Radioactive substance disintegrate by 10%in 1 month .How much fraction will disintegrate in 4 months?

1 Answer
May 14, 2018

35.6%35.6% decayed after 4 months

Explanation:

We have the equation:
N=N_0e^(-lambdat)N=N0eλt, where:

  • NN = current number of radioactive nuclei remaining
  • N_0N0 = starting number of radioactive nuclei remaining
  • tt = time passed (ss though can be hours, days, etc.)
  • lambdaλ = decay constant (ln(2)/t_(1/2))(ln(2)t12) (s^-1s1, though in the equation uses the same unit of time as tt)

10%10% decay, so 90%90% remain

0.9N_0=N_0e^(-lambda)0.9N0=N0eλ (tt being taken in months, and la,bdala,bda being "month"^-1month1)

lambda=-ln(0.9)=0.11"month"^-1λ=ln(0.9)=0.11month1 (to 2 d.p)

aN_0=N_0e^(-0.11(4))aN0=N0e0.11(4)

100%a=100%-(e^(-0.11(4))*100%)=100%-64.4%=35.6%100%a=100%(e0.11(4)100%)=100%64.4%=35.6% decayed