Question

The half-life of lead is 22 years. How long will it take for a sample of this substance t decay to 80% of its original amount?

Answer 1

Answer: 7 years

Step-by-step explanation:

$t_{\frac{1}{2} }$ = In2 / ∧

since the half life is given , we have :

22 = In 2/ ∧

∧ = In2/22

∧ = 0.032

Recall the formula for half life:

$\frac{N(t)}{N(0)}$ = $e^{-∧t}$

Therefore:

0.80 = $e^{-0.032t}$

Take the In of both sides

In 0.80 = - 0.032t

t = In 0.80 / - 0.032

t = 7 years