Question

A free electron and a free proton are exactly 0.80 cm apart. a)Find the magnitude of...

A free electron and a free proton are exactly 0.80 cm apart.

a)Find the magnitude of the acceleration of the proton

b)Find the magnitude of the acceleration of the electron.

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Answer #1

Force = k * qi * q2 ÷ r^2
k = 9 * 10^-9
charge of proton = +1.6 * 10^-19 Coulombs
charge of electron = -1.6 * 10^-19 Coulombs
r = 0.80 cm = 0.008 m

Force = 9 * 10^-9 * +1.6 * 10^-19 * -1.6 * 10^-19 ÷ ( 0.008)^2

Force = 3.6 * 10^-42 N

Half of this force causes the proton to accelerate towards the electron, and the other half causes the electron to accelerate towards the proton.

Force = mass * acceleration
Acceleration = Force ÷ mass

mass of proton = 1.67 * 10^-27 kg
mass of electron = 9.11 * 10^-31 kg

Proton acceleration = ½ * 3.6 * 10^-42 ÷ 1.67 * 10^-27 = 1.077 * 10^-17 m/s^2

Electron acceleration = ½ * 3.6 * 10^-42 ÷ 9.11 * 10^-31 = 1.97 * 10^-14 m/s^2

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