Finding the Distance of Closest Approach in Scattering Experiment

Scattering experiment is a process of bombarding particles on a target and observing the scattered particles. In this experiment, the distance of closest approach is the distance between the particle and the target when their paths are closest to each other. To find the distance of closest approach, the following formula can be used:

d = Z1 Z2 e^2 / 4πε0 K E

where d is the distance of closest approach, Z1 and Z2 are the atomic numbers of the particle and target respectively, e is the charge of an electron, ε0 is the permittivity of free space, K is the Coulomb constant, and E is the energy of the particle.

Given that a 6 MeV alpha particle is used in the scattering experiment, we can calculate the distance of closest approach using the above formula.

Solution:

- Identify the values given in the problem:

- Energy of the alpha particle (E) = 6 MeV
- Charge of an electron (e) = 1.6 × 10^-19 C
- Coulomb constant (K) = 9 × 10^9 Nm^2/C^2
- Permittivity of free space (ε0) = 8.85 × 10^-12 C^2/Nm^2
- Atomic number of alpha particle (Z1) = 2
- Atomic number of the target (Z2) = not given

- Estimate the atomic number of the target:

- The question does not mention the atomic number of the target. However, it is common to use gold (Au) foil as a target in alpha particle scattering experiments.
- The atomic number of gold is 79.

- Substitute the values in the formula and solve for d:

d = Z1 Z2 e^2 / 4πε0 K E

d = (2) (79) (1.6 × 10^-19)^2 / [4π(8.85 × 10^-12)(9 × 10^9)(6 × 10^6)]

d = 3.2 × 10^-15 m

- Answer:

Therefore, the distance of closest approach is 3.2 × 10^-15 m. The correct option is 4) 3.2 × 10^-15.

Note: The actual value of the distance of closest approach may vary depending on the target used in the experiment.