This is an example question which I have the answer to but can not seem to get the same answer through my workings, any help with the equation would be great.
A particular task exposes the operator to alpha radiation at an average dose of 200 ìGy each time the task is performed. If the company needs the task performed once per day over a 250-day working year and the maximum occupational dose limit is 20mSv per year, how many staff does the company need to assign to the task?
To solve this problem, we need to find the total dose of alpha radiation that will be received by all the staff over the 250-day working year, and then determine how many staff members can be assigned while still staying below the maximum occupational dose limit of 20 mSv per year.
Let's break down the problem step by step:
Step 1: Calculate the total dose per year
We know that each time the task is performed, the operator receives an average dose of 200 μGy (microgray). Since the task is performed once per day over a 250-day working year, the total dose per year can be calculated as follows:
Total dose per year = Dose per task × Number of tasks per year
= 200 μGy × 250
= 50,000 μGy
Step 2: Convert the total dose to milligrays (mGy)
The maximum occupational dose limit is given in milligrays (mGy), so we need to convert the total dose from microgray (μGy) to milligrays (mGy). There are 1,000 micrograys in a milligray, so we can divide the total dose by 1,000:
Total dose per year in mGy = 50,000 μGy ÷ 1,000
= 50 mGy
Step 3: Determine the number of staff members
To find out how many staff members can be assigned to the task, we divide the maximum occupational dose limit of 20 mSv (millisievert) per year by the total dose per year in milligrays:
Number of staff members = Maximum occupational dose limit per year ÷ Total dose per year in mGy
= 20 mSv ÷ 50 mGy
= 20,000 μSv ÷ 50,000 μGy
= 0.4
Since we cannot have a fraction of a staff member, we would need to round this number up to the nearest whole number. Therefore, the company needs to assign at least 1 staff member to the task in order to stay below the maximum occupational dose limit.
So, the company would need to assign at least 1 staff member to the task.