In the Bohr model of the hydrogen atom, the electron moves around the one-proton
ID: 2127558 • Letter: I
Question
In the Bohr model of the hydrogen atom, the electron moves around the one-proton nucleus on circular orbits of well-determined radii, given by
where
n Fe Fg 1 2 3 4In the Bohr model of the hydrogen atom, the electron moves around the one-proton nucleus on circular orbits of well-determined radii, given by is an integer that defines the orbit and aB = 5.29 times 10-11 m is the radius of the first (minimum) orbit, called the Bohr radius. Calculate the force of electrostatic interaction between the electron and the proton in the hydrogen atom for the first four orbits. Compare the strength of this interaction to the gravitational interaction between the proton and the electron.
Explanation / Answer
Fe=k*q1*q2/r^2....
Fg=G*m1*m2/r^2.......
For n=1...
Fe= 0.823*10^-7 N............Fg=3.622*10^-47 N......
for n=2.....
Fe=0.823*10^-7 N/4=0.20575*10^-7 N
Fg=0.9055*10^-47 N..........
For n=3.....
Fe = 0.823*10^-7 N/9=0.091444 N...
Fg=3.622*10^-47 N /9 =0.402*10^-47 N...
For n=4....
Fe= 0.823*10^-7 N/16=0.0514*10^-7 N..
Fg=3.622*10^-47 N/16......=0.2263*10^-47 N