Question

You received a shipment 20 days ago of 13 I for treatment of hyperthyroidism. What fraction of the original shipment would you still have with a half-life of 8.040 days for 31?

Answer 1

Answer:

we will have 17.8 % of the original value

Explanation:

As we know that by radioactive decay the total number of nuclei present at any instant of time is given as

$N = N_o e^{-\lambda t}$

here we need to find the fraction of total number of nuclei present

so we will have

$\frac{N}{N_o} = e^{-\lambda t}$

so we have

$\lambda = \frac{ln 2}{8.040}$

now we have

$\frac{N}{N_o} = e^{-\frac{ln 2}{8.040}(20)}$

$\frac{N}{N_o} = 0.178$

so we will have 17.8 % of the original value