The activity of a radioactive sample is the number nuclear disintegrations per s
ID: 500980 • Letter: T
Question
The activity of a radioactive sample is the number nuclear disintegrations per second, which is equal to the first-order rate constant times the number of radioactive nuclei present. The fundamental unit of radioactivity is the curie (ci), where 1 Ci corresponds to exactly 3.70 times 10^10 disintegrations per second This decay rate is equivalent to that of 1 g of radium-226. The molar mass of Ra-226 is 226.03 g/mol. Calculate the rate constant for the radium decay 1.39 times 10^-11 (Enter your answer in scientific notation.) Calculate the half-life for the radium decay. 4.99 times 10^10 (Enter your answer in scientific notation.) Starting with 3.5 g of the radium sample, what is the activity after 550 yrExplanation / Answer
A = N
= A/N
A = 3.7x 1010 dps
Amount of Radium = 1g
No of atoms in 1g of radium = 6.023x1023 / 226.03 = 2.66 x 1021
= A/N = 3.7x 1010 dps / 2.66 x 1021 = 1.39x10-11 s-1
= 1.39x10-11 s-1
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Half life of Radium
t1/2 = 0.693/
= 1.39x10-11 s-1
t1/2 = 0.693/1.39x10-11 s-1 = 4.99 x 1010 s
t1/2 = 4.99 x 1010 s
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Amount of Radium sample = 3.5g
No of atoms in 3.5g of radium = 3.5g x 6.023x1023 / 226.03 = 9.3x1021atoms
A = N
Ao = 9.3x1021atoms x 1.39x10-11 s-1 = 12.92x1010 dps
A = Aoe-t
t = 550 x 365x24x3600 = 1.73x1010 seconds
A =12.92x1010 x e(-1.39x10-11 s-1 x 1.73x1010 s)
A = 12.92x1010 dps x e(-0.24)
A = 12.92x1010 dps x 0.786 = 10.15x1010 dps
A = 10.15x1010 dps
1 Ci = 3.7 x 1010 dps
A = 10.15x1010 dps /3.7 x 1010 dps = 2.74 Ci
A = 2.74 Ci
The activity of 3.5g of radium after 550 years is 2.74 Ci
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