The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model, you can view hydrogen, the simplest atom, as having a single electron in a circular orbit 1.06×10-10 m in diameter.
(a) If the average speed of the electron in this orbit is known to be 2.20×106 m/s, calculate the number of revolutions per second it makes about the nucleus.
(b) What is the electron’s average velocity?
Solution:
Part A
The formula to be used is
average speedr=timedistance=td
Rearranging the formula–solving for the distance
d=r×t
Substituting the given values for 1 second period
d=(2.20×106m/s)(1s)=2.20×106meters
This is the total distance traveled in 1 sec.
With the given radius, the total distance traveled in 1 revolution is
1revolution=2πr=πd=π(1.06×10−10m)
Therefore, the total number of revolutions traveled in 1 second is
no. of revolutions=distance in 1 revolutiontotal distance=π(1.06×10−10)2.20×106=6.61×1015 revolutions (Answer)
Part B
In one complete revolution, the electron will go back to its original position. Thus, there is no net displacement. Therefore,
vv=ΔtΔx=0 m/s (Answer)