A deuteron of mass 3.34 x 10^-27 (kg), and charge 1e (of course) is moving in a
ID: 1640785 • Letter: A
Question
A deuteron of mass 3.34 x 10^-27 (kg), and charge 1e (of course) is moving in a cyclotron of uniform magnetic field 0.175 T, perpendicular to its velocity, with a kinetic energy of 1.64 MeV. (A) What is the velocity of the deuteron (which kinetic energy is 1.64 MeV)? Calculate (B) the radius of the path of the deuteron, and (C) the period of the particle in its motion around this circle. A deuteron of mass 3.34 x 10^-27 (kg), and charge 1e (of course) is moving in a cyclotron of uniform magnetic field 0.175 T, perpendicular to its velocity, with a kinetic energy of 1.64 MeV. (A) What is the velocity of the deuteron (which kinetic energy is 1.64 MeV)? Calculate (B) the radius of the path of the deuteron, and (C) the period of the particle in its motion around this circle.Explanation / Answer
Here ,
a) let the velocity is v
Using conservation of energy
0.50 * 3.34 *10^-27 * v^2 = 1.64 * 10^6 * 1.602*10^-19
solving for v
v = 1.254 *10^7 m/s
the velocity of deuteron is 1.254 *10^7 m/s
b)
radius of path = m * v/(B * q)
radius of path = 3.34 *10^-27 * 1.254 *10^7/(0.175 * 1.602 *10^-19)
radius of path = 1.49 m
c)
period of motion = 2 pi * m/(B * q)
period of motion = 2pi * 3.34 *10^-27/(0.175 * 1.602 *10^-19)
period of motion = 7.49 *10^-7 m