An industrial worker accidentally inhaled a radioisotope with an activity of 0.200 kBq. The substance swallowed has a very long effective half-life and therefore the activity will not change significantly during the worker’s lifetime. Every decay of the isotope releases 1.12 x 10-14 J of energy into the body and the radioisotope is not eliminated from the body.
Determine the amount of energy absorbed in one year by the worker from this substance.
To determine the amount of energy absorbed in one year by the worker from this substance, we need to calculate the total number of decays that will occur in one year and multiply it by the energy released in each decay.
Here's how you can calculate it:
1. Determine the number of decays in one year:
- One decay releases 1.12 x 10^(-14) J of energy.
- The activity of the substance is given as 0.200 kBq. Recall that 1 Bq (Becquerel) is equal to 1 decay per second.
- Since 1 year has 365 days, we can calculate the number of decays in one year using the following formula:
Number of decays in one year = Activity (in Bq) x 365 days x 24 hours x 60 minutes x 60 seconds
2. Calculate the amount of energy absorbed in one year:
- Multiply the number of decays in one year by the energy released in each decay:
Energy absorbed in one year = Number of decays in one year x Energy released per decay
Let's substitute the given values and calculate the answer step-by-step.
Activity = 0.200 kBq = 0.200 x 10^3 Bq
Number of decays in one year = (0.200 x 10^3 Bq) x (365 days/year) x (24 hours/day) x (60 minutes/hour) x (60 seconds/minute)
Energy absorbed in one year = Number of decays in one year x (1.12 x 10^(-14) J/decay)
Now, you can calculate the final answer using these formulas and the given values.