A block having 12 g of an element is placed in a room. This element is a radioactive element with a half-life of 15 years. After how many years will there be just 1.5 g of the element in the box ?

Answer

To solve the problem step by step, we need to determine how many years it will take for 12 grams of a radioactive element to decay to 1.5 grams, given that its half-life is 15 years.

### Step 1: Understand the concept of half-life
The half-life of a radioactive substance is the time required for half of the substance to decay. In this case, the half-life is 15 years.

### Step 2: Calculate the amount of substance after each half-life
Starting with 12 grams, we will calculate the remaining amount of the substance after each half-life:

- **After 1 half-life (15 years)**:
\[ \text{Remaining amount} = \frac{12 \text{ g}}{2} = 6 \text{ g} \]

- **After 2 half-lives (30 years)**:
\[ \text{Remaining amount} = \frac{6 \text{ g}}{2} = 3 \text{ g} \]

- **After 3 half-lives (45 years)**:
\[ \text{Remaining amount} = \frac{3 \text{ g}}{2} = 1.5 \text{ g} \]

### Step 3: Calculate the total time
Now we sum the time for each half-life to find the total time it takes to reach 1.5 grams:

- Total time = 15 years + 15 years + 15 years = 45 years

### Conclusion
Thus, the time taken for the amount of the element to reduce from 12 grams to 1.5 grams is **45 years**.

### Final Answer
**45 years**

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