Ten grams of `^57 Co` kept in an open container beta-decays with a half-life of 270 days. The weight of the material inside the container after 540 days will be very nearly

Options

A. `10 g`
B. `7.5 g`
C. `5 g`
D. `2.5 g`

Explanation

To solve the problem of how much `^57 Co` remains after 540 days, we will follow these steps:

### Step 1: Understand the half-life concept
The half-life of a radioactive substance is the time required for half of the substance to decay. In this case, the half-life of `^57 Co` is given as 270 days.

### Step 2: Determine the number of half-lives in 540 days
To find out how many half-lives fit into 540 days, we divide the total time by the half-life:
\[ \text{Number of half-lives} = \frac{540 \text{ days}}{270 \text{ days}} = 2 \]
This means that 540 days corresponds to 2 half-lives.

### Step 3: Calculate the remaining mass after 2 half-lives
Starting with 10 grams of `^57 Co`, we can calculate the remaining mass after each half-life:
- After 1 half-life (270 days), the mass will be:
\[ \text{Remaining mass} = \frac{10 \text{ grams}}{2} = 5 \text{ grams} \]
- After 2 half-lives (540 days), the mass will be:
\[ \text{Remaining mass} = \frac{5 \text{ grams}}{2} = 2.5 \text{ grams} \]

### Step 4: Consider the mass of the remaining material
While the mass of the cobalt decreases due to decay, it is important to note that the beta decay process produces electrons, which have negligible mass compared to cobalt. Thus, the total weight of the material in the container will still be very close to the original mass of cobalt.

### Conclusion
After 540 days, the weight of the material inside the container will be approximately:
\[ \text{Weight after 540 days} \approx 10 \text{ grams} \]

### Final Answer
The weight of the material inside the container after 540 days will be very nearly **10 grams**.

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