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If an alpha particle has 50 fm as its distance of closest approach when incident on a gold foil, what will be its kinetic energy?

If an alpha particle has 50 fm as its distance of closest approach when incident on a gold foil, what will be its kinetic energy?

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**Question (4 points):** If an alpha particle has 50 fm as its distance of closest approach when incident on a gold foil, what will be its kinetic energy? **Explanation:** This question involves calculating the kinetic energy of an alpha particle, using its closest approach distance on a gold foil. The distance of 50 femtometers (fm) suggests a nuclear interaction. Solving such a problem typically requires understanding concepts such as the conservation of energy, the charge of the alpha particle, and the properties of the gold nucleus.
Transcribed Image Text:**Question (4 points):** If an alpha particle has 50 fm as its distance of closest approach when incident on a gold foil, what will be its kinetic energy? **Explanation:** This question involves calculating the kinetic energy of an alpha particle, using its closest approach distance on a gold foil. The distance of 50 femtometers (fm) suggests a nuclear interaction. Solving such a problem typically requires understanding concepts such as the conservation of energy, the charge of the alpha particle, and the properties of the gold nucleus.
Expert Solution
Concept and Principle:
  • When a positively charged particle gets close to a nucleus it will start exchanging its kinetic energy for electrostatic potential energy caused by the nuclear repulsion.

 

  • The point at which the kinetic energy of the particle becomes zero and its potential energy becomes maximum is the closest point the charged particle can reach.

 

  • Thus we have the distance of the closest approach as,

d=14πε0zZe2K

Here ε0 is the permittivity of free space, z is the atomic number of the projectile, Z is the atomic number of the target, e is the charge of the electron, and K is the kinetic energy of the projectile.

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