In this question we have been asked to determine the time for a 6.25 mg sample of cr-51 to decay to 0.75 mg if it has a half-life of 27.8 days.
Given:
Initial mass of sample = 6.25 mg
Isotope = Cr-51
Final mass after decaying = 0.75 mg
Half-life of Cr (t1/2) = 27.8 days
Solution:
The rate of decay can be determined by the following equation:
N = Noe^−λt
First determine the rate constant:
λ = 0.693 ÷ t1/2
λ = 0.693/27.8
λ = 0.025 days
Mass of substance and number of days are proportional to each other. Now
Use the equation of radioactivity decay
M = Moe^−λt
0.750 = 6.25e^-0.025 x t
0.12 = e^-0.025 x t
Taking ln on both sides
ln(0.12) = ln(e^-0.025 x t)
-2.12 = -0.025 x t
t = 84.8 days
Hence, 6.25 mg sample will decay in 84.8 days.
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