In the Bohr model of the hydrogen atom, a single electron revolves around a single proton in a circle of radius r. Assume that the proton remains at rest.
a. By equating the electric force to the electron mass times its acceleration, derive an expression for the electron's speed. Express your answer in terms of electron`s charge e, its mass m and orbit radius r.
b. Obtain an expression for the electron's kinetic energy.
c. Obtain an expression for the total energy.
d. Calculate the total energy using 5.29*10^-11 m. Give your answer in joules.
e. Give the answer of part (d) in eV.
The Attempt at a Solution
a. F = m(v^2/r)
(k*Q^2)/(r^2) = m*(v^2/r)
k*Q^2*r = m*v^2*r^2, where Q = e = 1.60*10^-19 C
v = sqrt[(k*e^2)/(m*r)]??
b. KE = (m*v^2)/2 = 0.5*[(e^2*k)/(r)] = (e^2)/(8*pi*episilon_0*r) ??
c. E_total = KE + PE = [(e^2)/(8*pi*episilon_0*r)] + [(-e^2)/(4*pi*epsilon_0*r)]
d. E_ total = (e^2)/(8*pi*episilon_0*r) + (-e^2)/(4*pi*epsilon_0*r)
= [(e^2)/(4*pi*epsilon_0*r)]*[0.5 – 1]
= (-0.5)*[1.6*10^-19)^2]/[4*pi*epsilon_0*(5.29*10^-11 m)] = -2.18*10^-18 J ???
E. (-2.18*10^-18 J)/(1.602*10^-19 J/eV) = -13.6 eV?