formula for calculating dose rate for a solution

[neveragain]

Hi everybody!

Can't find a formula for calculating dose rate from the solution with the known mass of isotope dissolved in the solution.
Anybody knows it or can advise on where to find?

Thanks in advance!!

[SloGlo]

itts in here
http://www.nukeworker.com/study/hp/moe/index.shtml

[RAD-GHOST]

Sorry, that equation does not exist!

You could formulate that equation, but the variable would be almost endless.

RG........... !

[YO!]

                           
                               
Rate {(in solution (rad/hr)}= [(2.12 )(average energy in Mev.)(the concentration in microcuries / cm³)] / the density of the solution in gram /cm³

[RAD-GHOST]

YO, Thanks for the IM, but...........

What are the summations for your answer?  This equation is going to give what dose, at what distance, based on what parameters, restrictions and assumptions?  (Assumptions are Allowed, It's your Time to Shine)

Is this equation applicable to Alpha, Beta, Gamma and Neutron Emitters?

RG..

[bsdnuke]

Group:

The formula that was provided was for self absorption dose.  It is the root equation that was used traditionally for calculating internal dose from intakes of radioactive material.  If you are looking for external dose rate then the radioactivity of the solution (i.e., total activity) should be determined (concentration times volume) and then use an equation like 6*C*En for exposure rate at one foot (assumes that point source geometry is appropriate).  If the volume is large, then other equations that approximate the exposure rate would be appropriate.  Another approach is to use a code like Microshield.

Regards,

bsd

[Khak-Hater]

What's your application?  Are you trying to characterize it?  If you're just looking at characterizing a sample vial of the solution, then measure it at a distance of at least seven times the maximum dimension of either the source or detector [whichever's larger] and approximate it as a point source. 

No matter what your application KENO or MCNP would be the most accurate method to calculate it, but MicroShield would be your best bet [more user friendly], or if you don't have any of these applications, you could solve it analytically using the same point-kernal approximation method that MicroShield uses (e.g., in an excel spreadsheet).  All that MicroShield does is evenly divide the source activity into multiple point sources [distributed at uniform intervals throughout the source geometry], then calculate the shielding thickness and distance to the receptor points from each point source, then analytically solve each point source dose at the receptor point and sum each of these doses [an easy thing for a computer program to do]. 

If you want to do this manually [instead of using MicroShield], there's a pretty cool Excel overlay program called Crystal Ball that makes this a very easy process plus it provides uncertainty calculation capabilities [the software's primary function].  An added bonus of the Crystal Ball application is that you don't have to assume uniform source or shielding distribution [in a solution, you're probably pretty uniform anyway, but it's useful for looking at the effect of any potential stratification or clumping]. 

The weakness with any of these analytical approximations is with the associated buildup approximation for scatter gammas, which can be significantly off for certain geometries (e.g., very close to the source, shine situations, etc).  In these cases MCNP or Keno are much more accurate [keeping in mind that any monte carlo method itself is only a randomized numerical approximation]. 

Good luck,

mgm

[YO!]

YO, Thanks for the IM, but...........

What are the summations for your answer?  This equation is going to give what dose, at what distance, based on what parameters, restrictions and assumptions?  (Assumptions are Allowed, It's your Time to Shine)

Is this equation applicable to Alpha, Beta, Gamma and Neutron Emitters?

RG..

You asked for dose rate in a solution. This equation is for all of the above. The indication is that the dose rate is about one-half the calculated value at the surface of the solution.

I am not sure of what degree of accuracy you are looking for but the formula should help. The calculation can be found in THE HEALTH PHYSICS AND RADIOLOGICAL HEALTH HAND BOOK By Bernard Shleian (sp), Lester A. Slaback and ............ Maybe this will help with your search.

As far a the information about MCNP...........MCNP and Scale are the languages used to develop input models in the xyz quadrants. Most Engineers use one or the other, rarely both. I had to learn both. The input is then ran against Keno, Monte Carlo, Bonami, Fortran and etc. for an out put. An input for Nuclear Criticality Safety will give you a k_eff. based on the chemical composition of the solution, the type of container, and other parameters. Radiation Transport will give you an energy output based on element and type of shielding. These are compared to the Benchmarks to verify adequacy. The may be beyond the scope of your search.

if this will help I have it as a pdf........ it is very detailed


Radioprotection 2002
Vol. 37, no 2, pages 149 à 160
DOI: IO.105l/radiopro:2002004
Article
Determination of the gamma-ray effective
dose from different cylindrical radioactive
solution sources in a biological tissue by
using Monte Carlo calculations
M.A. MISDAQ’, A. MERZOUKI’
(Munuscript recriivrl27 March 2001, Accrpted 9 Februugl2002)
A new method was developed based on calculating the ahsorption coefficients, selfabsorption
coefficients and transmission coefîlcients of the gamma-photons emitted
by different radioisotopes for evaluating gamma dose equivalent rates, at 1 meter
from varions cylindrical radioactive solution sources utilized in medicine, in a
biological tissue. Resnlts obtained were compared with data given in literatnre. The
influence of the radioisotope half-life and gamma-photon energy and number of
photons per disintegration on the gamma dose equivalent rate, effective dose and
threshold initial activity of the considered solution sources was studied.

I use to do put a lot of effort into knowing as much as possible about all of this stuff, but I don't any more. I find that the more I learn or know, the more difficult life is for me in the work place. You know......as a female, it's OK to be attractive or smart but not both.

I just wanted to let you know that the equations are out there. It depends on where you look and how precise you need the answer to be!

Good Luck!!!

YO!

[RAD-GHOST]

Humm...

Now that I've read all the supporting technical documentation and it's been explained from those perspectives........

Sorry, that equation does not exist!

You could formulate that equation, but the variable would be almost endless!

Have A Great Day...RG!

[Khak-Hater]

RG,

Yes, your answer was correct and very succinct, but not overly useful for solving whatever problem for which fan_of_hormesis needed the formula.  I figured that there was some problem behind asking the question, so I threw out some ideas that they might use to solve it.  I apologize for my rambling answer to a very simple question.  I guess that the most succinct answer the question asked would be "No," but, once again, this wouldn't be overly useful.  By the way, I'm neither attractive nor smart.

Lots of love,

mgm

[RAD-GHOST]

In my opinion the follow up information was Excellent and Accurate, but I'm thinking that the individual was looking for an answer from a fundamental perspective.  If he had knowledge and access to those programs and modeling codes, he probably wouldn't have asked the question.  From what I've read of the feedback so far, each suggested solution is validated by a controlled set of parameters and variable.  I also have to agree that my answer probably wasn't the most informative, but it was accurate. 

How about a more fundamental perspective for deriving an equation?

What would the variables be?

Isotope(s) Activity
Decay Mode
Solution Density
Solution Volume
Container Geometry
Container Composition
 
and........


Later, RG!

[SloGlo]

If you are looking for external dose rate then the radioactivity of the solution (i.e., total activity) should be determined (concentration times volume) and then use an equation like 6*C*En for exposure rate at one foot (assumes that point source geometry is appropriate). 

knot arguing here.  just thinking that the second step after getting total activity wood be to find measurements of volume to figger out witch of the dose rate formulae is applicable.... plane, line, or point source.  because iffen it's a large volume (storage tank) yer gonna be using all three formula for applicable zoning of the dose rate.

[doctorbill]

There is no simple formula.  This is highly dependent on the geometry of the container and the dose point.  The best way to assess this is with a program such as Microshield.  You have to know the isotope activity concentrations, the density of the solution, and the composition of any external shielding, such as the container. 

If you do not have this software available, the best approach is to:

1.  Approximate the actual geometry with a simple geometry.  A rectangular solid with the length and volume of the actual container usually works best.

2.  Divide this rectangular solid into a grid of point sources.  For example, if you use 4 point sources, each point source would have 1/4 of the total activity for each isotope. 

3.  Calculate the dose rate at the dose point for each point source, accounting for the shielding of the solution, any external shielding, and air attenuation.  The latter can usually be neglected, unless you're dealing with low energy radiation or the dose point is a long distance from the container.