An alpha nucleus of energy 1 2 mv ^2 bombards a heavy nuclear target of charge Z e . Then the distance of closest approach for the alpha nucleus will be proportional to

Step-by-step solution

An -particle of mass m possesses initial velocity v , when it is at a large distance from the nucleus of an atom having atomic number Z . At the distance of closest approach, the kinetic energy of -particle is completely converted into potential energy. Mathematically, aligned & 1 2 mv ^2= 1 4 ₀ (2 e )( Ze ) r ₀ & r ₀= 1 4 ₀ 2 Ze ^2 1 2 mv ^2 aligned