Final answer:
To calculate the kinetic energy of a bare helium nucleus at 2.00% of the speed of light, use the kinetic energy formula with the given mass and velocity calculated from the speed of light. The kinetic energy is 1.19×1013 joules.
Step-by-step explanation:
The question asks to calculate the kinetic energy of a bare helium nucleus at 2.00% of the speed of light. Given the mass of the helium nucleus (6.64×10-27 kg), first, find the velocity by computing 2.00% of the speed of light (c = 3×108 m/s).
The velocity (v) is 0.02 × c = 0.02 × 3×108 m/s = 6×106 m/s. Next, use the kinetic energy formula KE = 1/2 × m × v2 where m is mass and v is velocity. KE = 1/2 × (6.64×10-27 kg) × (6×106 m/s)2 = 1.19×1013 joules. This is the kinetic energy of the helium nucleus at 2% the speed of light, which corresponds to answer choice (a).