(In this problem, we are going to treat the electron as a point particle, and as

Question

(In this problem, we are going to treat the electron as a point particle, and assume that the proton, which has a much greater mass, does not move.) An electron is in a circular orbit around a proton. The radius of the orbit of the electron is 0.529 × 10-10 m. Calculate the magnitude of the acceleration of the electron. Calculate the period of the electron. Calculate the kinetic energy of the electron. Calculate the electrical potential energy of the electron. (Careful with the sign of the potential energy!) Calculate the total energy of the electron eV.

Explanation / Answer

centripetal acceleration = coulombic force m*v2/r = q1*q1*k/r2 =>   mv2 = q1*q2*k/r Recall     KE =0.5*mv2     PE = -q1*q2*k/r => 2*KE = -PE acceleration = v2/r = (q1*q1*k/r2)/m =(1.60e-19 C*1.60e-19 C *8.99e9 N m2/C2 /[0.529e-10 m]2)/9.1e-31 kg acceleration =9.04 x 1022 m/s2 v = (a*r)1/2 = (9.04 x 1022 m/s2 *0.529e-10 m)1/2 = 2.19 x 106 m/s Period = 2r/v = (2**0.529e-10 m)/(2.19e6 m/s) =1.5201423e-16 ~ 1.52 x 10-16 seconds KE = -PE/2 = q1*q2*k/2r = (1.6e-19C *1.6e-19 C*8.99e9 Nm2/C2 / [2*0.529e-10 m] KE = 2.1752741e-18 ~ 2.18 x 10-18 J (or you can use the speed and mass to calculuate KE) PE = -2*KE = -2*2.1752741e-18 J = -4.3505482e-18 ~ -4.35 x10-18 J Total energy = KE + PE = -PE/2 + PE = PE/2 = -2.1752741e-18 ~-2.18 x 10-18 J In eV, = -2.1752741e-18 J*(1 eV/1.6e-19 J) = -13.595 eV ~ -13.6eV

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