Cobalt-57 is radioactive, emitting `beta-`particles.The half-life for this is 270 days. If 100 mg of this is kept in an open container, then what mass (in mg) of Cobalt-57 will remain after 540 days ?

Answer

To solve the problem of how much Cobalt-57 remains after 540 days, we can follow these steps:

### Step 1: Understand the half-life concept
The half-life of a radioactive substance is the time it takes for half of the substance to decay. For Cobalt-57, the half-life is given as 270 days.

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

### Step 3: Calculate the remaining mass after each half-life
Starting with an initial mass of 100 mg:
- After the first half-life (270 days), the mass will be:
\[ \text{Remaining mass} = \frac{100 \text{ mg}}{2} = 50 \text{ mg} \]
- After the second half-life (another 270 days), the mass will be:
\[ \text{Remaining mass} = \frac{50 \text{ mg}}{2} = 25 \text{ mg} \]

### Step 4: Conclusion
After 540 days, the remaining mass of Cobalt-57 will be 25 mg.

### Final Answer:
\[ \text{Remaining mass of Cobalt-57} = 25 \text{ mg} \]

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