A radioactive substance has `6.0 xx 10^18` active nuclei initially. What time is required for the active nuclei o the same substance to become `1.0 xx 10^18` if its half-life is 40 s.

Explanation

To solve the problem, we need to determine the time required for a radioactive substance to decay from an initial number of active nuclei to a final number, given its half-life. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We start with an initial number of active nuclei \( N_0 = 6.0 \times 10^{18} \) and want to find the time required for the number of active nuclei to reduce to \( N = 1.0 \times 10^{18} \). The half-life \( t_{1/2} \) of the substance is given as 40 seconds.

### Step 2: Use the Formula for Radioactive Decay
The number of active nuclei at time \( t \) can be expressed using the formula:
\[
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