In a Rutherford scattering experiment when a projectile of charge Z₁ and mass M₁ approaches a target nucleus of charge Z₂ and mass M₂, the distance of closest approach is r₀. The energy of the projectile is 

Concept:

The distance of closest approach (r₀) in a Rutherford scattering experiment is inversely proportional to the kinetic energy (K) of the projectile. Mathematically,

r₀ = k / K

where k is a constant that depends on the charges of the projectile and the target nucleus.

For a projectile of charge Z₁ and a target nucleus of charge Z₂, the constant k is given by:

k = (Z₁ Z₂ e²) / (4 π ε₀)

Thus, the energy of the projectile (K) can be written as:

K = (Z₁ Z₂ e²) / (4 π ε₀ r₀)

Calculation:

We are given the distance of closest approach r₀ and need to determine the relationship between the energy of the projectile and the charges Z₁ and Z₂.

⇒ K = (Z₁ Z₂ e²) / (4 π ε₀ r₀)

From this formula, we can see that the energy K is directly proportional to the product of the charges Z₁ and Z₂.

∴ The energy of the projectile is directly proportional to Z₁Z₂.