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Katyanochek1 [597]
2 years ago
5

If you start with 85 milligrams of Chromium 51, used to track red blood cells, which

Mathematics
1 answer:
zysi [14]2 years ago
8 0

About 92 days are taken for 90 % of the material to <em>decay</em>.

The mass of radioisotopes (m), measured in milligrams, decreases exponentially in time (t), measured in days. The model that represents such decrease is described below:

m(t) = m_{o}\cdot e^{-\frac{t}{\tau} } (1)

Where:

  • m_{o} - Initial mass, in milligrams.
  • m(t) - Current mass, in milligrams.
  • \tau - Time constant, in days.

In addition, the time constant is defined in terms of half-life (t_{1/2}), in days:

\tau = \frac{t_{1/2}}{\ln 2} (2)

If we know that m_{o} = 85\,mg, t_{1/2} = 27.7\,d and m(t) = 8.5\,mg, then the time required for decaying is:

\tau = \frac{t_{1/2}}{\ln 2}

\tau = \frac{27.7\,d}{\ln 2}

\tau \approx 39.963\,d

t = -\tau \cdot \ln \frac{m(t)}{m_{o}}

t = -(39.963\,d)\cdot \ln \frac{8.5\,mg}{85\,mg}

t\approx 92.018\,d

About 92 days are taken for 90 % of the material to <em>decay</em>.

We kindly invite to check this question on half-life: brainly.com/question/24710827

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