# KE of electron being attracted by 2 protons

Hi everyone,

I have a problem regarding this question. An electron is and it is being attracted to 2 stationary protons. The 2 protons are at a vertical distance of 6x apart and the electron passes through the centre of the line joining the 2 protons (3x below the top proton and 3x above the bottom proton), and at right angle to that line. The electron is released at a distance of 4x from the vertical mid-point of the 2 protons. What is the max KE of the electron?

I found the potential at the mid point of the 2 protons which the electron will pass through to be at e/6(pi)(Enot)x, and eV is the KE so it gives e^2/6(pi)(Enot)x. The answer is wrong and the one I've been given is a 15 at the denominator and not 6. Can anyone point out my mistake? thanks!

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nrqed
Homework Helper
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al_201314 said:
Hi everyone,

I have a problem regarding this question. An electron is and it is being attracted to 2 stationary protons. The 2 protons are at a vertical distance of 6x apart and the electron passes through the centre of the line joining the 2 protons (3x below the top proton and 3x above the bottom proton), and at right angle to that line. The electron is released at a distance of 4x from the vertical mid-point of the 2 protons. What is the max KE of the electron?

I found the potential at the mid point of the 2 protons which the electron will pass through to be at e/6(pi)(Enot)x, and eV is the KE so it gives e^2/6(pi)(Enot)x. The answer is wrong and the one I've been given is a 15 at the denominator and not 6. Can anyone point out my mistake? thanks!
It's because you forgot to take into account the fact that the electron has some potential energy at the initial position!
At the initial position, it is at a disatnce of 5x from both proton. Find the potential energy there. Then use conservation of energy and you will see that you will get ther answer (hint: 1/6 -1/10 = 1/15).

Patrick

nrqed
Homework Helper
Gold Member
al_201314 said:
Hi everyone,

I have a problem regarding this question. An electron is and it is being attracted to 2 stationary protons. The 2 protons are at a vertical distance of 6x apart and the electron passes through the centre of the line joining the 2 protons (3x below the top proton and 3x above the bottom proton), and at right angle to that line. The electron is released at a distance of 4x from the vertical mid-point of the 2 protons. What is the max KE of the electron?

I found the potential at the mid point of the 2 protons which the electron will pass through to be at e/6(pi)(Enot)x, and eV is the KE so it gives e^2/6(pi)(Enot)x. The answer is wrong and the one I've been given is a 15 at the denominator and not 6. Can anyone point out my mistake? thanks!
It's because you forgot to take into account the fact that the electron has some potential energy at the initial position!
At the initial position, it is at a disatnce of 5x from both proton. Find the potential energy there. Then use conservation of energy and you will see that you will get ther answer (hint: 1/6 -1/10 = 1/15).

Patrick

Thanks Pat for the help I can't imagine I didn't thought of that and to think that my final exams are in november! Thanks agaiN!

nrqed