In the Bohr model of the atom, an electron can be thought of a small sphere that
ID: 1441654 • Letter: I
Question
In the Bohr model of the atom, an electron can be thought of a small sphere that rotates around the nucleus. In a hydrogen atom, an electron (m_e = 9.11 x 10^-31 kg) orbits a proton at a distance of 5.3 x 10^-11 m from the proton. If the proton pulls on the electron with a force of 9.2 x 10^8 N, how many revolutions per second docs the electron make? A pebble stuck to the wheel of a bike tire spins with a frequency of 3 revolutions per second at a radius of 30cm. What is its speed? What is its acceleration? In class, we talked about swinging a bucket of water around your head. If your arms are 0.7 m long (a guess), how with what frequency should you spin the bucket lo prevent yourself from getting wet? Consider the following diagram for problems 9 and 10.Explanation / Answer
6. for circular motion,
force = m w^2 r
9.2 x 10^-8 = 9.11 x 10^-31 x w^2 x 5.3 x 10^-11
w = 4.365 x 10^16 rad/s
T = 2pi / w = 1.44 x 10^-16 s
7. w = 3 rev / s = 3 x 2pi rad/s = 6pi / s
speed = w r = 6pi x 0.30 =5.65 m/s
a = w^2 r = (6pi)^2 x 0.30 = 106.6 m/s^2
8. at top position,
N + mg = mw^2 r
N = mw^2 r - mg = 0
w = sqrt(g/r) = 3.74 rad/s or 0.60 rev/s