Answer:
11.4 nm
Explanation:
The magnetic force drives the circular motion of the electron.
Magnetic force on a charge, q, moving with velocity, v, in a magnetic field, B, moving at angle θ to the field is given by
F = qvB sin θ⁻⁰¹²³⁴⁵⁶⁷⁸⁹
q = charge on an electron = - 1.6 × 10⁻¹⁹ C
v = velocity of the electron = 1000 m/s
B = 0.5 T
Sin θ = sin 90° = 1
F = 1.6 × 10⁻¹⁹ × 1000 × 0.5 = 8.0 × 10⁻¹⁷ N
This force drives the circular motion
F = mv²/r
m = mass of an electron = 9.11 × 10⁻³¹ kg
v = 1000 m/s, r = radius of orbit = ?
8 × 10⁻¹⁷ = (9.11 × 10⁻³¹ × 1000²)/r
r = (9.11 × 10⁻³¹ × 1000²)/(8 × 10⁻¹⁷) = 1.14 × 10⁻⁸ m = 11.4 nm
