The amount of the sample of the radioactive isotope decays exponentially in time, the amount of mass of the sample as a function of time ( $m (t)$ ), in grams, is described below:

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

Where:

$m_{o}$ - Initial mass, in grams.

$t$ - Time, in years.

$\tau$ - Time constant, in years.

The time constant can be found from half life ( $t_{1/2}$ ), in years, described in statement:

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

If we know that $m_{o} = 300\,g$ , $t = 3.9\times 10^{9}\,yr$ and $t_{1/2} = 1.3\times 10^{9}\,yr$ , then the current amount of the sample is:

$\tau = \frac{1.3\times 10^{9}\,yr}{\ln 2}$

$\tau \approx 1.876\times 10^{9}\,yr$

$m = (300\,g)\cdot e^{-\frac{3.9\times 10^{9}\,yr}{1.876\times 10^{9}\,yr} }$

$m\approx 37.521\,g$

The current amount of the Potassium-40 sample is approximately 37.521 grams.

4 0

3 years ago

High levels of ozone in the atmosphere can cause , which can trigger respiratory problems.

Marianna [84]

ANSWER: Photochemical Smog

8 0

3 years ago

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Which layer of the atmosphere is closest to the earth?

yaroslaw [1]

Answer:

The troposphere

Explanation:

It begins at the surface of the earth and extends out.

5 0

2 years ago

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