Question

The half-life of a radioactive nuclear source is 9 days. What fraction of nuclei is left 

undecayed after 3 days.

Answer 1

Let’s use the formula for radioactive decay:

$$N=N_0e^{-\lambda t},$$ $$N=N_0e^{-\dfrac{0.693}{T_{1/2}}t},$$ $$N=N_0e^{-\dfrac{0.693}{9\ d}\cdot3\ d}=0.79N_0=79\%.$$

Therefore, 79% of nuclei is left undecayed after 3 days.