Question

Radiation exposure to human beings is usually given in rems (radiation equivalent for man). In SI units, the exposure is measured in sieverts (Sv). One rem equals \(0.0100 \mathrm{~Sv}\). At one time, the exposure due to the nuclear reactors in Japan was measured to be \(8217 \mathrm{mSv} / \mathrm{h}\). How many rems would a person exposed to the radiation for 35 min have absorbed? If one mammogram gives off 0.30 rems, how many mammograms would that exposure be equivalent to?

Short answer

Question: A person is exposed to a radiation source that emits 8217 mSv/h for 35 minutes. Calculate the radiation exposure in rems the person would absorb and determine the equivalent number of mammograms for that exposure, given that one mammogram gives off 0.30 rems of radiation. Answer: After being exposed to radiation for 35 minutes, the person would have absorbed an equivalent radiation of \(\frac{7 \times 8217}{120}\) rems, which is equal to \(\frac{7 \times 8217}{36}\) mammograms.

Step-by-step solution

Convert mSv/h to rems/h

We are given the conversion factor for rems and sieverts: 1 rem equals 0.0100 Sv. Since we have our exposure measurement in mSv/h, we'll first convert it to Sv/h by dividing by 1000. Then, we'll convert it to rems/h using the given conversion factor: $$ 8217\ \mathrm{mSv/h} \times \frac{1\ \mathrm{Sv}}{1000\ \mathrm{mSv}} \times \frac{1\ \mathrm{rem}}{0.0100\ \mathrm{Sv}} = \frac{8217}{10}\ \mathrm{rems/h} $$

Calculate radiation exposure for 35 minutes

We've found that the exposure is equal to 821.7 rems/h. To find out the exposure for 35 minutes, we need to convert minutes to hours and then multiply it with the exposure rate in rems/h: $$ 35\ \mathrm{min} \times \frac{1\ \mathrm{h}}{60\ \mathrm{min}} = \frac{7}{12}\ \mathrm{h} $$ Now, multiply the duration with the exposure rate to get the total exposure in rems: $$ \frac{7}{12}\ \mathrm{h} \times \frac{8217}{10}\ \mathrm{rems/h} = \frac{7 \times 8217}{120}\ \mathrm{rems} $$

Calculate equivalent mammograms

Now that we have the total exposure, we need to find how many mammograms that exposure would be equivalent to. We are given that one mammogram gives off 0.30 rems. To find the equivalent number of mammograms, divide the total exposure by the exposure of one mammogram: $$ \frac{\frac{7 \times 8217}{120}\ \mathrm{rems}}{0.30\ \mathrm{rems/mammogram}} = \frac{7 \times 8217}{36}\ \mathrm{mammograms} $$ Therefore, after being exposed to radiation for 35 minutes, the person would have absorbed an equivalent radiation of \(\frac{7 \times 8217}{120}\) rems, which is equal to \(\frac{7 \times 8217}{36}\) mammograms.