Question about Texas Instruments TI-84 Plus Calculator

# How do i find the constant in a half life equation?

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Hello,
I have no idea what can of data you have, so I am taking a theoretical stance. In a radioactive decay the period of half life is the time after which half the nuclei have desintegrated. Let us call that period tau τ.
The constant, usually called lambda, λ appears in the expoential. It is the constant term that multiplies the time variable, t.
If you have y1 nuclei at a time t, and y2 nuclei at time t+ τ., the ratio y2/y1 =1/2. It is also equal to e^(-λ* τ). Thus
e^(-λ* τ) =1/2.
and ln(e^(-λ* τ)) = ln(1/2)=-ln(2). But since ln(e¨(x)) = x, we get
-λ* τ= - ln(2) and
λ= ln(2)/ τ

In the enclosed screen capture the equation e^(-λ* τ) =1/2 is solved for λ

If you have experimental data, or a radioactive decay curve drawn you can obtain the constant λ , as the negative of the slope of the function at t=0. See on following graph. Disregard the values of the function before t=0 ( I should have restricted the window to the first quadrant.) The function drawn is e^(-0.365t)

Hope it helps.
Thank you for using FixYa

Posted on Nov 20, 2009

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Posted on Jan 02, 2017

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