The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 95% of the lead to decay?

Where represent the half life and the intial amount would be

And we want to find the time in order to have a 95% of decay so we can set up the following equation:

If we apply natural log on both sides we got:

And solving for t we got:

So then would takes about 14.26 hours in order to have  95% of the lead to decay

Step-by-step explanation:

For this case we can define the variable of interest amount of Pb209 and for the half life would be given:

Where represent the half life and the intial amount would be

And we want to find the time in order to have a 95% of decay so we can set up the following equation:

If we apply natural log on both sides we got:

And solving for t we got:

So then would takes about 14.26 hours in order to have  95% of the lead to decay

step-by-step explanation:

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