There are 100 g of lodine-131. After 16 days, how many grams of lodine-131 is left?

3 weeks ago

Solution 1

Guest #7253071
3 weeks ago

25g

Explanation:

According to a quick internet search, the half-life of I-131 is 8 days.

The amount left after 16 days can be calculated with the radioactive exponential decay formula:

$$A_(_t_)=A_0e^(^\frac{\ln(.5)}{T}^)^t$$

Where:

$$A_(_t_)$$ = the amount left as a function of time

$$A_0$$ = the original amount (100g)

T = the half-life of the isotope (8d)

t = time (16d)

So:

$$A_(_t_)=A_0e^(^\frac{\ln(0.5)}{T}^)^t\\A_(_t_)=(100g)e^(^\frac{\ln(0.5)}{8d}^)^(^1^6^d^)\\A_(_t_)=(100g)e^-^2^(^\ln(2))$$

$$A_(_t_)=25g$$

This answer is intuitive because the isotope has been through two half-lives:

$$100g(\frac{1}{2})(\frac{1}{2})=25g$$

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