Answer :
the initial acceleration of the proton is [tex]1.4 x 10^19 m/s^2[/tex] and the initial acceleration of the electron is [tex]2.5 x 10^11 m/s^2.[/tex]
The force between the electron and proton is given by Coulomb's law:
[tex]F = kq1q2/r^2[/tex]
where k is the Coulomb constant[tex](9.0 x 10^9 N*m^2/C^2)\\[/tex], q1 and q2 are the charges of the particles (in Coulombs), and r is the distance between them (in meters). In this case, the charges of the proton and electron are opposite in sign and equal in magnitude, so we can set [tex]q1 = q2 = 1.6 x 10^-19 C[/tex]. The distance between them is [tex]r = 2.00 x 10^-10 m\\[/tex]Plugging these values into Coulomb's law, we get:
F = [tex](9.0 x 10^9 N*m^2/C^2) * (1.6 x 10^-19 C)^2 / (2.00 x 10^-10 m)^2[/tex]
F = [tex]2.3 x 10^-8 N[/tex]
This is the magnitude of the force between the proton and electron. To find the acceleration of each particle, we can use Newton's second law:
F = m*a. where F is the force, m is the mass of the particle, and a is the acceleration. The mass of the proton is [tex]1.67 x 10^-27 kg\\[/tex], and the mass of the electron is 9.11 x 10^-31 kg. Plugging these values into the equation above, we get: a_proton = F/m_proton =[tex](2.3 x 10^-8 N) / (1.67 x 10^-27 kg) = 1.4 x 10^19 m/s^2[/tex] a_electron = F/m_electron = [tex](2.3 x 10^-8 N) / (9.11 x 10^-31 kg) = 2.5 x 10^11 m/s^2[/tex]
Therefore, the initial acceleration of the proton is [tex]1.4 x 10^19 m/s^2[/tex] and the initial acceleration of the electron is [tex]2.5 x 10^11 m/s^2.[/tex]
To learn more about Coulomb's law here:
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