In the model of the hydrogen atom due to Niels Bohr, the electron moves around the proton at a speed of 3.3 × 106 m/s in a circle of radius 5.7 × 10-11 m. Considering the orbiting electron to be a small current loop, determine the magnetic moment associated with this motion. (Hint: The electron travels around the circle in a time equal to the period of the motion.)

Respuesta :

Answer:

[tex]1.5048\times 10^{-23}\ Am^2[/tex]

Explanation:

q = Charge of proton = [tex]1.6\times 10^{-19}\ C[/tex]

r = Radius of circle = [tex]5.7\times 10^{-11}\ m[/tex]

v = Velocity of proton = [tex]3.3\times 10^6\ m/s[/tex]

Magnetic moment is given by

[tex]M=\frac{1}{2}qrv\\\Rightarrow M=\frac{1}{2}1.6\times 10^{-19}\times 5.7\times 10^{-11}\times 3.3\times 10^6\\\Rightarrow M=1.5048\times 10^{-23}\ Am^2[/tex]

The magnetic moment associated with this motion is [tex]1.5048\times 10^{-23}\ Am^2[/tex]