Calculate, at what angular speed is the electron orbiting the nucleus and what is its normal acceleration

Question

In the first approximation, it can be assumed that the electron in the hydrogen atom moves in a circular orbit at a constant velocity v. Calculate, at what angular speed is the electron orbiting the nucleus and what is its normal acceleration. Assume that the radius of orbit r =0.5 ∙ 10 -10 m and velocity of electron along this orbit v = 2.2 ∙ l0-6 m / s. [4.4 ∙ 10 -16 rad / s; 9.7-10 22 m / s 2].

Answer 1

First of all, the speed given in the question is wrong.

v = 2.2 x 10⁶ m/s (the problem says 2.2 x 10^-6 m/s)

r = 0.5 x 10^-10 m

ω = v/r

Plug in v and r and get

ω = 4.4 x 10¹⁶ rad/s

Note the answer for ω in the question has the wrong sign for the power of 10. Now get the normal acceleration from

a_n = v²/r = ωv = 9.68 x 10²² m/s²