Question

In the Bohr model, as it is known today, the electron is imagined to move in a circular orbit about a stationary proton. The force responsible for the electron's circular motion is the electric force of attraction between the electron and the proton.

If the speed of the electron were 3.1×10⁵ m/s , what would be the corresponding orbital radius?

Answer 1

Here, we can equate the electric force between electron and proton and centripetal force on the electron

kq1q2 / r² = mv² / r

kq1q2 / r = mv²

r = kq1q2 / mv²

here m is mass of electron ( not proton)

r = 9e9 * 1.6e-19 * 1.6e-19 / 9.1e-31 * (3.1e5)²

r = 2.635e-9 m

r = 2.635 nm