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22 March, 19:31

A radioisotope is place near a radiation detector, which registers 80 counts per second. Eight hours later, the detector registers five counts per section. What is the isotope's half-life?

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  1. 22 March, 19:38
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    The isotopes half life is 2 hours

    Since given the following:

    time = 8 hours * 3600s/hr = 28800 seconds

    A₀ = 80 Bq as the first registration of detector counts per second

    A = 5 Bq as the registration of detector counts per second eight hours later

    Using the formula:

    ∴ A = A₀ e^-λt

    ∴ A/A₀ = e^-λt

    ∴ ln (A/A₀) = - λt

    ∴ λ = - ln (A/A₀) / t = ln2 / t_{1/2}

    ∴ t_{1/2} = - ln2 / ln (A/A₀) (t)

    ∴ t_{1/2} = - ln2 / ln (5/80) (8 hours) = 2 hours
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