Final answer:
To determine the speed of a proton given its kinetic energy, use the equation K = (1/2)mv^2 and convert the kinetic energy to Joules. Then rearrange the equation to solve for velocity and plug in the values.
Step-by-step explanation:
To determine the speed of a proton given its kinetic energy, we can use the equation K = (1/2)mv^2, where K is the kinetic energy, m is the mass, and v is the velocity of the proton.
Since the kinetic energy is given as 2.2 keV, we need to convert it to Joules. 1 keV is equal to 1.6 x 10^-16 Joules, so 2.2 keV is equal to (2.2 x 1.6 x 10^-16) Joules.
We can rearrange the equation to solve for the velocity: v = sqrt((2K)/m). Plugging in the values, we get v = sqrt((2 x 2.2 x 1.6 x 10^-16) / (1.67 x 10^-27)). Solving this equation will give us the speed of the proton.