Radation Dosage word problem

[Taylor_1989]

Homework Statement

A friend tells you that she is planning to change her life by moving from the UK to the Brazilian resort of Guarapari, where she intends to make and sell food on the beach for the tourists for 8 hours a day, every day. Whilst pleased for her adventurous plan, you are a little concerned by your specialist knowledge that the radiation dose rate on the beach there is typically 14 μSv h$^{-1}$, due to exceptionally high natural background from the local sand and soil. However, the average background dose in town of 2.7 mSv year$^{-1}$ is the same as the UK. Use the above information to estimate the background dose she might expect from living and working there in order to decide which of following options for cautionary advice you would give to her.

select 1
a. Your background dose will increase by a factor of 45
b. Your background dose will double
c. Your background dose will be more than double the dose limit in the UK for a person who works with radiation
d. Your background dose will increase by a factor of 10
e. Your background dose will exceed the dose limit in the UK for a person who works with radiation.

Homework Equations

N/A

The Attempt at a Solution

I would like to know if I have followed the correct logic is answering this question?

The key points I took from the word problem are as followed

1. She is on the beach for 8hrs
2. she works 7 days a week
3. Time she is not on the beach is: 24-8=16hrs
4. Dosage per year when not on beach and in town is 2.7mSv per year

So my steps are a follows
Radiation exposure per hour when not on the beach
$$\frac{2.7\cdot 10^{-3}Sv}{1y}\cdot \frac{1y}{365d}=\frac{7.4\cdot10^{-6}Sv}{d}$$
$$\frac{7.4\cdot10^{-6}Sv}{d}\cdot \frac{1d}{24hr}=\frac{3.08\cdot 10^{-7}Sv}{hr}$$

working hours spent on beach per year
$$8 \cdot 365 = 2920hr $$

hours spent of beach per year
$$16 \cdot 365 = 5840 hr$$

Radiation exposure per year on beach
$$\frac{14 \cdot 10^{-6}}{hr} \cdot 2920hr= 0.04Sv$$

Radiation exposure per year off beach
$$\frac{3.08\cdot 10^{-7}sV}{hr} \cdot 5840hr =1.8\cdot 10^{-3}Sv$$ (rounded)

Total exposure
$$T=0.0418Sv$$

Now as radiation exposure in the Uk is $0.02Sv$ my ans is e)

Have I calculated this correctly?

 

[mfb]

Have I calculated this correctly?

Yes.

As this is a multiple choice question it doesn't matter here, but in general be careful how you round where. You rounded the beach exposure to 0.04 Sv and added 0.0018 Sv. The first number with more digits is actually 0.0409 Sv - if you add the two you get 0.0427, not 0.0418. If you want to have more than one significant digit for the sum, don't round the larger number to one digit.

 

[haruspex]

my ans is e)

Is that based on some info re UK dose limits that you have not included in your post?
Or did you mean option b?

 

[Taylor_1989]

Is that based on some info re UK dose limits that you have not included in your post?
Or did you mean option b?

The dosage is one I have read from the UK, with the number that mfb mentioned my ans should be c) as it is more than double the reccomended dosage. I was told to look up dosage or occupational worker in the Uk for this type of question and the general dosage eemed to be 20mSv or 0.02Sv

 

[haruspex]

The dosage is one I have read from the UK, with the number that mfb mentioned my ans should be c) as it is more than double the reccomended dosage. I was told to look up dosage or occupational worker in the Uk for this type of question and the general dosage eemed to be 20mSv or 0.02Sv

Ok.