Question

An electron with kinetic energy of 2000 eV (1 eV = 1.602 x 10-19 J) is fired horizontally across a horizontally oriented conducting plate with a surface charge density +4.00 x 106 C/m2. Taking the positive direction to be upward (away from the plate), what is the vertical deflection of the electron after it has travelled a horizontal distance of 4.00 cm?

Answer 1

Answer: 1.257 X 10∧-10 g

Explanation: Kinetic energy, K.E. = 1.602 X 10∧-19 J

Distance, L = 4/100 = 0.04 m

∴ Area, L²= (0.04 m)² = 4 X 10∧-4 m²

Charge density,Q = 4 X 10∧6 C/m²

Velocity, C = Q X L²= 4 X 10∧6 X 4 X 10∧-4 = 1.6 X 10³ m/s

Using, K.E. = 1/2MC² ( where M = mass)

∴  M = 2 X 1.609 X 10∧-19 /( 1.6 X 10³)² = 2 X 1.609 X 10∧-19/(2.56 X 10∧6)

M = 1.609 X 10∧-19/(1.28 X 10∧6)

∴ M = 1.257 X 10∧-13 Kg (or 1.257 X 10∧-10 g)