportion of the positr ins are annihilated remote from the source in the latter case. This problem was overcome by defining the region of positron annihilation in the folloiving manner. .Yfter the removal of i urface contamination the diamonds nere placed in x '2 inch cylindrical polyethylene containers and covered to a depth of inch n-it11 paraffin n a x The comparison sources were prepared by evaporating to dryness suitable aliquots of a solution of the comparstor in similar polyethylene container;, which n-ere also covered with paraffin wax. There was then, in both cases, sufficient solid material. including the top layer of the detector crystal, to ensure complete annihilation of the positron emission. Tests have shown t h a t the annihilation radiation counting rat6 for an open
source of CuG4was 37% lower than for a completely encapsulated source. Reference to Figure 1, where the annihilation peak areas for an encapsulated and open source are normalized, clearly illustrates this point, and the decrease in the relative area of the 1.34-m.e.v. gamma peak in the encapsulated case can be seen. No logical explanation has been found for the appearance of a peak a t 0.72 m.e.v., which is found with all encapsulated soiirces but never found when open sources are used. The energy of 0.72 m.e.v., which is reliable to = t O . O l m.e.v., does not correspond to any combination of sum, escape, or backscatter phenomena. T o maintain constant counting geometry, the sodium comparison sources were prepared in a similar manner. The diamonds were counted alternately for periods of ul) to 2 hours for 2 to 3 days and a t appropriate times after this to provide qualitative identification of the other impurities also present. The gamma spectrometer was generally set to cover t h r energy range of 0.1- to 2.0-m.e.v. The comparison samples were prepared to produce about 5000-per-minute total counts, and m r e counted a t convenient periods under conditions of idrntical geometry. INTERFERENCES
Koch ( 5 ) has listed all possible >ources of true interference-that is, cases where the radioisotope being wed to analyze Table II.
Specimen R1 R2 R3 R4
BL. 15 B L , 16 BL , 3 2
Diamond \\eight, mg. 38 6 50 0
T4 S 60 i 43 5 33 '7 6 5
for a particular element is also produced by a fast neutron reaction or second order process from another element. The magnitude of this type of interference will obviously depend on the ratio between the element being analyzed for and the interfering element, and also on the flux spectrum in the irradiation position. The only possible sources of interference in the manganese and copper determinations were second order processes which were considered to be negligible. Only two possible sources of error were considered likely, namely, from the reactions LMg24(n,p)Sa24 and A127(n,~)Sa24.The aluminum content of all these specimens has already been determined (6), but magnesium has never been dctected, possibly because of the low yield of the MgZE(n,7)?rIgz7 reaction. However, spectrochemical methods have never detected magnesium concentrat'ion greater than 10 p.p.m. even in the most impure natural diamonds (8). The sodium equivalents of magnesium and aluminum have been measured in the E irradiation position used in these determinat'ions. Samples of magnesium sulfate and a1umin:im wire containing less than 10 p.p.m. of sodium were irradiated together with a sample of sodium carbonate and their 9 a Z 4 act'ivities compared. T h e measured
Sodium Results for Seven Diamonds
Sodium Found, gram 1.8 x 5.4 x j.3x 2.3 X 9.1 x 8.7 x S.6 X
10-9 10-9 10-9
10--9 10-9 lOF0
1l:ixiniuni likely dev., 2; devia(counting) tion, 5 i5.0 & 13 Rel. std.
P.p.ni.,b>'-
n-eight, 0.047 0 . 10s
0.071 0.38 0.21 0.26 0.13
13.3 f2.1 fl.4 i2.D i2.0 3~8.6
VOL. 35, NO. 9, AUGUST 1963
& 10
&i k 6
f9
&T f.20
0
1287
equivalents of 1 hg. of sodium were 800 wg. of magnesium and 10 mg. of aluminum. From an examination of the *odium results in Table I1 and the previous aluminum determinations (6), the maximum interference from aluminum would introduce an error of less than 0.1%. Taking a maximum of 10 p.p.ni. for the magnesium concentration in these diamonds, the magnesium interference could have produced a positive bias of between 3 and 20%. Three other sources of interference must also be considered in nondestructive analysis. First, a high barkground due to other radioisotopes introduces large statistical errors when subtracting the relative photopeaks (Figure 2). This point will be dealt with in the next section. Second, other radionuclides formed may have gamma energies indistinguishable from those being measured. I n the majority of cases where the half lives of the two components differ by more than a factor of two, this problem can be solved by Iilotting a decay curve. Third, the presence of a high-energy gamma-emitting nuclide is usually accompanicd by phenomena produced by the crystal and surrounding media, namely, backscatter, annihilation, and escape peaks. The positions a n d intensities of these photopeaks can always be predicted, and again a decay curve usually retlloves all doubt as to the magnitude of the interference. In these analyses, only one of these forms of interference has not been resolved by a decay plot. Pair production in the crystal and surrounding media by the high energy gammas of Sa24 results in annihilation radiation when the ~iositrons are annihilated. This is a source of interference in the copper determinations when the sodium to copper ratio is sufficiently high, since the half lives of sodium and copper are very similar. The magnitude of the
annihilation production can be estimated from Figure 3. The ratio of the 1.3i-m.e.v. to the 0.51-m.e.v. peak is about 40, 1, from which it has been determined experimentally that thr copper/sodium ratio in the equivalent production of annihilation radiation is 240 50. This ratio only applied to the counting geometry and crystal used in this particular case, that is a 13/'4x 2 inch crystal a t maximum geometry, and with the copper source encapsulated. Although this correction has only been estimated to 2070, the actual correction factor applied in the present determinations has only in one caqe (diamond R3) exceeded 670, contributing less than 1% in most cases to the uncertainty in the final result.
process of graphical subtraction in the presence of calibration shift. The method employed for calculating the final result and estimating the standard deviations has been fully described elsewhere (e), and the final equationare given below in a slightly modified form. The mass of element in the diamond m is given by
R x
ni = -2 R
mass of pure element in
C
comparison source
i L)
where fi, is the weighted mean peak area for the specimen derived from all the spectra taken and corrected for Cecay to an arbitrary zero time, and R, is a similar mean for the comparato~. The weighted means are given bj-
DATA TREATMENT
Figures 2 and 4 are extreme cases of gamma spectra used in the manganese determinations, and Figure 5 is the spectrum from a manganese comparator sample. The manganese activity is dominant in Figure 4, but is subject to very strong background interference from Ka24 activity in Figure 2. Since the print-out from the 1363 analyzer is in octal notation, the ordinates in Figures 2 and 4 are plotted in the octal rather than the decimal numerical system (IO). Figures 5 and 6 illustrate gamma spectra of diamond 13L.15, 6 hours and 30 days after remoial from the reactor, and the decay curve of the S a Y 4activitj is ihown in Figure 7 , Figures 1 and 3 are 1 gamma spectra of co1q)er and qodium comparator samples. The peak areas nere taken as the region. above the broken lines. This is not the most satkfactory way of subtracting peaks from complex gamma spectra, and undoubtedly a curve stripping technique nould be more lirecise ( 2 , 9). Honever, the eytra precision attainable did not j u h f y the tedious
where
+
u(Rs) = [ ( A i B , ) / t i ] l esp. and Ri = ri, exp. A?',
A?'
(3; (4;
In Equations 3 and 4, -4, is the area above the broken lines in the spectra and B,, defined as the background, is the area below the broken line, for the itli reading. Ti is the mid-count time of the i t h reading from zero time, t , the counting time, and X is the decay constant of the nuclide taken from the literature. -1 full discussion of the factors affecting precision have been given in n previous account (e), together with methods of calculating the standard del-iat'ion and maximum likely deviations, and will not be repeated here. RESULTS AND DISCUSSION
The results of the analyses of 1s natural diamonds for manganese are given in Table 111, and the sodium and copper results of seven of these specimens are given in Tables I1 and IV, respectively. ;111 these result.5 have been
__
___
-
.030-
Y
z z
4
,030-
;. i z
su
'Coo-
l
.C?OL
30
'0
20
IC
.o
13
0 0
CHANNEL
Figure 3.
1288
7 0
85
0 0
NUMBER
Gamma spectrum of irradiated sodium
ANALYTICAL CHEMISTRY
_L .~ I ---.-A 0 5 0 63
CHANNEL
._
NUMBER
Figure 4. Ten-minute spectrum of diamond R4, 1 hour after removal from reactor
W -I
z z
4
U \
+
u1
3 z
0 U
I
a
5000:
20
10
10
LC.
13
'a
63
CHANNEL
80
PO
NUMBER
Figure 5. Thirty-minute spectrum o f diamond BL.15, a f t e r removal from reactor
calculated by the method g i v w ahoi e and have heen co1rect.d for all knonn sources of interferelice here ap1)rol)riate. From the rclvxted determinations iri Table 111, the t n o rcsultare seen to be within the sum of the maximum likelj- deviation- in all ca-ea but it is also apparent froin the-e fen cases, which may nut, howe\ er, lic representatix e, that thc standard devia-
Figure 6. Sixty-minute spectrum o f diamond BL.15, 3 0 days after removal from reactor
6 hours
tions do not adequately describe the uncertainty in the final rebult. This is probably owing to the method of >ubtraction employed, and small differences in counting geometry between a solid specimen and an evaporated layer comparison sample, which are important when counting very close to the crystal. The >ensitirity for any particular
Manganese Specimen D S , 10 DS. 10 (Repeat) DS.11 DS. 12 DS . I 3 DS. 14 D S . 15 DS. 16
DS.17 DS .4 DS.5
DS.6 Rl R 1 . (Repeat) R2 R 2 . (Repeat) R3 It3. (Repeat) R4 R4. (Repeat) BI,, I5 B1,. 16 R1, 32
17 0 21 0 12 7
13 9 I1 4 10 0
7 2
5 6 114 3 91 3 86 2 38 6 38 6 50 0 50 0 74 8 74 8 60 7 60 7
43 3 33 7 6 5
Table IV.
Specimen It 1
R2
R3 R4 BL. 15 BL. 16 BL.32
Diamontl weight, mg. 38.6 50.0
74.8 60.7 43.5 33.7
6.5
Found, gram 1 . 4 7 x 10-3 1 . 3 3 x 10-9 1 . 2 x 10-9 2 . 2 x 10-10 6 . 6 X 10-l' 1 . 3 x 10-10 1 . 4 x 10-10 1 . 7 x 10-10 1 . 6 x 10-10
x 10-10 3 . 7 x 10-10 4 . 7 x 10-10 2.73 x 10-1" 2 . 4 5 x 10-10 1.71 x 10-10 2.36 x 10-lo 1.96 x 10-1" 2.13 X 10-lO 4 . . 3 x 10-10 3.97 x 10-10 8 . 7 5 x 10-10 3.22 x 10-10 1 .oo x 10-10 2.1
P.p. m., by weight 0.087 0.079
n..n. _ x _ 0.017
0.0047
0.011 0.014 0.024 0.029 0.0018
0.0040 0.0054
0.0071 0.0064 0.0034 0.0047
0.0026 0.0028 0.074
0.065 0.020
0.0095
0.013
I
a
Maximum Rel. std. likely dev., yo devia(counting) tion, yo 15.0 f13 14.8 f 13 f22 59.3 f5.1 f 13 114.0 f.31 511.4 5 26 f.9.9 5 23 f.16 f6.6 5 29 113.0 15.6 f14 15.7
f 14 f.10
fl.7 f6.9
f 6
53.6 13.6
f10 f.14
53.6
5 10
12.4 f2.5 fl.4 f2.5 f2.2 f4.9
f f 1 1 f
f5.2
113
f
8 8 6 8 7 13
Copper Results f o r Seven Diamonds
Copper E'uund, gram 1 . 4 x 10-10 2 . 8 x 10-10
