What is the Absorbed Dose of Radiation for Ingested Radioactive Material?

  • Thread starter Red88
  • Start date
  • Tags
    Radiation
In summary, the problem involves calculating the total dose given to a 50kg body after ingesting a microgram of radioactive material with an initial activity of 10^5/sec and a physical lifetime of 4 hours, assuming all energy from alpha particle emissions is deposited throughout the tissue. With a body lifetime of 12 hours and a month's time (720 hours), the total dose is estimated to be 7.75 x 10^-5 J/kg. However, a more accurate approach would involve integration and results in a total dose of approximately 1.04 x 10^-6 J/kg.
  • #1
Red88
8
0

Homework Statement



Suppose you ingest a microgram radioactive material with an initial activity of 10^5/sec and a physical lifetime of 4 hours. Suppose also that all of the energy of each emission of alpha particles with energy of 0.3MeV per particle is deposited throughout your tissue. If you eliminate the material, making a body lifetime of 12 hours, what will be the total dose given to your body, of mass 50kg, after a month?

Homework Equations



According to my professor,

Activity = (No/T)exp(-t/T) where T is the lifetime of the substance

With both a physical half-life, tp, and a body or metabolic half-life, tm,
N = No(1/2)^(t(1/tp + 1/tm))
Dose = J/kg

1 eV = 1.602 x 10^-19 J


The Attempt at a Solution



10^5 dis/s X 2419200s (in a month) X (4hrs/12hrs) X (4.806 x 10^-14J)/(dis) X (1/50kg)
=> Dose = 7.75 x 10^-5 J/kg


Please respond ASAP - the homework is due tomorrow! I'll appreciate any help...

Regards,

Red88
 
Physics news on Phys.org
  • #2
I'm just finding this problem now, so I suppose it may be too late. It seems to me that an integration is required, since you need to know the total number of decays that are released within your body in the course of the month. The combination of radioactive decay and physical elimination gives a lifetime of

1/(LT) = 1/4 + 1/12 = 1/3 ,

so the effective lifetime is 3 hours. The total number of decays within your body would then be

(10^5)·[exp -(t/3)] per second, with t in hours, or

(3.6·10^8)·[exp -(t/3)] per hour. Integrating this over the 720 hours in a month would give

-(1/[1/3])·(3.6·10^8)·[exp -(t/3)] , evaluated from t = 0 to t = 720 hours, or

-(1.08·10^9)·[exp -(720/3)] - { -(1.08·10^9)·[exp -(0/3)] } , which is essentially

(1.08·10^9) · 1 , since exp -(720/3) is really tiny.

The isotope is pretty much "gone" within the first 36 hours, since exp(-12) is about 6·10^-6 , so the activity would be less than 1/sec by then.

With an exposure of 1.08·10^9 decays, the energy release is (1.08·10^9)·(4.806 x 10^-14 J) = 5.19·10^-5 J , or a dosage of 5.19·10^-5 J / 50 kg = 1.04·10^-6 J/kg .

We're in the same neighborhood, so I suspect you are given an approximate formula for making this calculation. What did they say the answer was?
 
  • #3
Alas we haven't been provided with a solution to the problem yet...your procedure seems more concise than mine so I hope that this is indeed the solution to this problem. Thanks for your help!
 

What is absorbed dose of radiation?

The absorbed dose of radiation is a measure of the amount of energy deposited by radiation in a specific material. It is typically measured in units of gray (Gy) or rad.

How is absorbed dose of radiation different from exposure?

Absorbed dose refers to the amount of energy actually absorbed by a material, while exposure is a measure of the amount of radiation present in a particular area. Absorbed dose takes into account factors such as the type of radiation and the material it is passing through, while exposure does not.

What factors can affect the absorbed dose of radiation?

The absorbed dose of radiation can be affected by the type of radiation, the energy of the radiation, the distance from the source, and the shielding materials present. It can also be influenced by biological factors such as the size of the exposed area and the type of tissue being exposed.

How is absorbed dose of radiation measured?

Absorbed dose is typically measured using a dosimeter, which is a device that can detect and measure the amount of radiation that is absorbed by a material. Different types of dosimeters may use different methods, such as chemical reactions or electronic devices, to measure absorbed dose.

What are the potential health effects of exposure to high levels of absorbed dose of radiation?

Exposure to high levels of absorbed dose of radiation can cause damage to cells and tissues, which can lead to various health effects such as radiation sickness, acute radiation syndrome, and an increased risk of developing cancer. The severity of these effects depends on the amount of absorbed dose and the type of radiation.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
728
  • Introductory Physics Homework Help
Replies
2
Views
816
  • High Energy, Nuclear, Particle Physics
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
5K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
8K
  • Advanced Physics Homework Help
Replies
3
Views
3K
  • High Energy, Nuclear, Particle Physics
Replies
2
Views
4K
Back
Top