Finding Sphere Diameter for Radiation Equilibrium?

[kmoh111]

Homework Statement

This problem comes from Frank Attix's book Intro to Radiological Physics and Rad Dosimetry.
From ch. 4 - problem #1:

Approximately what diameter for a sphere of water would be required to approach radiation equilibrium wihin 1% at its center, assuming it contains a uniform dilute solution of 60Cobalt (1.25 MeV gamma rays). Use u(en) and u as approximations to the effective gamma ray attenuation coefficient; this will over- and under-estimate the size respectively.

Homework Equations

u - is the attenuation coefficient for primary photons only
u(en) - is the effective attenuation coefficient for ideal broad beam attenuation


Attix gives the solutions as 312 cm and 144 cm

The Attempt at a Solution

I come close to one of the answers but I'm not sure how u and u(en) come into play here.

(4/3) pi r^3 = .01(1.25MeV).

This gives r = .144

 

[kmoh111]

This thread can be disregarded. I was able to solve the problem.

The solution to this problem is to use exponential attenuation:

N = N(0) exp(-uL). The approach is to solve for L for given u and u(en) values when 99% of the photons are allowed to pass thru the sphere.

 

[andelson]

This thread can be disregarded. I was able to solve the problem.

The solution to this problem is to use exponential attenuation:

N = N(0) exp(-uL). The approach is to solve for L for given u and u(en) values when 99% of the photons are allowed to pass thru the sphere.

hi..one of my classmates has asked about this problem too, i was thinking of this solution too, but i can't find the real values for u(en) and u...

i would like to ask, where can i find those values, i keep searching the net but gave me none... hope you would help us.

thanks :)

andy from philippines

God bless

 

[kmoh111]

You can find mass attenuation coefficients at:
http://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html

 

[andelson]

thank you so much kmoh111

God bless :)

 

[andelson]

hi me again :(

ive tried to solve the problem using exponential attenuation but i always got a different answer...however i tried to use equation 3.14 (build up factor) in attix book... where B is approximately equal to 1.06... here's how it went..

0.99 = (1.06) exp(-uL) and 0.99 = (1.06) exp(u(en)L)

i used u = 0.46903 and u(en)= 0.216626 (this is base from the link that you've given me before)

but i got, L = 0.145 cm and L = 0.313 cm :( Attix gives the solutions as 312 cm and 144 cm



did i lack something in my equation? :(

pls help us...any comments will be very much appreciated

million thanks..


andy :(