# Sodium-24 has a half-life of 15.0 hours. Suppose you had a sample containing 0.010 moles of Na-24. How many hours would be required to reduce your sample to 6.25 x 10^-4 moles?

May 24, 2016

$t i m e = 60.0 \setminus h r s$

#### Explanation:

${n}_{i} = {n}_{r} \cdot {2}^{n}$

${n}_{i} \text{ is the initial number of moles present of the radioisotope.}$

${n}_{r} \text{ is the number of moles remaining after a certain time }$

$n \text{ is the number of periods," = (time)/T" where T is the half-life.}$

${n}_{i} = {n}_{r} \cdot {2}^{n}$

${n}_{i} / {n}_{r} = {2}^{n}$

${2}^{n} = \frac{0.010 \setminus m o l}{6.25 \times {10}^{- 4} \setminus m o l}$

${2}^{n} = 16$

${2}^{n} = {2}^{4}$

$\left(n = 4\right)$

n= (time)/T"

$t i m e = n \times T \text{ (half-life)}$

$t i m e = 4 \times 15.0 h r s$

$t i m e = 60.0 \setminus h r s$