Three electrons form an equilateral triangle

In summary, the potential energy of three electrons forming an equilateral triangle with a proton at the center can be calculated using the equation ΔU = (kq1q2)/r, where s = 1.00 × 10-9m, p+ Charge = 1.60 × 10-19C, e- Charge = -1.60 × 10-19C, and r = s/√(3) = 5.77 × 10-10m. However, the solution may not work if there is an error in the equation, such as a double minus sign in the term with denominator 5.77x10^-10. The potential energy of the proton due to the
  • #1
t.kirschner99
18
0
1. Homework Statement

Three electrons form an equilateral triangle 1.00nm on each side. A proton is at the center of the triangle. What is the potential energy of this group of charges?
Known Variables:
s = 1.00 × 10-9m
p+ Charge = 1.60 × 10-19C
e- Charge = -1.60 × 10-19C
r = s/√(3) = 5.77 × 10-10m

Homework Equations



ΔU = (kq1q2)/ r

The Attempt at a Solution


[/B]
ΔU = k[(3(-1.60×10-19)2))/(1.00×10-9) - ((3(1.60×10-19)(-1.60×-19))/(5.77 × 10-10))]

For some reason I cannot get the answer, and I was wondering if anyone could spot my error. Thanks!
 
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  • #2
The term with denominator 5.77x10^-10 should be negative but you have a double minus sign which makes it positive. The potential energy of the proton due to the 3 electrons should be negative due to the attraction.
 

Related to Three electrons form an equilateral triangle

What is an equilateral triangle?

An equilateral triangle is a triangle with all three sides of equal length and all three angles of equal measure.

How do three electrons form an equilateral triangle?

In a three-electron system, the electrons repel each other and arrange themselves in a way that minimizes this repulsion. This results in an equilateral triangle formation.

Why is it important to study the formation of an equilateral triangle with three electrons?

Understanding the arrangement of electrons in an equilateral triangle can help us gain insight into the behavior of electrons in atoms and molecules. It also has applications in fields such as chemistry and materials science.

What are the properties of an equilateral triangle formed by three electrons?

An equilateral triangle formed by three electrons has equal side lengths and angles measuring 60 degrees. It is also a stable configuration due to the balanced repulsion between the electrons.

Can three electrons form an equilateral triangle in any other configurations?

No, an equilateral triangle is the only stable configuration for three electrons due to the repulsion between them. Any other configuration would result in an unequal distribution of charges and would be energetically unfavorable.

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