There are several methods of solving this radioactivity problem. One of the easiest is:

\(\frac{Original mass}{2^n}\)  = Residual mass

Where n = number of activity =  \(\frac{exposure  time}{half  life}\)

Given: 

Original mass = 5g, exposure time = 200 days , half life = 50 days, Residual mass = ?

Substituting all the given parameters appropriately, we have

 n = \(\frac{200}{50}\)

 n = 4

\(\frac{Original  mass}{2^n}\) = Residual mass

\(\frac{5}{2^4}\)  = Residual mass

\(\frac{5}{16}\) = Residual mass

Residual mass = 0.3125g = 0.31g