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

1 Answer
1s2s2p
May 14, 2018

#35.6%# decayed after 4 months

Explanation:

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

  • #N# = current number of radioactive nuclei remaining
  • #N_0# = starting number of radioactive nuclei remaining
  • #t# = time passed (#s# though can be hours, days, etc.)
  • #lambda# = decay constant #(ln(2)/t_(1/2))# (#s^-1#, though in the equation uses the same unit of time as #t#)

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

#0.9N_0=N_0e^(-lambda)# (#t# being taken in months, and #la,bda# being #"month"^-1#)

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

#aN_0=N_0e^(-0.11(4))#

#100%a=100%-(e^(-0.11(4))*100%)=100%-64.4%=35.6%# decayed

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