A Geiger counter is placed at a distance of 5 m from a `gamma` radiation source. The half-life of `gamma` radiation source is 40 minutes and the count rate recorded by the Geiger counter is `400 s^(-1)`. If the distance between the source and the counter is changed, then the count rate recorded will be `10s^(-1)` after 2 hours. Find the new distance between the source and the counter.

Explanation

To solve the problem step by step, we will follow the given information and apply the relevant physics concepts.

### Step 1: Understand the Problem
We have a gamma radiation source with a half-life of 40 minutes, and initially, the Geiger counter records a count rate of 400 counts per second at a distance of 5 meters. After 2 hours, the count rate drops to 10 counts per second. We need to find the new distance between the source and the counter.

### Step 2: Calculate the Number of Half-Lives
First, we need to determine how many half-lives have passed in 2 hours.

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