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The initial acceleration of proton and electron is 3.45 x 10¹⁸ m/s² and 6.33 x 10²¹ respectively.
What is electrostatic force?
The electrostatic force F between two charged objects placed distance apart is directly proportional to the product of the magnitude of charges and inversely proportional to the square of the distance between them.
F = kq₁q₂/r²
where k = 9 x 10⁹ N.m²/C²
Given is the charge on proton and electron is q =1.6 x 10⁻¹⁹ C, distance r =2 x 10⁻¹⁰m , then the force will be
F = k q²/r²
Substituting the above values in the formula, we get the electrostatic force,
F = (9 x 10⁹) (1.6 x 10⁻¹⁹)²/(2 x 10⁻¹⁰)²
F = 5.76 x 10⁻⁹ N
The acceleration of electron when both proton and electron released is
acceleration = electrostatic force / mass of electron
Putting the values, we have initial acceleration of electron
a = (5.76 x 10⁻⁹)/(9.1 x 10⁻³¹)
a = 6.33 x 10²¹ m/s²
The acceleration of proton is due to the electrostatic force of attraction between proton and electron is given by
acceleration = electrostatic force / mass of proton
inserting the values, we get the initial acceleration
a '= (5.76 x 10⁻⁹)/( 1.67 x 10⁻²⁷)
a'= 3.45 x 10¹⁸ m/s²
Thus, initial acceleration of proton and electron is 3.45 x 10¹⁸ m/s² and 6.33 x 10²¹ respectively.
Learn more about electrostatic force.
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