Distance Problem Find Distance Between Alpha Particles

  • Thread starter mustang
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In summary: I gave the formula in two different ways. The first way was in terms of k, q1, and q2 and the second way was in terms of just one number, kq1q2. You must have both q1 and q2 so the second way is more convenient.In summary, the conversation discusses a problem involving two alpha particles with given values for k, q, and g. The formula for potential energy for two charged particles is mentioned and the student attempts to solve the problem using this formula, but their answer is incorrect due to rounding and providing the answer in coulombs instead of meters. The teacher points out the mistakes and suggests a more convenient way to use the formula.
  • #1
mustang
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0
Problem.
Given= k_e=8.98755*10^9 Nm^2/C^2, q_p=1.6021*10^-19 C, and g=9.8 m/s^2.
Two alpha particles (helium nuclei), each consisting of two protons and two neutrons, have an electrical potential energy of 6.35*10^-19 J.
What is the distance between these particles at this time? Answer in m.
Note:I figure out that 1 alpha particle is 3.2*10^-19C. So using the Potential energy of electric formula I squared 3.2*10^-19. Afterwards I divided it by 6.35*10^-19 and multplied that by 8.98755*10^9C to get the answer of 1.45313788*10^-9C. However the answer was incorrect what did I do wrong?
 
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  • #2
It would be better to write the formula rather than just reciting what you did.

The formula for potential energy for two charged particles with distance r between them is: -(kq1q2)/r (then anti-derivative of the force function with respect to r).

You are given that k=8.99*10^9, that q1 and q2 are both equal to 3.2*10^-19C (actually, you are not given that, you are given that one proton is 1.6021*10^-19 C and an alpha particle has two protons so: 3.20*10^-19 C- Since the potential is given with only 3 sig. figures, I also rounded off k.)and, finally, the the potential is 6.35*10^-19.

That is, the equation says (8.99*10^9)(3.20*10^-19)(3.20*10^-19)/r=
6.35*10^-19 or (92.1*10^-29)/r= 6.35*10^-19. Then 92.1*10^-29= (6.35*10^-19)r so r= (92.1*10^-29)/(6.35*10^-19)= 14.5*10^-10 or
1.45* 10^-9 m.

There are two things wrong with your answer:
1) Since the potential was given with only 3 significant figures, you answer "1.45313788*10^-9" claims too much accuracy.
2) The problem asked for "distance" and specifically said "answer in m" but your answer is "1.45313788*10^-9C" giving the answer in Coulombs as if it were charge!
 
  • #3
Formula

The formula for this equation is PE_electric=k_c*q1*q2/r. Also when I asked my teacher he said that he didn't get 1.45*10^-9C. He said that I did my math wrong.
 
  • #4
Also when I asked my teacher he said that he didn't get 1.45*10^-9C. He said that I did my math wrong.

Well, that was pretty much what I said in (2) wasn't it? Please read my response again.
 

1. What is the distance problem in relation to alpha particles?

The distance problem in relation to alpha particles refers to the difficulty in accurately measuring the distance between two alpha particles during a collision or decay event. This is due to the incredibly small size of alpha particles and the limitations of current measurement techniques.

2. Why is it important to find the distance between alpha particles?

Finding the distance between alpha particles is crucial for understanding the fundamental properties of matter and the forces that govern the universe. It can also provide insights into the structure and behavior of atoms and subatomic particles.

3. How is the distance between alpha particles calculated?

The distance between alpha particles is typically calculated using sophisticated mathematical models based on the trajectory of the particles and other physical parameters. It can also be estimated through experimental data and observations.

4. How does the distance between alpha particles affect nuclear reactions?

The distance between alpha particles plays a significant role in the initiation and progression of nuclear reactions. Depending on the distance, the particles may collide and fuse to create new elements, or they may repel each other and prevent further reactions.

5. What are some challenges in accurately measuring the distance between alpha particles?

Some challenges in accurately measuring the distance between alpha particles include the small size of the particles, the short duration of collisions, and the effects of other particles and forces in the surrounding environment. Technological limitations and uncertainties in measurement techniques can also contribute to inaccuracies.

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