Question

What is the significance of impact parameter

Answer 1

The impact parameter {\displaystyle b} b is defined as the perpendicular distance between the path of a projectile and the center of a potential field {\displaystyle U(r)} U(r) created by an object that the projectile is approaching (see diagram). It is often referred to in nuclear physics (see Rutherford scattering) and in classical mechanics.

The impact parameter is related to the scattering angle {\displaystyle \theta } \theta by[1]

{\displaystyle \theta =\pi -2b\int _{r_{\mathrm {min} }}^{\infty }{\frac {dr}{r^{2}{\sqrt {1-(b/r)^{2}-2U/mv_{\infty }^{2}}}}}} \theta =\pi -2b\int _{{r_{{\mathrm {min}}}}}^{\infty }{\frac {dr}{r^{2}{\sqrt {1-(b/r)^{2}-2U/mv_{\infty }^{2}}}}}

where {\displaystyle v_{\infty }} v_{{\infty }} is the velocity of the projectile when it is far from the center, and {\displaystyle r_{\mathrm {min} }} r_{{\mathrm {min}}} is its closest distance from the center.

Answer 2

The impact parameter, which is an analogous length, determines how far an alpha particle must travel before it scatters from a nucleus.

• The alpha particle's velocity vector's perpendicular distance from the nucleus's center when it is distant from the atom is what is known as the impact parameter.
• Due to its inverse square law nature, the alpha particle experiences a weak repulsive force for large impact parameters, and the alpha particle passes almost undeflected.
• The alpha particle is scattered via a high angle for tiny impact parameters because the repulsive force is strong.
• The impact parameter and the type of the potential field determine the trajectory of the scattered alpha particles.
• If the projectile were to unpivot during the scattering phase, the impact parameter would be the distance perpendicular to the adjacent approach.

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