For this problem we can use half-life formula
and radioactive decay formula.
Half-life formula,
t1/2 = ln
2 / λ
where, t1/2 is half-life and λ is radioactive
decay constant
t1/2 = 14.8 hours
Hence,
14.8 hr = ln 2 / λ
λ = ln 2 / 14.8 hr
Radioactive decay law,
Nt = No e∧(-λt)
where, Nt is amount of compound at t time, No is
amount of compound at t = 0 time, t is time taken to decay
and λ is radioactive decay constant.
Nt = ?
No = 227.0 mg
λ = ln 2 / 14.8 hr = 0.693 / 14.8 hr
t = 3.7 days = 3.7 x 24 hours
By substituting,
Nt = 227 mg e∧((-0.693/14.8)x3.7 x24))
Nt = 3.5 mg
Hence, mass of remaining sample after 3.7 days = 3.5 mg
