X-Ray Transmission and Moseley’s Law

Mohd Faiz Mohd Zin∗

West Virginia University(Dated: March 12, 2012)

Our experimental data have failed to obey Moseley’s law but we have managed to develop aMaltese cross shape photofilm and also the hidden object photofilm. Then we also have succeded inmeasuring 0.93±0.01 mm for tenth value of thickness for aluminum in linear absorption experiment.We have performed x-ray scattering to plot the graph of the ratio of intensity against the Atomicnumber but our graph have many ’kink’ that does not show the linearity of the ratio with Atomicweight of the element. However, we did see the difference of having changing the position betweenNickel and Cobalt as we have lesser kink by reversing their position.

I. INTRODUCTION

X-ray is a highly penetrating rays that were emittedwhen high energy electrons struck metal target. Thestrength of it’s penetration is because of it’s high fre-quency electromagnetic energy which is at 3 × 1016.[1]X-rays can be produced by two atomic processes, oneis from Bremstrahlung radiation and the other is by x-ray fluorescence which is produced when electrons maketransitions between lower atomic energy leves in heavyelements. This kind of x-ray is known as characteristicsx-rays which have definite energies that can be deter-mined by the atomic energy level.[? ]

FIG. 1. Occurence of characteristic x-ray

Characteristic x-ray occurs when incident high energyelectron from outside ejected and scattered the electronbound in an atom as shown in FIG1. After the electronbound ejected from the shell, there is a vacant in the en-ergy level. So, the electron from high energy level willoccupied this vacancy and there will be emission of char-acteristic x-ray which contains energy that is associatedwith the difference between the atomic energy levels ofthe targeted atom.

In this experiment the main focus is on the x-rayfluorescence which we want to observe Moseley’s lawwhich the square root of frequency of characteristic x-raysis proportional to the atomic number of the elements,√υ ∝ Z where υ is the frequency of characteristic x-rays

and Z is the atomic number of the elements.[3] We alsoused features in the combination absorption and scat-tered spectra of various materials to construct a Moseleytype plot.

∗ Contact: mmohdzin@mix.wvu.edu

II. THEORY

The maximum photon energy, hυ is equal to the max-imum available electron kinetic energy, eV. So, the min-imum x-ray wavelength is given by:[3]

λmin = hc/eV (1)

Then Moseley had observed that the characteristicwavelength decreased as the atomic number of target ma-terial increased.[3]

For shortest characteristic x-ray, Kα line, it follows therelationship:

1

λ= R(Z − s)2(

1

n21− 1

n22) (2)

where n1 = 1; n2 = 2; R: Rydberg constant; s: screeningconstan and Z: characteristic integer which is an atomicnumber.

Through this technique, Moseley were able to discov-ered the incorrect ordering of some atoms in the periodictable and that some atoms were missing from the pe-riodic table. By plotting the square root of the x-rayfrequency versus the atomic number, a Moseley plot canbe constructed.[3]

III. EXPERIMENTAL DESIGN

For the setup of this experiment, we used TEL-X-OMETER as our x-ray sources and Geiger-Mller tubeas a detector. Scaler monitor is connected to measurethe count rate per second that is detected by the GMtube.

The first thing we did in this experiment is perform-ing and checking the alignment of the TEL-X-OMETERaccording to the instruction manual. Then we performthe photographic process by taking developing an x-rayphoto of both Maltese Cross and the hidden object inthe slide. Then we measure linear absorption by pass-ing x-rays through different thickness of aluminum andmeasure the counts per second.

For x-ray scattering, we reflect x-rays off of variouselements and directing the reflected beam through filterof various elements and record the counts per second.

2

And the last part will be the analyzing of the element’sabsorption lines to observed the Moseley’s law.

Take note that as we did not manage to complete bothlinear absorption and x-ray scattering due to technicaldifficulty, we have taken the data with the courtesy ofother researcher prior to us in order to continue our an-alyzation of the data to study the Moseley’s law.[? ]

IV. RESULT AND ANALYSIS

IV.1. Photographic Process

We managed to develop a film containing the shape ofMaltese cross and also the hidden object in the slide asshown in both of FIG. 2 and FIG. 3. The white area in-side the film is the region where the x-radiation weren’table to fall on as it can’t penetrate the Maltese crossshape and hidden object shape slides while the black re-gion is where the tracing of the x-ray formed.

FIG. 2. Picture of a Maltese cross Film

FIG. 3. Picture of a hidden object Film

IV.2. Measuring linear absorption

In Table I is the result of our measured the intensity(count per second) with different total thickness (mm)obtained by putting up different slides at different E.S.Then we calculate its logarithmic value and for slidesmore than 0.00mm thickness, we calculate the subtrac-tion between Log I with Log I0 where log I0 is the log-arithmic value of the intensity where total thickness iszero.

TABLE I. The count rates that determine the intensity ofradiation with different thickness by having different slidesused with the logarithmic value used [5]

Slide Number E.S. Total Intensity Log I LogIo/I

Thickness(mm) (cps)(±10) (±1.0)

562.033 4 0.00 1789 3.2

562.017 4 0.10 872 2.9 0.31±0.03

562.018 4 0.25 444 2.6 0.60±0.06

562.019 4 0.50 266 2.4 0.83±0.08

562.018 3 0.75 217 2.3 0.92±0.09

562.019 4

562.020 4 1.00 159 2.2 1.10±0.10

562.018 3 1.25 131 2.1 1.10±0.10

562.020 4

562.018 2 1.75 79 1.9 1.40±0.10

562.019 3

562.020 4

562.021 4 2.00 78 1.8 1.40±0.10

562.020 3 3.00 42 1.6 1.60±0.20

562.021 4

562.019 2 3.50 19 1.2 2.00±0.20

562.020 3

562.021 4

With the value of Intensity (cps), we plot the dataagainst the total thickness (mm) as shown in FIG.4.

FIG. 4. The exponential graph of intensity (cps) with thetotal thickness (mm)

0 0.5 1 1.5 2 2.5 3 3.50

200

400

600

800

1000

1200

1400

1600

1800

Thickness,t(mm)

Inte

nsity,I

(cp

s)

Intensity,I(cps) vs. Thickness,t(mm)

Gaussian Fit

From FIG.4, the exponential curve formed where:

I = I0e−µt (3)

and then we can obtain:

µ =log I0It

(4)

3

For FIG.4, we have the equation of fit as given:

f(x) = a1exp(−((x− b1c1

)2 + a2exp(−((x− b2c2

)2 (5)

Where a1= 9.278e20; b1 = -8.211; c1 = 1.282; a2 =1.778e6; b2 = -19.56; c2 = 6.783.

Then we tabulate and plot the graph of Log (I0/I) asa function of t as shown in FIG. 5. FIG.5 shows that the

FIG. 5. The graph of Log(I0/I) with the total thickness,t(mm)

graph of Log (I0/I) as a function of t with gaussian fit oftwo terms as given:

f(x) = axb + c (6)

where a = 1.556 ± 2.263, b = 0.3152 ± 0.4717, c = -0.433± 2.162. It can be observed that FIG.5 has the curveethat is more inclined to fall away at greater values ofthickness,t (mm).

Since log I0/I) is smaller than the correct exponentialvalue, then I alone must be responsible for the deviationand is larger than the theory predicts. So we can inferthat the x-radiation is becoming more penetrating as itpasses through the aluminum. This is consistent with thelaw of conservation of energy if not just one homogenouswavalength but a heterogenous mixture of wavelengthscomprises the primary x-ray beam.

Then we try to find the tenth value thickness for alu-minum. Using equation of fit (5), we can use a tenthvalue of intensity which is 1789/10 = 178.9 cps into theequation and determine the x value. We have measureour tenth value thickness for aluminum is at 0.93 ± 0.01mm. The accepted value for 30kV radiation is ablout0.9mm which we can say that our experimental value isagreeable with the accepted value.[3]

IV.3. X-Ray Scattering and Moseley’s Law

For this part, we have measured the count rates atnine different slides with eight different rotary radiator

TABLE II. The count rates for Blank slide with eight differentelement[5]

Blank slide

Rotary Radiator Atomic Counts Time(s) intensity(cps)±10

Element Weight

Vanadium 50.94 60 10 6.0

Chromium 52.00 97 10 9.7

Manganese 54.94 58 10 5.8

Iron 55.85 93 10 9.3

Nickel 58.71 77 10 7.7

Cobalt 58.93 127 9.9 12.8

Copper 63.54 56 10 5.6

Zinc 65.37 49 10 4.9

TABLE III. The count rates for Zinc Filter slide with eightdifferent elements [5]

Zinc Filter slide

Rotary Radiator Atomic Counts intensity I/I0

Element Weight (cps)±10

Vanadium 50.94 10 1.0 0.2±0.3

Chromium 52.00 20 2.0 0.2±0.5

Manganese 54.94 20 2.0 0.3±0.8

Iron 55.85 36 3.6 0.4±0.5

Nickel 58.71 22 2.2 0.3±0.4

Cobalt 58.93 34 3.4 0.3±0.6

Copper 63.54 14 1.4 0.2±0.8

Zinc 65.37 20 2.0 0.4±0.9

elements.FIG.6 to FIG.13 shows the plot of the graph with the

ratio of I/I0 against eight different elements with increas-ing atomic weight. According to Moseley’s law, we shouldhave obtained a linear increase of the ratio intensity withthe increase of atomic weight. In FIG. 6 we can see theincrease only rose from Chromium to Iron and the linear-ity of the graph is disrupted by the value of Nickel andCobalt while we would see the linear proportion backfrom Copper to Zinc.

For FIG.7, there exists two ’kink’ on the graph for Cop-per Filter Slide although there is an increase in the ratiothroughout those elements. In this figure, Vanadium-Chromium and Nickel-Cobalt are the cause of the ’kink’on the graphs.

For FIG. 8, Chromium and Iron form ’kink’ betweentwo elements while from Nickel, the ratio drops downuntil Copper and increase back for Zinc.

For FIG. 9 in Nickel Filter, Chromium and Nickel-Cobalt form ’kink’ on the graph. For other figures ofother element filters, we can see the same pattern of ’kink’which usually form by Vanadium-Chromium and Nickel-Cobalt.

4

TABLE IV. The count rates for Copper Filter slide with eightdifferent elements[5]

Copper Filter slide

Rotary Radiator Atomic Counts intensity I/I0

Element Weight (cps)±10

Vanadium 50.94 20 2.0 0.3±1.6

Chromium 52.00 14 1.4 0.1±1.0

Manganese 54.94 14 1.4 0.2±1.7

Iron 55.85 20 2.0 0.2±1.1

Nickel 58.71 28 2.8 0.4±0.8

Cobalt 58.93 36 3.6 0.3±1.3

Copper 63.54 16 1.6 0.3±1.7

Zinc 65.37 28 2.8 0.6±1.8

TABLE V. The count rates for Copper Filter slide with eightdifferent elements[5]

Zinc Filter slide

Rotary Radiator Atomic Counts intensity I/I0

Element Weight (cps)±10

Vanadium 50.94 20 2.0 0.3±1.6

Chromium 52.00 14 1.4 0.1±1.0

Manganese 54.94 14 1.4 0.2±1.7

Iron 55.85 20 2.0 0.2±1.1

Nickel 58.71 28 2.8 0.4±0.8

Cobalt 58.93 36 3.6 0.3±1.3

Copper 63.54 16 1.6 0.3±1.7

Zinc 65.37 28 2.8 0.6±1.8

FIG. 6. I/I0 versus Atomic weight for Zinc Filter slide

IV.4. Changing position between Cobalt and Nickel

Thus, we can generalize that there is something wrongfor our arrangement of the graph. As the atomic weightincreases, so the total atoms in the elements increases andthis account for the rise to an increase in the intensity of’scattered’ radiation following inelastic collision.

From Cobalt filter to Nickel filter, we can observe the

TABLE VI. The count rates for Cobalt Filter slide with eightdifferent elements[5]

Cobalt Filter slide

Rotary Radiator Atomic Counts intensity I/I0

Element Weight (cps)±10

Vanadium 50.94 24 2.4 0.4±1.6

Chromium 52.00 28 2.8 0.3±1.0

Manganese 54.94 26 2.6 0.5±1.6

Iron 55.85 36 3.6 0.4±1.0

Nickel 58.71 44 4.4 0.6±0.7

Cobalt 58.93 36 3.6 0.3±1.2

Copper 63.54 6 0.6 0.1±1.8

Zinc 65.37 10 2.8 1.0±2.0

TABLE VII. The count rates for Nickel Filter slide with eightdifferent elements[5]

Nickel Filter slide

Rotary Radiator Atomic Counts intensity I/I0

Element Weight (cps)±10

Vanadium 50.94 24 2.4 0.4±1.6

Chromium 52.00 28 2.4 0.2±1.0

Manganese 54.94 26 1.6 0.3±1.6

Iron 55.85 36 2.8 0.3±1.0

Nickel 58.71 44 3.0 0.4±0.8

Cobalt 58.93 36 3.8 0.3±1.2

Copper 63.54 6 2.2 0.4±1.7

Zinc 65.37 10 0.6 1.0±2.0

FIG. 7. I/I0versus Atomic weight for Copper Filter slide

discontinuity from Nickel to Copper element. Moseleyperceived that if we reverse the classification of Nickeland Cobalt, the experimental result can have a simpleprogression. To determine whether this is true for ourdata, we reverse that as shown in FIG.14 to FIG.16 andfor Zinc and Copper filter we could see a progressionfrom Chromium to Iron and a discontinuity from Nickelto Copper while have shown a less kink compared withinitial graph. For Cobalt filter, there is a discontinuity

5

TABLE VIII. The count rates for Vanadium Filter slide witheight different elements[5]

Vanadium Filter slide

Rotary Radiator Atomic Counts intensity I/I0

Element Weight s (cps)±10

Vanadium 50.94 24 2.4 0.4±1.6

Chromium 52.00 28 2.8 0.3±1.0

Manganese 54.94 26 2.6 0.5±1.6

Iron 55.85 36 3.6 0.4±1.0

Nickel 58.71 44 4.4 0.6±0.7

Cobalt 58.93 36 3.6 0.3±1.2

Copper 63.54 6 0.6 0.1±1.8

Zinc 65.37 10 2.8 1.0±2.0

FIG. 8. I/I0 versus Atomic weight for Cobalt Filter slide

FIG. 9. I/I0 versus Atomic weight for Nickel Filter slide

between Nickel and Copper but there still exist a kinkfrom Iron to Nickel.

Based on our graphs, we can see that the ratio of Vana-dium is always higher than Chromium and this shouldnot be true theoretically. We cannot think of any reasonother than taking account of that as the error in per-forming the experiment. Also the error bar for the ratiois quite big in relative with its value which is average inthe factor of 2 and so the resolution for our graph is notideal in observing the Moseley’s law.

So, while we still able to glimpse a little bit of linearitybetween the ratio of intensity with the atomic weight, the

FIG. 10. I/I0 versus Atomic weight for Vanadium Filter slide

FIG. 11. I/I0 versus Atomic weight for Iron Filter slide

FIG. 12. I/I0 versus Atomic weight for Manganese Filter slide

FIG. 13. I/I0 versus Atomic weight for Chromium Filter slide

graph we obtain is very vague and did not show truly theproportionality between atomic weight and the ratio of

6

FIG. 14. I/I0 versus Atomic weight for Zinc Filter slide

FIG. 15. I/I0 versus Atomic weight for Copper Filter slide

FIG. 16. I/I0 versus Atomic weight for Cobalt Filter slide

intensity.

V. ERROR ANALYSIS

In this experiment, we have a random error with ourscaler monitor and GM tube in measuring the intensity(count per second) with ±10. This error is large by afactor of 8 or 9 compare with its value. This error is thenaccount for our ratio intensity that yields a larger rangeof data that we consider to make our data points doesnot yield to Moseley’s law.

For example, Vanadium have the range of error thatis overlap with the Chromium’s value and so it may bein this account that we have failed to obtain the exactvalue of differences between those two values. Next time,we should have increasae our resolution of data and tryto account more significant figures into our data as cal-culation can reduce our data resoulution.

For linear absorption, we have curve fitting the ex-ponential curve using the function in equation (5). Byobtaining the statistical error of that curve fitting we cantake account of the error in obtaining the uncertainty ofour tenth value thickness for aluminum. We obtained thethickness in the range from 0.92 to 0.94 mm.

VI. CONCLUSION

We can conclude that we weren’t able to observedMoseley’s law by using our data. We may have observedthe differences by changing the position of Nickel andCobalt but still the data points of Vanadium does nottheoretically follow the law in our graph. The reason isin our data resolution that we have discussed in ErrorAnalysis section.

Despite all that, we were able to develop a film thatforms a good quality picture of Maltese cross and thehidden object. For linear absorption, we have measuredthe tenth value of the thickness to be (0.93 ±0.01) mmand this is considered to be agreeable with accepted valuefor aluminum which is around 0.9mm

[1] Melissinos A., “Experiments in Modern Physics” Aca-demic Press, 1966.

[2] Taylor, Zafiratos, Dubson, “Modern Physics” Pearson,Prentice Hall, NJ, 2004.

[3] Description Folder, , West Virginia University, 2012.[4] Preston, Dietz, “The Art of Experimental Physics,” John

Wiley and Sons, X-Ray section, 1991.[5] C. Kelly, ”Data points for linear absorption were taken by

courtesy of C. Kelly PHYS 341 Fall 2011.