Question 31.15: The isotope nitrogen-13 has a half-life of 10 min. A sample ...
The isotope nitrogen-13 has a half-life of 10 min. A sample initially contains 8.0 × 10^{10} undecayed nuclei.
a Write down an equation to show how the number undecayed, N, depends on time, t.
b Determine how many nuclei will remain after 10min, and after 20 min .
c Determine how many nuclei will decay during the first 30 min.
N = N_{0} e^{–λt}
b After 10 minutes, half the nuclei will decay, so half will remain undecayed, or 4.0 × 10^{10} After a further 10 minutes, half the remaining
number will decay, leaving one-quarter of the original number, or 2.0 × 10^{10}
c After 30 minutes, three half-lives have elapsed. Number of original nuclei decaying in this time= \frac{1}{2} + \frac{1}{4} + \frac{1}{8} = \frac{7}{8} of total = 7.0 \times 10^{10}