Nucleus a decays into the stable nucleus b with a half-life of 22.07 s. at t=0 s there are 1,293 a nuclei and no b nuclei. at what time will there be 779 b nuclei?

29.38 seconds

Explanation:

Half life, T = 22.07 s

No = 1293

Let N be the number of atoms left after time t

N = 1293 - 779 = 514

By the use of law of radioactivity

Where, λ is the decay constant

λ = 0.6931 / T = 0.6931 / 22.07 = 0.0314 decay per second

so,

take natural log on both the sides

0.9225 = 0.0314 t

t = 29.38 seconds

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