Question

Inglés El isòtopo del plomo Pb-209 decae a un ritmo proporcional a la cantidad presente en el instante t y tiene una vida media de 3.3 horas. Si un gramo de este isòtopo està presente incialmente ¿Cuanto tiempo tardarà en descomponerse al 90% del plomo? The Pb-209 isotope of lead decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If one gram of this isotope is present initially, how long will it take to decompose to 90% of the lead? Can someone please solve it STEP BY STEP without skipping any step please? It would be really helpful. I´m lost ):

Answer 1

Amount of radioactive sample after time 't' is given by:

N = N0*e^(-$\lambda$*t)

$\lambda$ = decay constant = (ln 2)/T_half

T_half = Half-life of Pb-209 = 3.3 hrs

N0 = Initial Amount of Pb-209

N = final amount after decomposing = N0 - 90% of N0 = N0 - 0.9*N0 = 0.1*N0

time taken in decomposing = ? hr

So,

0.1*N0 = N0*e^(-t*ln (2)/3.3)

0.1 = e^(-t*ln (2)/3.3)

-t*ln (2)/3.3 = ln 0.1

t = -3.3*ln (0.1)/ln 2

t = 10.96 hrs

Let me know if you've any query.