 ## Question Number 1 Sub Section A

Calculation of Effective Specific power can be conducted in Non Destructive way using two methods, namely the empirical method and the computational method.

The Computational Method uses the standard formula

Peff = Sigma Ri * Pi

## A. Calculation of Ri

Where Ris the abundance of the i-th radio-nuclide in the material. This is expressed as a unit of massfraction. The Pi is expressed as the specific-power of the i-th radio-nuclide in the material in Watts/Gram. The determination of Ri can be carried out by using a Gamma-ray-spectroscope which is placed at a distance from the Radio-active material which is stored in a sealed container. Me multi-channel analyzer is also accompanying the spectroscopy.

The measurements are taken with the aid of a germanium-detector which has a 500 Square-millimeter active-area with 10mm thickness and resolution of 560 ev for 122 Kev Gamma-rays. The detector is operated at a gain of 0,075 KEV/Channel. The count rate is kept at 5000 counts/second. By adopting the GUNNINK data Analysis, the calculation was arrived for the determination of Ri. Here, the selected peak-areas are and selected peak-multiples with the description of fundamental-peak shapes. The entire method however is based on a simple formula which says

Ri= I1/I2 * ε2 /ε1 * p2/p1 * ta/tb

here, the elements of the formula are

I1, I2 = Gamma Ray-Intensities which are measured during the experiment.

ε1, ε2 = the efficiency levels at which the Spectroscope detects the peak values.

P1, P2= Gamma-Ray Emission probabilities.

ta/tb are the expected half-life of the isotopic elements.

We are Ignoring the ta/tb values specifically here, to accommodate the Assignment Requirement. The practical equation however includes certain parameters in addition to the Ideal Equation. The parameters are

1. There are plenty of isotopes in the material being tested apart from Plutonium 238, 242 and 241 Am.
2. If the relative abundance of plutonium is greater than 50%, it can be detected alone. Otherwise, it has to be determined along with the other isotopes with the help of an ALGORITHM based on practical readings which may vary *.
3. The intensity of peaks may overlap each other during the actual recording. because the wavelength sometimes overlap with each other under the region of 94-105 KEV.
4.  The Entire equation becomes Non-linear. because the efficiency of the measuring and reading can vary based on
1. the gamma-ray interactions with the detector
2.  The attenuation factor of the various filters and other masks. These are sued in order to mask the harmful-radioactive elements which may leak out.
3.  Self-Attenuation by Plutonium in the material