The distance r between the pions when the criteria are satisfied is 1.45 × 10⁻¹⁶ m
If we consider the potential energy (U) between the pions, then (U) can be expressed as:
Given that at some instance, the potential energy becomes negligible compared to the final K.E.
As such the conservation of the total energy in the system can be given as:
Again, if we consider the ratio of the potential energy to the kinetic energy to be about 0.01, then:
∴
Equating both equations (1) and (2) together, we have:
where:
- r = distance
- k = Columb's constant
- q = charge on a proton
- m_o = rest mass of each pion in the previous question
- c = velocity of light
- = calculated velocity of proton in the previous question
Replacing their values in the above equation, the distance (r) between the pions is calculated as:
distance (r) = 1.45 × 10⁻¹⁶ m
Therefore, we can conclude that the distance r between the pions when the criteria are satisfied is 1.45 × 10⁻¹⁶ m
Learn more about electric potential energy here:
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