In an effort to better understand the behavior of atomic systems, the Danish phy

Question

In an effort to better understand the behavior of atomic systems, the Danish physicist Niels Bohr (1885-1962) introduced a simple model for the hydrogen atom. In the Bohr model, as it is known today, the electron is imagined to move in a circular orbit about a stationary proton. The force responsible for the electron's circular motion is the electric force of attraction between the electron and the proton. The radius of the electron's orbit is 5.29×1011m, its mass is me=9.11×1031kg, and the electron's speed is 2.19×106m/s.

Find the speed of the electron for a nucleus of charge +2e.

Explanation / Answer

Electrostatic force = m (centripetal acc.)

k q1 q2 / r^2 = m v^2 / r

k q1 q2 / r = m v^2

(9 x 10^9) (1.6 x 10^-19) (2 x 1.6 x 10^-19) / (5.29 x 10^-11) = (9.11 x 10^-31) v^2

v = 3.09 x 10^6 m/s

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