A certain radioactive sample contains 2.4 10^3 nuclides at a certain time (t = 0

Question

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. 34. For this sample the ratio of the decay rates at t = 0 to t = 3.0 h is: A) 1.0 B) 8.0 C) 4.0 D) 16 E) none of these ANS: C PTS: 1 DIF: Moderate REF: 19.2 KEY: Chemistry | general chemistry | nuclear chemistry | radioactivity and nuclear bombardment reactions | rate of radioactive decay MSC: Quantitative 35. The value of the rate constant for this process is: A) 2.2 h^-1 B) 4.6 10^-1 h^-1 C) 1.6 h^-1

Explanation / Answer

34)

we know that

decay rate = k x N

where

k = decay constant

N = number of nuclides at the time

now

at t = 0

decay rate at t=0 = k x 2.4 x 10^3

at t= 3 hr

decay rate at t = 3 = k x 6 x 10^2

now

ratio is given by

decay rate at t=0 / decay rate at t=3 = k x 2.4 x 10^3 / k x 6 x 10^2

decay rate at t=0 / decay rate at t=3 = 4

so

the ratio of decay rates at t=0 to t=3 h is 4

so

the answer is option C) 4

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