A radioisotope has a half life of 10 days. If totally there is `125 g ` of it left, what was its mass 40 days earlier ?

Options

A. `600g`
B. `1000g`
C. `1250g`
D. `2000g`

Explanation

To solve the problem step by step, we will use the concept of half-life in radioactive decay.

### 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 10 days.

### Step 2: Determine the number of half-lives
We need to find out how many half-lives fit into the 40 days we are considering. We can calculate this by dividing the total time by the half-life:
\[ \text{Number of half-lives} (n) = \frac{\text{Total time}}{\text{Half-life}} = \frac{40 \text{ days}}{10 \text{ days}} = 4 \]

### Step 3: Use the formula for radioactive decay
The formula relating the original mass of the isotope to the remaining mass after a certain number of half-lives is:
\[ \text{Original mass} = \text{Remaining mass} \times 2^n \]
Where:
- Remaining mass = 125 g
- \( n = 4 \) (from Step 2)

### Step 4: Substitute the values into the formula
Now we can substitute the values into the formula:
\[ \text{Original mass} = 125 \text{ g} \times 2^4 \]
Calculating \( 2^4 \):
\[ 2^4 = 16 \]
Thus,
\[ \text{Original mass} = 125 \text{ g} \times 16 = 2000 \text{ g} \]

### Step 5: Conclusion
The mass of the radioisotope 40 days earlier was **2000 grams**.

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