J.R. S. answered 05/27/21
Ph.D. University Professor with 10+ years Tutoring Experience
First, you need to look at the activity series of metals (or the standard reduction potentials) and see if iron (Fe) is more or less reactive than silver (Ag).
Looking at standard reduction potentials (that's the table I happen to have handy), I find the following:
Ag+ + e- ==> Ag(s) Eº = 0.80
Fe2+ + 2e- ==> Fe(s) Eº = -0.41
So, Ag+ will be reduced and Fe(s) will be oxidized and so yes, a reaction will take place. The reaction is...
2AgNO3(aq) + Fe(s) ==> Fe(NO3)2(aq) + 2Ag(s)