Basal Physics of Nuclear Anesthetic Abrasion of Gamma-Rays

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 11 October 20:09   

    This is the sixth affiliate of a wikibook advantaged .

    We covered the alternation of gamma-rays with amount from a anecdotic angle in the and we saw that the Compton and Photoelectric Furnishings were the above mechanisms. We will accede the accountable afresh actuality but this time from an analytic perspective. This will acquiesce us to advance a added accepted compassionate of the phenomenon.

    Note that the analysis actuality aswell refers to the abrasion of X-rays since, as we acclaimed afore gamma-rays and X-rays are about the aforementioned concrete entities.

    Our analysis begins with a description of a simple radiation agreement which can be performed calmly in the class and which some of the aboriginal antecedents in this acreage did. We will then body on the advice acquired from such an agreement to advance a simple blueprint and some simple concepts which will acquiesce us generalise the bearings to any abrasion situation.

    The agreement is absolutely simple. It involves battlefront a attenuated axle of gamma-rays at a actual and barometer how abundant of the radiation gets through. We can alter the activity of the gamma-rays we use and the blazon of arresting actual as able-bodied as its array and density.

    The beginning start-up is illustrated in the amount below. We accredit to the acuteness of the radiation which strikes the cushion as the adventure intensity, I0, and the acuteness of the radiation which gets through the cushion as the transmitted intensity, IX. Apprehension aswell that the array of the cushion is denoted by x.

    


    From what we covered in the we can acknowledge that some of the gamma-rays will be subjected to interactions such as the Photoelectric Aftereffect and the Compton Aftereffect as they canyon through the absorber. The transmitted gamma-rays will in the capital be those which canyon through after any interactions at all.

    We can accordingly apprehend to acquisition that the transmitted acuteness will be beneath than the adventure intensity, that is

    


    But by how abundant you ability ask. Afore we accede this let us denote the aberration amid IX and I0 as ?I, that is

    


    Let us alpha exploring the consequence of ?I by agreement altered absorbers in about-face in the radiation beam. What we would acquisition is that the consequence of ?I is awful abased on the diminutive amount of the arresting material. For archetype we would acquisition that ?I would be absolutely low in the case of an cushion create from (Z=6) and actual ample in the case of (Z=82).

    We can accretion an acknowledgment of why this is so from the afterward figure:

    


    The amount illustrates a top diminutive amount cushion by the ample circles which represent alone atoms and a low diminutive amount actual by abate circles. The adventure radiation axle is represented by the arrows entering anniversary cushion from the left. Apprehension that the atoms of the top diminutive amount cushion present beyond targets for the radiation to bang and appropriately the affairs for interactions via the Photoelectric and Compton Furnishings is almost high. The abrasion should accordingly be almost large.

    In the case of the low diminutive amount cushion about the alone atoms are abate and appropriately the affairs of interactions are reduced. In additional words the radiation has a greater anticipation of getting transmitted through the cushion and the abrasion is appropriately lower than in the top diminutive amount case.

    With account to our spaceship affinity acclimated in the the diminutive amount can be anticipation of as the admeasurement of alone meteors in the meteor cloud.

    If we were to absolutely ascendancy our beginning start-up and anxiously analyse our after-effects we would acquisition that:

    


    Therefore if we were to bifold the diminutive amount of our cushion we would access the abrasion by a agency of two cubed, that is 8, if we were to amateur the diminutive amount we would access the abrasion by a agency of 27, that is three cubed, and so on.

    It is for this cause that top diminutive amount abstracts (e.g. Pb) are acclimated for radiation protection.

    A additional access to exploring the consequence of ?I is to see what happens if we change the body of the absorber. We can see from the afterward amount that a low body cushion will accord acceleration to beneath abrasion than a top body cushion back the affairs of an alternation amid the radiation and the atoms of the cushion are almost lower.

    


    So in our affinity of the spaceship entering a meteor billow anticipate of meteor clouds of altered body and the affairs of the spaceship colliding with a meteor.

    A third agency which we could alter is the array of the absorber. As you should be able to adumbrate at this date the thicker the cushion the greater the attenuation.

    Finally in our agreement we could alter the activity of the gamma-ray beam. We would acquisition after traveling into it in any abundant detail that the greater the activity of the gamma-rays the beneath the attenuation. You ability like to anticipate of it in agreement of the activity with which the spaceship approaches the meteor billow and the likelihood of a apathetic spaceship accepting through as against to a spaceship travelling with a college energy.

    We will accede a algebraic archetypal actuality which will advice us to accurate our beginning observations in added accepted terms. You will acquisition that the algebraic access adopted and the aftereffect acquired is absolutely agnate to what we encountered beforehand with . So you will not accept to clump your way through any new maths below, just a altered appliance of the aforementioned anatomy of algebraic analysis!

    Let us alpha absolutely artlessly and accept that we alter alone the array of the absorber. In additional words we use an cushion of the aforementioned actual (i.e. aforementioned diminutive number) and the aforementioned body and use gamma-rays of the aforementioned activity for the experiment. Alone the array of the cushion is changed.

    From our acumen aloft it is simple to acknowledge that the consequence of ?I should be abased on the radiation acuteness as able-bodied as the array of the absorber, that is for an infinitesimally baby change in cushion thickness:

    


    the bare assurance advertence that the acuteness is bargain by the absorber.

    Turning the arrangement in this blueprint into an equality, we can write:

    


    where the connected of proportionality, μ, is alleged the .

    Dividing beyond by I we can carbon this blueprint as:

    


    So this blueprint describes the bearings for any tiny change in cushion thickness, dx. To acquisition out what happens for the complete array of an cushion we artlessly add up what happens in anniversary baby thickness. In additional words we accommodate the aloft equation. Cogent this added formally we can say that for thicknesses from x = 0 to any additional array x, the radiation acuteness will abatement from I0 to IX, so that:

    


    


    


    


    This final announcement tells us that the radiation acuteness will abatement in an exponential appearance with the array of the cushion with the amount of abatement getting controlled by the Beeline Abrasion Coefficient. The announcement is apparent in graphical anatomy below. The blueprint plots the acuteness adjoin thickness, x. We can see that the acuteness decreases from I0, that is the amount at x = 0, in a accelerated appearance initially and then added boring in the archetypal exponential manner.

    
Graphical representation of the assurance of radiation acuteness on the array of absorber: Acuteness against array on the larboard and the accustomed logarithm of the acuteness against array on the right.


    The access of the Beeline Abrasion Accessory can be apparent in the next figure. All three curves actuality are exponential in nature, alone the Beeline Abrasion Accessory is different. Apprehension that if the Beeline Abrasion Accessory has a low amount the ambit decreases almost boring and if the Beeline Abrasion Accessory is ample the ambit decreases actual quickly.

    


    Exponential abrasion bidding using a small, average and ample amount of the Beeline Abrasion Coefficient, .


    The Beeline Abrasion Accessory is appropriate of alone arresting materials. Some like carbon accept a baby amount and are calmly penetrated by gamma-rays. Additional abstracts such as advance accept a almost ample Beeline Abrasion Accessory and are almost acceptable absorbers of radiation:

    


    Linear Abrasion Coefficients (in cm-1) for a ambit of abstracts at gamma-ray energies of 100, 200 and 500 keV.


    The abstracts listed in the table aloft are air, baptize and a ambit of elements from carbon (Z=6) through to advance (Z=82) and their Beeline Abrasion Coefficients are accustomed for three gamma-ray energies. The first point to agenda is that the Beeline Abrasion Accessory increases as the diminutive amount of the cushion increases. For archetype it increases from a actual baby amount of 0.000195 cm-1 for air at 100 keV to about 60 cm-1 for lead. The additional point to agenda is that the Beeline Abrasion Accessory for all abstracts decreases with the activity of the gamma-rays. For archetype the amount for chestnut decreases from about 3.8 cm-1 at 100 keV to 0.73 cm-1 at 500 keV. The third point to agenda is that the trends in the table are constant with the assay presented earlier.

    Finally it is important to acknowledge that our assay aloft is alone carefully true if we are ambidextrous with attenuated radiation beams. Additional factors charge to be taken into annual if ample radiation beams are involved.

    As with using the Bisected Activity to call the an indicator is usually acquired from the exponential abrasion blueprint aloft which helps us anticipate added acutely about what is traveling on. This indicator is alleged the Bisected Amount Band and it expresses the array of arresting actual which is bare to abate the adventure radiation acuteness by a agency of two. From a graphical point of appearance we can say that when:

    


    the array of cushion is the Bisected Amount Layer:

    


    The Bisected Amount Band for a ambit of absorbers is listed in the afterward table for three gamma-ray energies:

    


    Half Amount Layers (in cm) for a ambit of abstracts at gamma-ray energies of 100, 200 and 500 keV.


    The first point to agenda is that the Bisected Amount Band decreases as the diminutive amount increases. For archetype the amount for air at 100 keV is about 35 meters and it decreases to just 0.12 mm for advance at this energy. In additional words 35 m of air is bare to abate the acuteness of a 100 keV gamma-ray axle by a agency of two admitting just 0.12 mm of advance can do the aforementioned thing. The additional affair to agenda is that the Bisected Amount Band increases with accretion gamma-ray energy. For archetype from 0.18 cm for chestnut at 100 keV to about 1 cm at 500 keV. Thirdly agenda that about to the data in the antecedent table there is a alternate accord amid the Bisected Amount Band and the Beeline Abrasion Coefficient, which we will now investigate.

    As was the case with the Radioactive Adulteration Law, area we explored the accord amid the Bisected Activity and the Adulteration Constant, a accord can be acquired amid the Bisected Amount Band and the Beeline Abrasion Coefficient. We can do this by using the analogue of the Bisected Amount Layer:

    


    when

    


    and inserting it in the exponential abrasion equation, that is:

    


    to give

    


    Therefore

    


    


    


    


    


    


    and

    


    These endure two equations accurate the accord amid the Beeline Abrasion Accessory and the Bisected Amount Layer. They are actual advantageous as you will see if analytic after questions apropos to abrasion and frequently anatomy the first move in analytic a after problem.

    We adumbrated aloft that the Beeline Abrasion Accessory was advantageous if we were because an arresting actual of the aforementioned body but of altered thicknesses. A accompanying accessory can be of amount if we ambition to cover the density, ρ, of the cushion in our analysis. This is the Accumulation Abrasion Accessory which is authentic as the:

    


    The altitude assemblage acclimated for the Beeline Abrasion Accessory in the table aloft is cm-1, and a accepted assemblage of body is the g cm-3. You ability like to acquire for yourself on this base that the cm2 g-1 is the agnate assemblage of the Accumulation Abrasion Coefficient.

    Two questions are accustomed beneath to advice you advance your compassionate of the actual presented in this chapter. The first one is almost aboveboard and will exercise your appliance of the exponential abrasion equation. The additional catechism is a lot added arduous and will advice you chronicle exponential abrasion to radioactivity and radiation exposure.

    Question 1

    How abundant aluminium is appropriate to abate the acuteness of a 200 keV gamma-ray axle to 10% of its adventure intensity? Accept that the Bisected Amount Band for 200 keV gamma-rays in Al is 2.14 cm.

    Answer

    The catechism phrased in agreement of the symbols acclimated aloft is:

    
             ,     when x = ?


    We are told that the Bisected Amount Band is 2.14 cm. Accordingly the Beeline Abrasion Accessory is

    


    Now accumulation all this with the exponential abrasion equation:

    


    we can write:

    


    Therefore

    


    


    


    


    So the array of aluminium appropriate to abate these gamma-rays by a agency of ten is about 7 cm. This almost ample array is the cause why aluminium is not about acclimated in radiation aegis - its diminutive amount is not top abundant for able and cogent abrasion of gamma-rays.

    You ability like to try this catechism for the case if Pb is the cushion - but you will charge to acquisition out the Bisected Amount Band for the 200 keV gamma-rays yourself!

    Heres a adumbration though: accept a attending at one of the tables above.

    And heres the acknowledgment for you to analysis if youve finished: 2.2 mm.

    In additional words a almost attenuate array of Pb is appropriate to do the aforementioned job as 7 cm of aluminium.

    Question 2

    A 105 MBq antecedent of 137Cs is to be independent in a Pb box so that the acknowledgment amount 1 m abroad from the antecedent is beneath than 0.5 mR/hour. If the Bisected Amount Band for 137Cs gamma-rays in Pb is 0.6 cm, what array of Pb is required? The Specific Gamma Ray Connected for 137Cs is 3.3 R hr-1 mCi-1 at 1 cm.

    Answer

    This is a adequately archetypal catechism which arises if anyone is using radioactive materials. We ambition to use a assertive abundance of the actual and we ambition to abundance it in a advance alembic so that the acknowledgment amount if we are alive a assertive ambit abroad is beneath some akin for assurance reasons. We understand the radioactivity of the actual we will be using. But its quoted in SI units. We attending up a advertence book to acquisition out the acknowledgment amount for this radioisotope and acquisition that the Specific Gamma Ray Connected is quoted in acceptable units. Just as in our question!

    So let us alpha by accepting our units right. The Specific Gamma Ray Connected is accustomed as:

    
3.3 R hr-1 mCi-1 at 1 cm from the source.


    This is according to:

    
3300 mR hr-1 mCi-1 at 1 cm from the source,


    which is according to:

    
mR hr-1 mCi-1 at 1 m from the source,


    on the base of the Changed Aboveboard Law. This aftereffect bidding per becquerel is

    
mR hr-1 Bq-1 at 1 m from the source,


    since 1 mCi = 3.7 x 107 Bq. And accordingly for 105 MBq, the acknowledgment amount is:

    
mR hr-1 (105MBq)-1 at 1 m from the source,

    


    That is the acknowledgment amount 1 beat from our antecedent is 891.9 mR hr-1.

    We ambition to abate this acknowledgment amount according to the catechism to beneath than 0.5 mR hr-1 using Pb.

    You should be able at this date to use the exponential abrasion blueprint forth with the Bisected Amount Band for these gamma-rays in Pb to account that the array of Pb appropriate is about 6.5 cm.

    Click [http://homepage.mac.com/kieranmaher/nmBookSupport/attenuation.html HERE] to admission an online MCQ accoutrement the actual in this chapter.

    [[Category:Physics]]

    [[Category:Health]]

 


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