What is 'K' in K=1/4pi Epsilon 0?

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The discussion clarifies that 'k' in the equation 1/2mv² = kQq/r represents the Coulomb constant, valued at approximately 8.988 x 10^9 Nm²/C². It is defined as k = 1/4πε₀, where ε₀ is the electric constant, also known as the permittivity of free space. The confusion arose from the distinction between k and ε₀, with participants emphasizing the importance of using the correct constant in calculations related to atomic physics and electrostatics.

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Hey So for those that don't know, I'm reading this from Atomic Physics, basically where they teach you how the size of a nucleus was determined by shooting alpha particles at it. due to repulsion an alpha particle can get only 'so-close' to nucleus(they're both positively charged), and the the so-close is labelled as point P, the closest to the nucleus and alpha gets.

So here's a formula they teach us to use:

1/2mv2 = kQq/r

What is k called? what is the name of this constant, and what is it equal to since I was told it was the electric constant and went about solving it with that value, but at the back in the answer section they used the value 9x10^9!
Thanks guy! :D
 
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