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By mass spectral analysis, a sample of strontium is known to contain 2.64x1010 atoms of Sr-90 as the only radioactive element. The absolute disintegration rate of this sample is measured as 1238 disintegrations per minute. Calculate the half-life (in years) of Sr-90. Answer: 28.49 Question 14 Not answered Marked out of 1.00 Question text How long will it take (in years) for the disintegration rate of this sample to drop to 878 disintegrations per minute

Respuesta :

It will take 14.13 years for the disintegration rate of this sample to drop to 878 disintegrations per minute.

Given that,

Half life of Sr-90 = 28.49 years

This decay process is first order decay kinetics

So according to [tex]1^{st}[/tex] order reaction

Half life = 0.693/k

k= 0.693/28.49

k= 0.0243 [tex]years^{-1}[/tex]

According to the integrated rate law for [tex]1^{st}[/tex] order reaction

ln[Rn] = ln[Rn][tex]{o}[/tex] - kt  …..(1)

where, Rn = 878 disintegrations/minute

Rn[tex]_{o}[/tex] = 1238 disintegrations/minute

Putting the values in equation (1)

ln[878] = ln[1238] - 0.0243 × t

6.7776 = 7.1212 - 0.0243 × t

0.0243t = 0.3436

t= 14.13 years

Hence, it will take 14.13 years for the disintegration rate of this sample to drop to 878 disintegrations per minute.

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