- #1

Taylor_1989

- 402

- 14

## 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?