Question

32p is a radioactive isotope with a half-life of 14.3 days. if you currently have 38.1 g of 32p, how much 32p was present 9.00 days ago?

Answer 1

T=14.3 d
m₁=38.1 g
t=9.00 d
m₂-?

m₂=2m₁·e^[-(T-t)ln2/T]

m₂=2·38.1·e^[-(14.3-9)ln2/14.3]=58.94 g
58.94 g ³²P was present 9.00 days ago

Answer 2

58.94 g of the radioactive isotope was available 9 days ago.

From the question given above, the following data were obtained:

Amount remaining (N) = 38.1 g

Half-life ($t_{1/2}$) = 14.3 days

Time (t) = 9 days

Original amount (N₀) =?

Next, we shall determine the number of half-lives that has elapsed.

Half-life ($t_{1/2}$) = 14.3 days

Time (t) = 9 days

Number of half-lives (n) =?

$n = \frac{t}{t_{1/2}} \\\\n = \frac{9}{14.3} \\\\n = \frac{90}{143}$

Finally, we shall determine the amount of the radioactive isotope that was available 9 days ago (i.e original amount)

Amount remaining (N) = 38.1 g

Number of half-lives (n) = $\frac{90}{143}$

Original amount (N₀) =?

N₀ = 2ⁿ × N

N₀ = $2^{\frac{90}{143}} * 38.1$

N₀ = 58.94 g

Therefore, 58.94 g of the radioactive isotope was available 9 days ago.

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