Respuesta :
Answer:
[tex] N(t) =N_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]
Where [tex]t_{1/2}= 3.3 hr[/tex] represent the half life and the intial amount would be [tex] N_o = 1[/tex]
And we want to find the time in order to have a 95% of decay so we can set up the following equation:
[tex] 0.05 = 1 (0.5)^{t/3.3}[/tex]
If we apply natural log on both sides we got:
[tex] ln(0.05) = \frac{t}{3.3} ln (0.5)[/tex]
And solving for t we got:
[tex] t= 3.3 *\frac{ln(0.05)}{ln(0.5)}= 14.26[/tex]
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:
[tex] N(t) =N_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]
Where [tex]t_{1/2}= 3.3 hr[/tex] represent the half life and the intial amount would be [tex] N_o = 1[/tex]
And we want to find the time in order to have a 95% of decay so we can set up the following equation:
[tex] 0.05 = 1 (0.5)^{t/3.3}[/tex]
If we apply natural log on both sides we got:
[tex] ln(0.05) = \frac{t}{3.3} ln (0.5)[/tex]
And solving for t we got:
[tex] t= 3.3 *\frac{ln(0.05)}{ln(0.5)}= 14.26[/tex]
So then would takes about 14.26 hours in order to have 95% of the lead to decay
