A 443.4 ng sample of an unknown radioactive substance was placed in storage and

Question

A 443.4 ng sample of an unknown radioactive substance was placed in storage and its mass measured periodically. After 47 days the amount of radioactive substance had decreased to 55.43 ng. How many half-lives of the unknown radioactive substance have occurred?

Question 15 of 24 sapling learning A 443.4 ng sample of an unknown radioactive substance was placed in storage and its mass measured periodically. After 47 days the amount of radioactive substance had decreased to 55.43 ng. How many half-lives of the unknown radioactive substance have occurred? Number half- lives half lives

Explanation / Answer

Given data:

Initial amount of radioactive substance Ai = 443.4 ng.

Final amount of radioactive substance Af = 55.43 ng.

t = 47 days

Radioactive deacys follows First order kinetics Let us calculate First order rate constant k (or lambda)

Formula, k = (1/t) x ln(Ai/Af)..............(since natural log used 2.303 do not appear in formula)

k = (1/47) x ln(443.4/55.43)

k = (1/47) x 2.079

k = 0.0442 per day

Noe let us calculate half life period ( t1/2).

Formula, ( t1/2). = ln 2 / k

t1/2 = 0.693 / 0.0442..............(since ln 2 = 0.693

t1/2= 15.682 days

No. of half lives = t / t1/2.

= 47 / 15.682

= 2.99

= 3 half lives

3 Half lives have occured.

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Note a simple direct formula,

Af/Ai = 1 / 2n .........(n be the number of half lives

put all known values

so. 443.4 / 55.43 = 1 / 2n.

2n = 7.999

i.e. 2n = 8 that means n = 3 as we know that 23 = 8

So number of half lives = n = 3.

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