Question

In Bohr's model for the Hydrogen atom, the electron when it is at the third level rotates in a circular orbit around the proton, at a radius of 4.7 x 10^-10 m. The proton has a positive electric charge of 1.6 x10^-19 C, while the electron has the same charge with an opposite sign. The electrical force between the two particles is responsible for the centripetal force that keeps the electron in its orbit. The mass of the proton is 2,000 times greater than that of the electron, so we can assume that the proton is still and only the electron rotates. The mass of the electron is 9.11x ​​10^-31 kg

1) Make a drawing that explains the electric field lines from the proton to the electron that hold them together and sketch the orbit of the electron. Indicate the electron velocity vector on the drawing.






2) Using Coulomb's Law, calculate the value of the electric force between the proton and the electron.


3) From Newton's law, find the value of the centripetal acceleration of the electron.





4) Now calculate the value of the velocity of the electron in its orbit


5) Find the value of the angular momentum (L = m v r) of the electron and verify that this value is equal (approximately) to twice the Planck constant (h bar = 1.05 x 10^-34 kg m² / s)

Answer 1