Question

#6) The electron is imagined to move in a circular orbit about a stationary proton in the Bohr model (we will talk more about the Bohr model later). If the speed of the electron were 6.5 x 105 m/s, what would be the corresponding orbital radius? Mass of an electron is 9.11 x 101 kg, and magnitude of charge for an electron and proton is 1.60 x 10 1s Ceach. Coulomb's constant k is 9.0x 10 N m2/c2 6.5 x 10 m/s

Answer 1

mass of electron, m = 9.11 X 10^-31 kg

magnitude of charge of proton= magnitude of charge of electron= q = 1.6 X 10^-19 C.

velocity of electron , v = 6.5 X 10⁵ m/s

let Bohr radius be r.

Magnitude of the electrostatic force on the electron = magnitude of the centripetal force on the electron

k (q² / r² ) = mv²/r

Thus, r = (k q² )/ (mv²) = ( (9X10⁹) X (1.6 X 10^-19 )²) / ( 9.11 X 10^-31 X (6.5 X 10⁵)²) = 5 .986 X 10^-8 m = 598.6 Angstrom (ans)