An electron and a proton are held on an x axis, with the electron at x = + 1.000

Question

An electron and a proton are held on an x axis, with the electron at x = + 1.000 m and the proton at x = -1.000 m. (a) How much work is required to bring an additional electron from infinity to the origin? (b) If, instead of the second electron coming in from infinity, it is initially at x = +20.00 m on the axis and is given an initial velocity of 500.0 m/s toward the origin, does it reach the origin? If so, what is its speed at the instant it reaches the origin? If not, how close to the origin does it come? middot middot

Explanation / Answer

Potential energy of the electron when released at 20 m = [(9*10^9)*{(1.6*10^-19)^2}]*[(1/19) - (1/21)] J
1.155*10^-26 J > 0
It already has some KE. KE is given by
KE = {(1/2)*(9.1*10^-31)*(500^2)} = 11.37*10^-26 J As potential energy of the system when electron is at origin is zero which is less than starting potential energy, and the kinetic energy is about 10 times larger, the electron should reach origin
The KE of electron when it reaches origin =
(11.37 - 1.155)*10^-26 J = 10.215*10^-26 J
So KE is 10.215/11.37 = 0.898 times smaller. So v^2 should be 0.898 times smaller or
v^2 = (500^2)0.898 = 224604 or
required speed = sq rt[224604) = 473.92 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.