Do u have the statements ?
Answer:

Explanation:
From the question we are told that
Nucleus diameter 
a 12C nucleus
Required kinetic energy 
Generally initial speed of proton must be determined,applying the law of conservation of energy we have

where
=initial kinetic energy
=final kinetic energy
=initial electric potential
=final electric potential
mathematically

where
=distance b/w charges
=nucleus charge 
=constant
=proton charge
Generally kinetic energy is know as

Therefore
Generally equation for radius is 
Mathematically solving for radius of nucleus


Generally we can easily solving mathematically substitute into v_1









Therefore the proton must be fired out with a speed of 
Answer:
n = 1.42
Explanation:
The refractive index for a medium is given by the ratio of the speed of light in vacuum to the speed of light in a medium.

So, the refractive index of the medium is 1.42.