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Part A
If the amount of radioactive indium-111 in a sample prepared for specialist diagnostic studies decreases from 3.2 g to 0.10 g in 12.5 days, what is the half-life of Indium-111

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Eduard22sly

The half-life of the radioactive Indium-111 is 2.5 days

Determination of the number of half-lives that has elapsed

  • Original amount (N₀) = 3.2 g
  • Amount remaining (N) = 0.1 g
  • Number of half-lives (n) =?

N × 2ⁿ = N₀

0.1 × 2ⁿ = 3.2

Divide both side by 0.1

2ⁿ = 3.2 / 0.1

2ⁿ = 32

2ⁿ = 2⁵

n = 5

How to determine the half-life

  • Number of half-lives (n) = 5
  • Time (t) = 12.5 days
  • Half-life (t½) =?

t½ = t / n

t½ = 12.5 / 5

t½ = 2.5 days

Learn more about half life:

https://brainly.com/question/26280499

The half-life of the radioactive sample is approximately 2.5 days.

Data;

  • Initial amount = 3.2g
  • final amount =0.1g
  • half-life = ?

Half-Life

The half-life of a radioactive of a radioactive sample is the time it takes for the sample to decay to half it's original size.

Let us solve for the decay constant.

[tex]k=\frac{2.303}{t}*log\frac{x}{y}\\ K = \frac{2.303}{12.5}*log\frac{3.2}{0.1}\\ k = 0.2773 days^-^1[/tex]

Using the decay constant, we can solve for the half-life of the In-111.

[tex]T_\frac{1}{2} = \frac{0.693}{k}\\ T\frac{1}{2} = \frac{0.693}{0.2773} = 2.499day\\ T\frac{1}{2} = 2.5[/tex]

The half-life of the radioactive sample is approximately 2.5 days.

Learn more on half-life here;

https://brainly.com/question/2320811

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