Final answer:
The kinetic energy of protons accelerated to 23 mm/s by a cyclotron is 4.424 x 10^-31 joules, calculated using the formula KE = (1/2)mv^2, with m as the mass of a proton and v as the final velocity.
Step-by-step explanation:
The student's question is asking for the final kinetic energy of protons accelerated by a cyclotron from rest to a final velocity of 23 mm/s. To find the kinetic energy (KE), we can use the formula KE = (1/2)mv2, where m is the mass of the proton and v is its final velocity. The mass of a proton is approximately 1.67 x 10-27 kg. Converting the given velocity to meters per second (23 mm/s is 0.023 m/s), we can calculate the kinetic energy:
KE = (1/2)(1.67 x 10-27 kg)(0.023 m/s)2
KE = (1/2)(1.67 x 10-27 kg)(5.29 x 10-4 m2/s2)
KE = 4.424 x 10-31 J
Therefore, the final kinetic energy of the protons is 4.424 x 10-31 joules.