Question

PLEASE HELP

The half-life of phosphorous-32 is approximately 24.3 days.
How much of a 3 gram sample of phosphorus-32 would remain after 10 days?
ROUND TO THREE DECIMAL POINTS.

Answer 1

`A\approx2.255 \text{ grams}`

Explanation:

We can use the standard formula for half-life:

`\displaystyle A=A_0\left((1)/(2)\right)^(t)/(d)`

Where A₀ is the initial amount, d is the time for one half-life, and t is the number of days.

Because the half-life is 24.3 days, d = 24.3:

`\displaystyle A=A_0\left((1)/(2)\right)^(t)/(24.3)`

We want to find the amount of a 3-gram sample after 10 days. Hence, substitute and evaluate:

`\displaystyle \begin{aligned} A & = (3)\left((1)/(2)\right)^((10))/(24.3) \\ \\ & \approx 2.255\text{ grams}\end{aligned}`

In conclusion, about 2.255 grams will remain afetr 10 days.