In the Bohr model of the hydrogen atom, the electron is rotating in a circular o
ID: 1564469 • Letter: I
Question
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 = 0.529×1010 m. (Hint: when a point object is in a circular trajectory, its acceleration toward the center is always v2/r )
a) Find the tangential speed of the electron in the first Bohr orbit.
b) Find the magnitude and the direction of the electric field vector due to the proton at the location of the electron.
c) 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
Here
ao = 0.529*10-10 m, k = 9.0*109, m= 9.1*10-31 kg
a) From F = ma,
ke2/ao2 =mv2/ao
Hence the tangential speed of the electron v =e[k/(mao)] = 2.19*106 m/s
b) E = ke/ao2 = 5.15*1011 V/m
Direction: towards the proton
c) Using
V = ke/ao= 27.2 V