college physics
posted by vishal on .
In the Bohr theory of the hydrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is approximately 0.542 multiplied by 1010 m. (The actual value is 0.529 multiplied by 1010 m.)
(a) Find the electric force exerted on each particle, based on the approximate (not actual) radius given.
N
(b) If this force causes the centripetal acceleration of the electron, what is the speed of the electron?
m/s

F=k•q₁•q₂/r²
k =9•10⁹ N•m²/C²
e =1.6•10⁻¹⁹ C.
F=k•e²/r²=
=9•10⁹•(1.6•10⁻¹⁹)²/(0.542•10⁻¹⁰)² =
=7.84•10⁻⁸ N
ma=mv²/R= F
v=sqrt(FR/m)=
=sqrt(7.84•10⁻⁸•0.542•10⁻¹⁰/9.1•10⁻³¹)=
=2.16•10⁶ m/s