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Radioactive Decay
09-20-2019, 01:57 PM
Post: #1
Radioactive Decay
The Journal of Nuclear Medicine {vol 19, num 11} pgs. 1270-1271
Calculation of Radioactive Decay with a Pocket Calculator
JAMES S. ROBERTSON
Mayo Clinic
Rochester, Minnesota


"Radioactive decay is customarily expressed by the equation
(1) A = A₀ e^(-λt)
where t = time; λ = decay constant in t⁻¹ units; A = activity, usually μCi or mCi; A₀ activity at t = 0; and e = 2.718 …, the natural logarithm base.
However, the decay parameter most readily available is not λ, but the half-life, T. Therefore, the relationship λT = ln(2) = 0.693 … is invoked and the decay equation
becomes
(2) A = A₀ e^(-0.693t/T)
From this it would appear that the way to calculate A, given A₀, t and T, is first to determine x = -0.693 t/T and then to obtain A/A₀ from e^(x). However, a simplifying feature that is overlooked in this procedure is that e^(-0.693) = …½, and the decay equation may therefore be expressed as
(3) A = A₀ ½^(t/T)
Thus, if a pocket calculator having a y^x function is used, A/A₀ may be calculated simply by entering 0.5 as y, calculating t/T as x, and calling y^x. This saves several steps when compared with using Eq. 2. For negative values of t, the same procedure works, but alternatively the number 2 may be entered as y and the absolute value of t used.
These procedures are similar to the slide-rule method of setting T against 0.5 or 2.0 on a log-log scale and reading A/A₀ against t, a method now in danger of being forgotten with the proliferation of inexpensive pocket calculators."

'Ahh, memories'

BEST!
SlideRule
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09-20-2019, 02:40 PM
Post: #2
RE: Radioactive Decay
(09-20-2019 01:57 PM)SlideRule Wrote:  (1) A = A₀ e^(-λt) ...
(2) A = A₀ e^(-0.693t/T) ...

... simplifying ...

(3) A = A₀ ½^(t/T)

Why go thru all these ?
(3) is the *definition* of half-life
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