Give the relationship between impact parameter and scattering angle.
(N/A) The impact parameter $b$ is defined as the perpendicular distance of the initial velocity vector of the alpha particle from the center of the nucleus. The relationship between the impact parameter $b$ and the scattering angle $\theta$ is given by the formula:
$b = \frac{1}{4\pi\epsilon_0} \cdot \frac{Ze^2 \cot(\theta/2)}{K}$
where:
$Z$ is the atomic number of the target nucleus,
$e$ is the elementary charge,
$K$ is the kinetic energy of the incident alpha particle,
$\theta$ is the scattering angle,
$\epsilon_0$ is the permittivity of free space.
$b = \frac{1}{4\pi\epsilon_0} \cdot \frac{Ze^2 \cot(\theta/2)}{K}$
where:
$Z$ is the atomic number of the target nucleus,
$e$ is the elementary charge,
$K$ is the kinetic energy of the incident alpha particle,
$\theta$ is the scattering angle,
$\epsilon_0$ is the permittivity of free space.
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