A radioactive sample has an initial activity of 2.00 10^6 cpm (counts per minute

Question

A radioactive sample has an initial activity of 2.00 10^6 cpm (counts per minute), and after 4.0 days, its activity is 9.0 10^5 cpm. What is its activity after 29 days? A) 8.7 cpm B) 6.1 10^3 cpm C)3.3 10^2 cpm D) 1.5 10^-9 cpm E) none of these ANS: B PTS: 1 DIF: Moderate REF: 19.2 KEY: Chemistry | general chemistry | nuclear chemistry | radioactivity and nuclear bombardment reactions | rate of radioactive decay MSC: Quantitative A certain radioactive sample contains 2.4 10^3 nuclides at a certain time (t = 0); 3.0 h later the sample contains 6.0 10^2 nuclides. For this sample the ratio of the decay rates at t = 0 to t = 3.0 h is:

Explanation / Answer

33)

we know that

for radioactive decay

ln (A/Ao) = -kt

in this case

given

Ao = 2 x 10^6

A = 9 x 10^5

t = 4 days

so

ln ( 9 x 10^5 / 2 x 10^6) = - k x 4

k = 0.199627

so

decay constant (k) = 0.199627

now

given

time (t) = 29 days

so

ln (A/Ao) = -kt

ln (A / 2 x 10^6) = - 0.199627 x 29

A/ (2 x 10^6) = 3.0605 x 10-3

A = 6.12 x 10^3

so

the activity after 29 days is 6.12 x 10^3 cpm

so

the answer is option B) 6.1 x 10^3 cpm

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