A radioactive element reducess to `32st` of its initial value in 1000 years . What is half life of the element ?

Explanation

To find the half-life of a radioactive element that reduces to \( \frac{1}{32} \) of its initial value in 1000 years, we can follow these steps:

### Step 1: Understand the decay process
The problem states that the radioactive element reduces to \( \frac{1}{32} \) of its initial value. This means that the element has undergone several half-lives.

### Step 2: Determine how many half-lives are involved
The fraction \( \frac{1}{32} \) can be expressed as a power of \( \frac{1}{2} \):
\[
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