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[QUE/CM-06008]

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  1. Consider a beam of alpha particles incident on a nucleus of atomic number \(Z\) and that the nucleus is a sphere of radius \(R\). Assume that the charge \(Ze\) of the nucleus is uniformly distributed inside the nucleus. What should be the energy, \(E_b\) of an alpha particle in the beam having an impact parameter \(b\). so that it just touches the surface of the nucleus, i.e. distance of minimum approach becomes equal to \(R\)? Find the corresponding scattering angle \(\theta(b,E_b)\) using the formula derived in the class.
  2. How do you expect your answers to change for alpha particle with different values of impact parameter \(b\). Consider situations  (i) \(b<R\), (ii) \(b \approx R\) (iii) \( b> R\).
  3. What do you expect to happen to the alpha particle if(i) if it energy is less than \(E_b\); (ii) if it energy is greater than \(E_b\). Will the alpha particle get scattered at large angles?       or, is the scattering angle expected to be small?

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