Question

A bare helium nucleus has two positive charges and a mass of 6.64×10−27 kg. Calculate its kinetic energy in joules at 2.00% of the speed of light.

A. 1.20×10−13 J
B. 3.57×10-12 J
C. 5.20×10−11 J
D. 7.57×10-10 J

Answer 1

To calculate the kinetic energy of a bare helium nucleus at 2.00% of the speed of light, use the formula for kinetic energy and substitute the given values.

Step-by-step explanation:

To calculate the kinetic energy of a bare helium nucleus at 2.00% of the speed of light, we can use the formula for kinetic energy:

Kinetic Energy = (1/2) * mass * velocity^2

First, we need to determine the velocity of the helium nucleus at 2.00% of the speed of light. The speed of light is approximately 3.00 x 10^8 m/s. Two percent of the speed of light is (0.02 * 3.00 x 10^8 m/s) = 6.00 x 10^6 m/s.

Now we can substitute the values into the formula:

Kinetic Energy = (1/2) * (6.64 x 10^-27 kg) * (6.00 x 10^6 m/s)^2

Calculating this expression gives us a kinetic energy of approximately 3.57 x 10^-12 Joules. Therefore, the correct answer is B. 3.57 x 10^-12 J.