Calculate the smallest possible distance between the two electrons

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In summary, the question involves calculating the smallest possible distance between two electrons that are fired at 3.5 x 10^6 m/s directly at each other. The attempt to solve the problem using the equation Ee=Ek is shown, but the answer does not match. Another method is suggested, but the correctness of the answer is questioned. Ultimately, it is determined that the correct answer is 4.5x10^-6m, which is obtained by taking the square root of the initial kinetic energy calculation.
  • #1
XJellieBX
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Question:
Two electrons are fired at 3.5 x 10^6 m/s directly at each other.
(a) Calculate the smallest possible distance between the two electrons.

Attempt:
I tried Ee=Ek for this question and this is how it went.
Note*(q1=q2)

Ee=Ek
kq^2 = 0.5mv^2
r
r= kq^2
0.5mv^2
= (9.0x10^9(N x m^2)/C^2)(1.6x10^-19C)^2
0.5(9.1x10^-31kg)(3.5x10^6m/s)^2
= 4.1x10^-11m


I don't seem to be getting the right answer. Can someone please tell me what I'm doing wrong?
 
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  • #2
Your initial kinetic energy is not just 0.5mv^2, it's double that, since both electrons are moving. Try that.
 
  • #3
The answer still doesn't match, but I'm thinking the book is wrong. So thank you=)
 
  • #4
what is the answer?
 
  • #5
It says 4.5x10^-6m.
 
  • #6
i did it quickly, and i got the same answer u got in the first part. I did it another completely different way. interesting.. well i gtg.. i will try to look at this problem later.. but i don't think its right to assume the book is wrong.
 
  • #7
They've taken the square root. I don't know why.
 
  • #8
That would work if the electrostatic force was used, but I can't see how that fits.
 

1. What is the formula for calculating the smallest possible distance between two electrons?

The formula for calculating the smallest possible distance between two electrons is given by Coulomb's law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

2. How do you determine the charges of the two electrons in the calculation?

The charges of the two electrons can be determined based on their respective atomic numbers. Electrons have a negative charge of -1, so the charges of the two electrons will be -1 and -1, respectively.

3. Is there a limit to the smallest possible distance between two electrons?

According to quantum mechanics, there is a limit to the smallest possible distance between two electrons, known as the Bohr radius. This distance is approximately 0.529 Å (angstroms) or 5.29 x 10^-11 meters.

4. Can the smallest possible distance between two electrons be measured?

Due to the uncertainty principle in quantum mechanics, it is not possible to measure the exact distance between two electrons. However, the Bohr radius provides a theoretical limit for the smallest possible distance.

5. How does the smallest possible distance between two electrons affect the properties of an atom?

The distance between electrons plays a crucial role in determining the properties of an atom, such as its size, stability, and reactivity. The smaller the distance between electrons, the stronger the attraction between them, leading to a more stable and compact atom.

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