Question

The amount of $_{53} I^{128}$ (half-life = 25 minutes) left after 50 minutes will be:

A. One-half
B. One-third
C. One-fourth
D. Nothing

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Answer

:

The correct answer is C.

To determine the amount of $_{53} I^{128}$ left after 50 minutes, we need to consider its half-life of 25 minutes. The number of half-lives that have passed can be calculated as:

$$ n = \frac{\text{total time}}{\text{half-life}} $$

Here, the total time is 50 minutes and the half-life is 25 minutes:

$$ n = \frac{50 \text{ minutes}}{25 \text{ minutes}} = 2 $$

This means that 2 half-lives have occurred. For each half-life, the amount of the substance halves.

The fraction of the substance remaining after $n$ half-lives is calculated using the formula:

$$ \left( \frac{1}{2} \right)^n $$

Substituting $n = 2$:

$$ \left( \frac{1}{2} \right)^2 = \frac{1}{4} $$

Therefore, after 50 minutes, the amount of $_{53}I^{128}$ remaining will be:

$$ \frac{1}{4} $$

Final Answer: C


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