# Technetium 99 is used for brain scans. If a laboratory receives a shipment of 178 g of this isotope, how much will remain after 15 hours? The half life of Technetium 99 is 6 hours.

Jan 19, 2017

The answer is $= 31.47 g$

#### Explanation:

We apply the law of dadioactive decay

$m \left(t\right) = {m}_{0} {e}^{- \lambda t}$

$m \left(t\right) =$ mass at time t

${m}_{0} =$ mass at $t = 0$

$\lambda =$ decay constant

${t}_{\frac{1}{2}} =$ half life

$\lambda = \ln \frac{2}{t} _ \left(\frac{1}{2}\right) = \ln \frac{2}{6} = 0.1155 {h}^{-} 1$

$t = 15 h$

$m \left(15 h\right) = 178 \cdot {e}^{- 0.1155 \cdot 15}$

$= 178 \cdot 0.1768 = 31.47 g$

The mass of Technetium 99 remaining after 15 h $= 31.47 g$