# How to calculate the uncertainity errors

do any one explain me pl. i would like to know the uncertainty error in measuring the specific activity of the primordial radionuclides

Hi there.
I would like to ask you about your grasp of computing uncertainties in general. Are these experimental data points that you are using?

mfb
Mentor
It is impossible to answer anything specific with a question as vague as that.

we have meausred the primordial radionuclides in the sediments using NaI gamma ray detector. we measured the counts of the radionucldies and the activity of the radionuclides such as U, Th and K. we would be adding some uncertainity errors along with the specific activity with + and - sign. i would like to know the uncertainity formula in calculating it.

gleem
The uncertainty of the measured activity of a radionuclide is a combination of many uncertainties. As you a probably aware there is an intrinsic uncertainty associated with determining the activity of a radionuclide which is related to the number of events recorded in a given time ( i.e. the uncertainty in N counts is N½. However this is just the lower limit of the total uncertainty of the measurement if you have perfect knowledge of all the factors that affect the measurement. The other uncertainties are related to the imprecision of your knowledge of the experimental parameters of your equipment for which you must correct and each will have an associated uncertainty.

All radiation that passes through your detector may not be recorded as an event so you have an efficiency factor that needs determination.

You will only detect events that enter the detector i.e., only a certain fraction of the total disintegrations of the source will enter the detector. This is a geometric factor

You will have superimposed on your data "false" events from other radiation sources for which you must correct. This is the background correction.

You will have events from your source that should not have been detected but were scattered back into your detector that needs to be assessed and corrected for if necessary.

Depending on the nature of the radiation you may need to correct for absorption of the radiation by the source itself.

For high count rates you may need depending on the detector to correct for a period of time in which the detector is not responsive to other events i.e. dead time correction.

Depending on the detector system there may be other corrections so one must totally understand the detector system.

Accurate activity measurements can be very challenging. All the correction will have uncertainties associated with them.

Thus the total uncertainty σ is related to the other uncertainties by σ2 = Number of counts + ∑σi2 where σi's are the uncertainties of all the detector correction factors.

You can simplify the measurement process a great deal if you have a standard calibrated source of the same radionuclide as you are studying. You may be able to combine the above uncertainties into one number equal to that of the standard source provided your source and the standard source are physically equivalent and the background conditions remain the same.

thank you, i had understood the concept behind it. i whole heartedly thank you as i would derive the equation with the uncertainity errors. including the activity, background counts and the time interval for each count.

further on as Th-232 has to be estimated from the soil/sediments. as it is not a gamma ray emitter, the daughter product of Tl-208 is considered. how safe is this approximation, since Tl-208 is of third branch of the decay series, do we need to multiply the amounts by 3. or the counts directly gives the acitivity of the Th-232.

further i have been working on environmental radiation, to estimate the amounts. as per the Bharathidasan Univesity , we need some reviwers who could evaluate the thesis and send back the report. i request to the persons who are willing to do me a a favour regarding this.

whether poissons's distribution give the exact value of the errors associated at same instant of time.

gleem
further on as Th-232 has to be estimated from the soil/sediments. as it is not a gamma ray emitter, the daughter product of Tl-208

Th-232 → α + Ra-228 → β- +Ac-228 → β- + Th-228

Ac-228 has a reasonable gamma to measure

do we need to multiply the amounts by 3. or the counts directly gives the acitivity of the Th-232.

No. For a decays series in which the parent has a very long half life or small decay constant (λ) the the activity of the parent is related to that of any daughter (n) by the relation

See any modern physics text.

whether poissons's distribution give the exact value of the errors associated at same instant of time.

The Poisson distribution give the uncertainty (standard deviation) for the measured number of events (n) recorded as n½. The error in the event rate (r) is given by

σ(r) = (r/t)½ = n½/t

where t is the counting time

Remember that the activity = r⋅correction factors

thank you