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# Calculation of Radioactive Disintegration Constant

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A radio active substance has a half life of 30 days. Calculate
(a) the radioactive disintegration constant (b) The average life
(c) the time taken for ¾ of the original number of atoms to disintegrate and
(d) the time taken for 1/8 of the original number of atoms to remain unchanged

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We have, T= 30 days
(a) The radioactive disintegration constant &#955; = 0.693/T = 0.0231 per day (Ans)

(b) Average life Ta = 1/&#955; = 1/0.0231 = 43.29 Days (Ans)

(c) Number of atoms disintegrated ¾ N0 and the number of atoms left behind = ¼ N0
N = N0 Exp (-&#955;t)
N/ N0 = Exp (-&#955;t)

But in this case, N/ N0 = ¼
Or Exp (-&#955;t) = ¼ &#955;t = loge (4) = 2.3026 log10 (4)

Substituting the value of &#955;,
t = 2.3026 x 0.6021 / 0.0231 = 60 days (Ans)

(d) In this case, N/ N0 = 1/8

N/ N0 = Exp (-&#955;t)

Or, t = 2.3026 x log10 (8) / 0.0231
= 90 days (Ans)

Please see the attached document also.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!