Final answer:
The radius of the circular path followed by the electron is 1.00 × 10^5 m.
Step-by-step explanation:
To determine the path of the electron, we can use the formula F = qvB sin(theta), where F is the magnetic force, q is the charge of the electron, v is the velocity of the electron, B is the magnetic field strength, and theta is the angle between the velocity and the magnetic field.
Since the electron is moving vertically upward and the magnetic field is directed horizontally away from the radius, the angle theta is 90 degrees. Therefore, sin(theta) = 1. Plugging in the given values, we have:
F = (1.6 × 10^-19 C)(1.82×10^6 m/s)(0.450 T)(1) = 1.66 × 10^-13 N.
We can rearrange the formula to solve for the radius of the circular path, using the formula F = mv^2/r, where m is the mass of the electron. Rearranging for r, we have:
r = mv / F = (9.11 × 10^-31 kg)(1.82×10^6 m/s) / (1.66 × 10^-13 N) = 1.00 × 10^5 m.