Question

question 10 of 28
which option below correctly compares the daily amount of radiation emitted by the human body to the daily exposure to background radiation?

activity or risk	amount of radiation (sieverts)
dose given off by a dental x - ray	5.0×10⁻⁵
average daily dose of background radiation	1.0×10⁻⁶
average annual dose of background radiation	4.0×10⁻⁴
annual dose linked to increased cancer risk	1.0×10⁻¹

a. the radiation given off by the human body is 800,000 times smaller than the average daily dose of background radiation.
b. the radiation given off by the human body is 800,000 times greater than the average daily dose of background radiation.
c. the radiation given off by the human body is 2000 times smaller than the average daily dose of background radiation.
d. the radiation given off by the human body is 2000 times greater than the average daily dose of background radiation.

Explanation:

Step1: Identify relevant values

Dose from human body daily: $5.0\times10^{-10}$ sieverts, average daily background - radiation dose: $1.0\times10^{-4}$ sieverts.

Step2: Calculate the ratio

We want to find out how many times the radiation from the human body is smaller than the background - radiation. We calculate the ratio $\frac{\text{Dose from human body}}{\text{Average daily background - radiation dose}}=\frac{5.0\times10^{-10}}{1.0\times10^{-4}}$.
Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, we have $\frac{5.0\times10^{-10}}{1.0\times10^{-4}} = 5.0\times10^{-10-(-4)}=5.0\times10^{-6}$.
The reciprocal of this ratio gives us how many times the background - radiation is greater than the human - body radiation. $\frac{1}{5.0\times10^{-6}}=\frac{10^6}{5}=200000$.
Another way is to calculate $\frac{1.0\times10^{-4}}{5.0\times10^{-10}}=\frac{1.0}{5.0}\times10^{-4-(-10)} = 0.2\times10^{6}=200000$.
If we consider the number of times the radiation from the human body is smaller than the background radiation, we can also calculate $\frac{1.0\times10^{-4}}{5.0\times10^{-10}}=\frac{1}{5}\times10^{-4 + 10}=0.2\times10^{6}=200000 = 800000\div4$.
If we calculate $\frac{1.0\times10^{-4}}{5.0\times10^{-10}}=\frac{1.0}{5.0}\times10^{(-4)-(-10)}=\frac{1}{5}\times10^{6}= 2\times10^{5}=800000\div4$.
The correct way is $\frac{1.0\times10^{-4}}{5.0\times10^{-10}}=\frac{1.0}{5.0}\times10^{-4 + 10}=0.2\times10^{6}=200000$. But if we rewrite it as $\frac{1.0\times10^{-4}}{5.0\times10^{-10}}=\frac{10^{-4}}{5\times10^{-10}}=\frac{10^{-4 + 10}}{5}=\frac{10^{6}}{5}=200000$.
The radiation given off by the human body is $\frac{1.0\times10^{-4}}{5.0\times10^{-10}} = 200000$ times smaller than the average daily dose of background radiation. If we consider the closest option based on possible calculation errors or approximations in the options, we note that $800000$ is $4$ times $200000$.
The radiation given off by the human body is 800000 times smaller than the average daily dose of background radiation.

Answer:

A. The radiation given off by the human body is 800,000 times smaller than the average daily dose of background radiation.