An electron has mass m_e = 9.11 times 10^-31 kg and charge q_e = -1.6 times 10^-

Question

An electron has mass m_e = 9.11 times 10^-31 kg and charge q_e = -1.6 times 10^-19 C, A has mass m_p = 1.67 times 10^-27 kg and charge q_p = 1.6 times 10^-19 C. The electron and proton in the Bohr model of the third excited state of the hydrogen atom are separated by r = 8.464 times 10^-10 m. Calculate E_p. the magnitude of the electric field on the electron due to the proton. Calculate F, the magnitude of the force between the electron and proton. Calculate a_e, the magnitude of the acceleration of the electron. Calculate a_p the magnitude of the acceleration of the proton.

Explanation / Answer

a) Electric field due to proton on Electron Ep = KQ/r^2

K is constant = 9E9 kg m^2/C^2

Q is charge of proton =1.6 *10^-19 C

r is the distance between the proton and electron

so

Ep = (9*10^9 * 1.6 *10^-19)/(8.464 *10^-10)^2

Ep = 2.01 *10^9 N/C

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b)

Force F = KQ1Q2/r^2

F = Ep * Q

F = 2.01 *10^9 * -1.6 *10^-19

F = -3.216 *10^-10 N

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c)

as Force F = ma

accleration a = F/m

a = -3.216 *10^-10/(9.11 *10^-31)

a on electron = -3.53 *10^20 m/s^2

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d)

accleration on proton

ap = F/mp = -3.216 *10^-10/(1.67*10^-27)

ap = -1.925 *10^17 m/s^2

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e) this is a attractive force as it exists between two opposite charges

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