Posted by Ali on Monday, August 18, 2014 at 3:23pm.
Radioactive nuclei are produced in an irradiated sample at the rate of 10 s1. If the number in the sample builds up to a maximum of 1000, calculate the mean life and the halflife of the radioactive nuclei
Using dN / dt = P  λ N
dN / dt = 1000n /10/ 1 = 100
P  λ N = 10 – λ 1000N
Half life is 
(In2) / λ = (In2) / 1000) = 6.93x10^4 seconds
Not sure of mean life any advice appreciated ...

physics  Damon, Monday, August 18, 2014 at 4:25pm
if none were added
dN/dt = k N
number produced per second = 10
number lost per second = k n
so
dN/dt = 10  k N
N is maximum when dN/dt = 0
0 = 10  k (1000)
k = .01
so we know that for this fission reaction (without the inflow)
dN/dt = .01 N
dN/N = .01 dt
ln N = .01 t + C
N = Ni e^(.01 t)
when is N/Ni = .5?
ln .5 = .01 t
t = 69.3 seconds half life
mean life = 1.443 * half life (see http://www.britannica.com/EBchecked/topic/371549/meanlife ) 
physics  Ali, Monday, August 18, 2014 at 4:39pm
THANK YOU .....

physics  Damon, Monday, August 18, 2014 at 4:49pm
You are welcome :)