The half-life of a radioactive isotope is 2.5 hour. The mass of it that remains undecayed after 10 hour is (If the initial mass of the isotope was 16g).

Options

A. 32g
B. 16g
C. 4g
D. 1g

Explanation

To solve the problem of finding the remaining mass of a radioactive isotope after a certain period, we can follow these steps:

### Step 1: Understand the half-life concept
The half-life of a radioactive isotope is the time required for half of the isotope to decay. In this case, the half-life is given as 2.5 hours.

### Step 2: Determine the number of half-lives
To find out how many half-lives fit into the total time of 10 hours, we can use the formula:
\[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} \]
Substituting the values:
\[ \text{Number of half-lives} = \frac{10 \text{ hours}}{2.5 \text{ hours}} = 4 \]

### Step 3: Calculate the remaining mass
The remaining mass after a certain number of half-lives can be calculated using the formula:
\[ \text{Remaining mass} = \text{Initial mass} \times \left(\frac{1}{2}\right)^{n} \]
where \( n \) is the number of half-lives. Here, the initial mass is 16 g and \( n = 4 \):
\[ \text{Remaining mass} = 16 \text{ g} \times \left(\frac{1}{2}\right)^{4} \]
Calculating \( \left(\frac{1}{2}\right)^{4} \):
\[ \left(\frac{1}{2}\right)^{4} = \frac{1}{16} \]
Now substituting back:
\[ \text{Remaining mass} = 16 \text{ g} \times \frac{1}{16} = 1 \text{ g} \]

### Final Answer
The mass of the radioactive isotope that remains undecayed after 10 hours is **1 gram**.

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