# Calculation of Radioactive Disintegration Constant

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 Â¾ 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 λ = 0.693/T = 0.0231 per day (Ans)

(b) Average life Ta = 1/λ = 1/0.0231 = 43.29 Days (Ans)

(c) Number of atoms disintegrated Â¾ N0 and the number of atoms left behind = Â¼ N0

N = N0 Exp (-λt)

N/ N0 = Exp (-λt)

But in this case, N/ N0 = Â¼

Or Exp (-λt) = Â¼ λt = loge (4) = 2.3026 log10 (4)

Substituting the value of λ,

t = 2.3026 x 0.6021 / 0.0231 = 60 days (Ans)

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

N/ N0 = Exp (-λt)

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

= 90 days (Ans)

Please see the attached document also.

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