A projectile of mass m, charge Z., initial speed v and impact parameter b is scattered by a heavy nucleus of charge Z. Use angular momentum and energy conservation to obtain a formula connecting the minimum distance (s) of the projectile form the nucleus to these parameters. Show that for b = 0, s reduces to the closest distance of approach `r_(0)`.

Explanation

To solve the problem, we will use the principles of conservation of angular momentum and conservation of energy. Let's break down the solution step by step.

### Step 1: Define the System
We have a projectile of mass \( m \) and charge \( Z' \) (where \( Z' \) is the charge of the projectile) moving with an initial speed \( v \) and an impact parameter \( b \). It is scattered by a heavy nucleus of charge \( Z \).

### Step 2: Angular Momentum Conservation
The angular momentum \( L \) of the projectile about the nucleus is conserved. At a large distance (initially), the angular momentum is given by:
\[
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