Any help would be appreciated! Thanks! In the Bohr model of the hydrogen atom, t

Question

Any help would be appreciated! Thanks!

In the Bohr model of the hydrogen atom, the electron is rotating in a circular orbit around a proton. The lowest possible orbit is called the "First Bohr Orbit" and its radius is given as a0 = 0.529 x 10-infinity m. (Hint: when a point object is in a circular trajectory, its acceleration toward the center is always v2/r) Find the tangential speed of the electron in the first Bohr orbit. Find the magnitude and the direction of the electric field vector due to the proton at the location of the electron. Find the electric potential (in volts) due to the proton at the location of the electron. Note that the electric potential is zero at infinity.

Explanation / Answer

Mass of electron m = 9.1 * 10^-31 Kg

Charge on electron e = 1.6 * 10^-19 C

Radius of the orbit r = 0.529*10^-10 m

(a)

Tangential speed of electron v = Sqrt[(K e^2)/(m r)]

                                             = 2.187*10^6 m/s

(b)

Electric field E = Ke/r^2

                       = (9*10^9 * 1.6*10^-19)/(0.529*10^-10)^2

                        = 51.457*10^10 N/m    (Along the tangential to the orbit)

(c)     

Electric potential V = E* r

                             = 27.22 volt

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