# Nuclear Chain Reaction and Atoms

• September 2nd 2009, 10:01 AM
Dragon
Nuclear Chain Reaction and Atoms
In a particular nuclear chain reaction, an atom ejects a neutron which causes an average of 1.3 atoms to do the same thing. What is the total number of atoms involved in the chain reaction after 30 generations?

A.) 8,730
B.)14,556
C.)8,729
D.)11,350
• September 2nd 2009, 10:45 AM
CaptainBlack
Quote:

Originally Posted by Dragon
In a particular nuclear chain reaction, an atom ejects a neutron which causes an average of 1.3 atoms to do the same thing. What is the total number of atoms involved in the chain reaction after 30 generations?

A.) 8,730
B.)14,556
C.)8,729
D.)11,350

If at generation $k$ you have $N_{k-1}$ atoms ejecting a neutron then in generation $k$ we have:

$N_{k}=1.3N_{k-1}=1.3^{k+1}N_0$

So the total number to have emited a nutron in $30$ generations is:

$NN_{30}=N_0(1+1.3+1.3^2+ ... + 1.3^{30})$

Assume we start with $N_0=1$, then we have a geometric series that you should be able to sum.

(this is counting the first decay as generation zero, if you want it to be generation 1 then adjust the above accordingly)

CB