Question

# A radioactive nuclide has a half-life of 30.7 y. What fraction of an initially pure sample...

A radioactive nuclide has a half-life of 30.7 y. What fraction of an initially pure sample of this nuclide will remain undecayed at the end of 86.8 y?

STEPS : 1- WE NEED TO CALCULATE DECAY CONSTANT λ

2- WITH λ WE CAN CALCULATE REAMING RADIOACTIVE MATERIAL

FORMULA: half-life t1/2=ln2 /λ (λ is the decay constant )

so λ=ln2/t1/2 (t1/2 given = 30.7 years)

λ= 0.693/30.7 = 0.02257

NOW Nt = N0e−λt

N0 is the initial quantity

Nt   is the remaining quantity after time, t
t1/2 is the half-life
t time (given 86.8year)
λ is the decay constant

Nt /N0=e−λt

Nt /N0=e−(.02257 X 86.8)

Nt /N0=e−(.02257 X 86.8)

Nt /N0=0.140

Nt =0.1410 No

14.10 % will remain after 86.6 years.

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