Find the separation of the 14n and 15n isotopes at the detector. express your answer with the appropriate units.

Measured masses (14 n) = 2.33*10 -26 kg 
measured mass of ( 15n)  = 2.46 * 10 -26 kg

For circular motion centripetal force (mv^2 / r)  magnetically force (Bqv)

mv^2 / r  = Bvr 
r  =  mv^2 / Bq

for N14 :-  

r1  =  (2.46*10-26)  * 513000^2 /  0.510 * 1.6* 10 -19)
for N15:-

r2  =   (2.33 *10-26 )  *  513000^2  / 0.510  * 1.6 * 10 -19

so separation is :-   2r2 - 2r1  =  2 ( r2  -  r1) 

You didn't post a list of words.

They are all full and don't need any more electrons in there outer shell.