Consider a certain type of nucleus that has a half-life of 32 min. calculate the percent of original sample of nuclides remaining after 1.9 hours have passed

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%