What is the electrostatic force acting on an alpha particle when it reaches a distance of 4.2x10^-14m from a nucleus containing 75 protons?

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mwmovr40 | College Teacher | (Level 1) Associate Educator

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Electrostatic forces obey the inverse square law which means the magnitude of the force will increase as the distance decreases.  Electric forces are also directly proportional to the product of the  electric charges.  This relationship is related by Coulomb's Law:

Fe = kQ1Q2/d^2

Where k is the electrostatic constant, also known as Coulomb's constant, and is equal to 9.0x10^9Nm^2/C^2

Q1 and Q2 are the interacting charges, and d is their distance of separation.

For this example, Q1 is the charge on an alpha particle = 2x(1.6x10^-19C) = 3.2x10^-19C;  Q2 is the charge on the nucleus = 75x(1.6x10^-19C) = 120x10^-19C.  d= 4.2x10^-14m

Fe = (9.0x10^9)(3.2x10^-19)(120x10^-19)/(4.2x10^-14m)^2

Fe = 196X10^-1N = 19.6N 

Because both charges are positive, and like charges repel each other, the direction of the force will be in such a direction as to repel the charges.


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