Decaying & 1/2 life?

Question

a radio active substance decays from 16g to 12.5g in 5 years. what is the half like of this substance? round your answer to one decimal place

Answer 1

The half life is calculated as follows:

Let;

dQ/dt=the rate of decay at any time

Q = the remaining quantity at any time

Qo = the initial quantity

k = constant of proportionality

The rate of change is proportional to the amount present. Thus;

dQ/dt = -kQ , (negative because it is decreasing)

dQ/Q = -kdt

lnQ = -kt + lnC, where lnC = constant of integration

lnQ - lnC = -kt

ln(Q/C) = - kt

Q = C e^(-kt)

If t = 0, Q = Qo, hence C = Qo. Thus

ln(Q/Qo) = -kt

If t = 5, Q = 12.5. Therefore;

ln(12.5/16) = -5k

-0.24686 = -5k

,

k = 0.04937, thus;

ln(Q/16) = -0.04937t

If Q = 8;

ln(8/16) = -0.0493t

-0.69315 = -0.0493t

t = 14.1 years

.

Answer 2

14.0 years.

Go to the referenced website.  It has a free calculator for all this sort of stuff.

Answer 3

11.4 years.

Work. If it lost 3.5g in 5 years, how long to lose 8g?

3.5/5 = 8/x

40 = 3.5x

x = 11.4285 years

Answer 4

edward's answer is totally wrong.

You have to use logarithms.

A = A0*e^-(.693t/T)

t is the time, T is the half life, A is the amount you have at time t, and A0 is the amount you started with.

So solve for T.