To initiate a nuclear reaction, an experimental nuclear physicist wants to shoot a proton into a 5.50-fm-diameter 12C nucleus. The proton must impact the nucleus with a kinetic energy of 2.30 MeV. Assume the nucleus remains at rest. With what speed must the proton be fired toward the target?

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