Final answer:
To find the radius of the circular orbit, we use the equation for centripetal force experienced by a charged particle in a magnetic field. We rearrange the equation to solve for the radius and plug in the given values to find the answer.
Step-by-step explanation:
To find the radius of the circular orbit of the electron, we can use the equation for the centripetal force experienced by a charged particle moving in a magnetic field:
F = (q * v * B) / r
Where:
F is the centripetal force
q is the charge of the electron
v is the velocity of the electron
B is the magnetic field flux density
r is the radius of the circular orbit
We are given the energy of the electron (450eV), which we can convert to kinetic energy by using the equation:
KE = 1/2 * m * v^2
Where:
KE is the kinetic energy
m is the mass of the electron
v is the velocity of the electron
From the kinetic energy, we can solve for the velocity of the electron. Then, we can rearrange the equation for centripetal force to solve for the radius of the circular orbit:
r = (q * v) / (B * F)
Plugging in the given values, we can calculate the radius of the circular orbit to be 0.015 meters.