Question

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?

Answer 1

29.38 seconds

Step-by-step 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

`N=N_(0)e^(-\lambda t)`

Where, λ is the decay constant

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

so,

`514=1293e^(-0.0314t)`

`2.5155=e^(0.0314t)`

take natural log on both the sides

0.9225 = 0.0314 t

t = 29.38 seconds