t1/2 = ln 2 / λ = 0.693 / λ
Where t1/2 is the half life of the element and λ is decay constant.
32 = 0.693 / λ
λ = 0.693 / 32 (1)
Nt = Nο eΛ(-λt) (2)
Where Nt is atoms at t time, λ is decay constant and t is the time taken.
t = 1.9 hours = 1.9 x 60 min
From (1) and (2),
Nt = Nο e⁻Λ(0.693/32)*1.9*60
Nt = 0.085Nο
Percentage = (Nt/Nο) x 100%
= (0.085Nο/Nο) x 100%
= 8.5%
Hence, Percentage of remaining atoms with the original sample is 8.5%
