Question

Alpha particles travel through a magnetic field of 0.360 T and are deflected in an arc of 0.0820 m.  Assuming the alpha particles are perpendicular to the field, the energy of an individual alpha particle is ___ x 10^-15 J.

Answer 1

Magnetic field B = 0.36 T

Deflected radius of an arc r = 0.082 m

Charge of alpha particle q = 2e = 3.20435 × 10^-19 C

Mass of alpha particle m = 6.64 × 10⁻²⁷  kg

Magnetic Force = Bqv

Centripetal Force = mv²/r

Bqv = mv²/r

v = Bqr/m

v = (0.36)( 3.20435 × 10^-19)( 0.082) / (6.64 × 10⁻²⁷)

v = 1.42458 × 10⁶ m/s

Energy of alpha particle E = (1/2)mv²

E = (1/2)( 6.64 × 10⁻²⁷)( 1.42458 × 10⁶)²

E = 4.7296 × 10⁻¹⁵ J

Energy of alpha particle is 4.7296 × 10⁻¹⁵ J.