We can use two equations for this problem.
t1/2 = ln 2 / λ
= 0.693 / λ
Where t1/2 is the half-life of the element
and λ is decay constant.
5 s = 0.693 / λ
λ = 0.693 / 5 s
(1)
Nt = Nο eΛ(-λt)
Nt/No = eΛ(-λt) (2)
Where Nt is atoms at t time, No is the initial amount of substance, λ is decay
constant and t is the time taken.
t = 1 minute = 60 s
From (1) and (2),
Nt/No = eΛ(-(0.693 / 5 s) 60 s)
Nt/No = 2.445 x 10⁻⁴
Hence, the fraction of the original nuclei would remain after 1 minute is 2.445 x 10⁻⁴.
