Question

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

Answer 1

About 92 days are taken for 90 % of the material to decay.

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 decay.

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