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 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
https://brainmass.com/physics/half-life/calculation-radioactive-disintegration-constant-6565
SOLUTION This solution is FREE courtesy of BrainMass!
Please see the attached document also.
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 ¾ N0 and the number of atoms left behind = ¼ N0
N = N0 Exp (-λt)
N/ N0 = Exp (-λt)
But in this case, N/ N0 = ¼
Or Exp (-λt) = ¼ 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.
© BrainMass Inc. brainmass.com December 24, 2021, 4:46 pm ad1c9bdddf>https://brainmass.com/physics/half-life/calculation-radioactive-disintegration-constant-6565