Question

Determine half-life of ${}^{112}Ag$, if in $6.20$ hours, a $50.0-$gram sample of ${}^{112}Ag$ decays to $12.5$ grams?

• A. $1.60hours$
• B. $3.10hours$
• C. $6.20hours$
• D. $12.4hours$
• E. $18.6hours$

Answer 1

The correct option is B $3.10hours$

Radio active decay is given by above formula where

$N\left(t\right)$ is amount of sample at time $t$

$N_0$ is initial amount of sample

$t_1/2$ is half life

so in above question $N\left(t\right)$$=$$12.5grams$

$N_0$$=$$50grams$

$t$$=$$6.2hours$

so $\left(12.5/50\right)$$=$$\left(0.5{)}^{(}6.2/t_0.5\right)$

$6.2/t_0.5$$=$2

or $t_0.5$$=$$6.2/2$$=$$3.1hours$