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Problem 32 Medium Difficulty

Iodine-131 is used to treat thyroid cancer.
(a) The isotope decays by $\beta$ particle emission. Write a balanced equation for this process.
(b) Iodine-131 has a half-life of 8.04 days. If you begin with $2.4 \mu \mathrm{g}$ of radioactive $^{131} \mathrm{I},$ what mass remains after 40.2 days?


a. $I_{53}^{131}->X e_{54}^{131}+e_{-1}^{0}$
b. $\frac{1}{32} \times 2.4 \mu g=0.075 \mu g$


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Video Transcript

first will write the nuclear reaction for the decomposition of iodine 31 through beta mission producing scene on 1 31 Then we can use the half life in order to calculate the rate constant in units of one over days. Then we use the first order integrated rate law where we take the natural log of what remains over. What we start with is equal to negative. Katie plug in our negative K value. Forget time that passes 40.2 days doing a little bit of algebra. Get the natural log of X, then is equal to this expression here. So the natural log of X is negative. 2.5895 Take the anti natural log and X is going to be 0.5 point 0751 micrograms.