Nuclear Chemistry: Kinetics of Radioactive Decay and Radioactive Dating

[redpanda320]

Homework Statement

A laboratory rat is exposed to an alpha-radiation source whose activity is 11.3 mCi. What is the activity of the radiation in disintegrations per second? in becquerels? The rat has a mass
of 315 grams and is exposed to the radiation for 12.3 seconds, absorbing 39% of the emitted alpha particles, each having an energy of 9.10X10^-13 Jeules. Calculate the absorbed does in millirads and grays. If the RBE of the radiation is 9.5, calculate the effective absorbed dose in mrem and Sv.
Activity of the radiation in disintegrations per second= 4.2X10^8 dis/s
Activity of the radiation in becquerels= 4.2X10^8 Bq

Homework Equations

ln (N_t/N₀)= -kt
k= 0.693/t_1/2
E=mc²

The Attempt at a Solution

I started answering the question by converting the given amount of mCi to Ci.
Then converting that amount into dis/s and then into Bq.

After that, I was not exactly sure how to approach part B. A push in the right direction would help

 

[redpanda320]

can anyone at least tell me a method or something for how to figure out how to calculate the absorbed dose in grays?

 

[Blueshift5]

me out a lot.

I would like to clarify that the given information does not provide enough details to accurately solve the problem. The first step would be to determine the half-life of the alpha-radiation source, as it is needed to calculate the activity. Once the half-life is known, the activity can be calculated using the given formula k= 0.693/t1/2.

As for part B, it is important to note that the absorbed dose is a measure of energy deposited in a material and is different from the activity of the radiation. It is calculated using the formula D= E/m, where E is the energy deposited and m is the mass of the material. In this case, the energy deposited can be calculated by multiplying the number of absorbed alpha particles (39% of the emitted particles) by their individual energy (9.10X10^-13 Jeules).

To calculate the absorbed dose in millirads, the energy deposited (in Joules) needs to be converted to rads using the conversion factor 1 rad= 0.01 J/kg. Similarly, to calculate the absorbed dose in grays, the energy deposited needs to be converted to Gy using the conversion factor 1 Gy= 1 J/kg.

To calculate the effective absorbed dose in mrem and Sv, the absorbed dose needs to be multiplied by the radiation weighting factor (RBE) of 9.5. The RBE takes into account the different biological effects of different types of radiation. Finally, to convert the absorbed dose from rads to rem, and from Gy to Sv, the conversion factors 1 rem= 0.01 Sv and 1 Gy= 1 Sv need to be used.

Overall, it is important to have all the necessary information and units correct in order to accurately solve the problem. If any information is missing or incorrect, it can greatly affect the final results.