Mass of the electron is 9.11 x 10-31kg. Charge of an electron is -1.602 x 10-19
ID: 1586779 • Letter: M
Question
Mass of the electron is 9.11 x 10-31kg.
Charge of an electron is -1.602 x 10-19 C.
Charge of a proton is 1.602 x 10-19 C.
Coulomb’s constant: k = 8.99 x 109 Nm2 /C 2 1:
Radius of the electron’s orbit in hydrogen atom In a simple model of the hydrogen atom, the electron revolves in a circular orbit around the proton with a speed of 2.2 x 106 m/s.
Determine the radius of the electron’s orbit. [Hint: consider the centripetal force: Fc = mev 2 /r] 2: An electron in an electric field Determine the magnitude and direction (i.e., along the field or opposite to the field) of the acceleration experienced by an electron in an electric field of 756 N/C.
Explanation / Answer
hydrogen has 1 proton and 1 electron
centripetal force = electrostatic force
mv^2 / r = Kq1q2/r^2
(9.11*10^-31) * (2.2*10^6)^2 = (8.99*10^9)*(1.602*10^-19)^2 ) / r
r = 5.22*10^-11 m
the radius of orbit = 5.22*10^-11 m
b) when electron is placed in an electric field of 756 N/C
Force experienced = qE
F = (1.6*10^-19)*(756) = 1.21*10^-16 N (in the direction opposite to electric field)
acceleration = FORCE/mass
a = F/m = (1.21*10^-16 / 9.1*10^-31)
a = 1.33*10^14 m/s2 (in the direction opposite to electric field)