In a simplified model of a hydrogen atom, the electron moves around the proton nucleus in a circular orbit of radius 0.53 × 10−10 m

For the answer to the question above,
 a) Use F = k * q1 * q2 / d² 
where k = 8.99e9 N·m²/C² 
and q1 = -1.602e-19 C (electron) 
and q2 = 1.602e-19 C (proton) 
and d = distance between point charges = 0.53e-10 m 
The negative result indicates "attraction". 

b) Here, just use F = ma 
where F was found above, and 
m = mass of electron = 9.11e-31kg, if memory serves 
a = radial acceleration 

c) Now use a = v² / r 
where a was found above 
and r was given 

d) period T = 2π / ω = 2πr / v 
where v was found above 
and r was given