The Bohr model of the hydrogen atom pictures the electron as a tiny particle mov

Question

The Bohr model of the hydrogen atom pictures the electron as a tiny particle moving in a circular orbit about a stationary proton. In the n=1 orbit the distance from the proton to the electron is 5.29*10^-11 m, and the linear speed of the electron is 2.18*10^6 m/s. (a) what is the angular velocity of the electron? (b) how many orbits about the proton does it make each second? (c) what is the electron's centripetal acceleration The Bohr model of the hydrogen atom pictures the electron as a tiny particle moving in a circular orbit about a stationary proton. In the n=1 orbit the distance from the proton to the electron is 5.29*10^-11 m, and the linear speed of the electron is 2.18*10^6 m/s. (a) what is the angular velocity of the electron? (b) how many orbits about the proton does it make each second? (c) what is the electron's centripetal acceleration

Explanation / Answer

Angular speed

omega = v / r = ( 2.18 * 10 ^ 6 m/s ) / 5.29* 10 ^ -11 m

= 4.12 * 10 ^ 16 rad /s

2)

number of orbits revolved by the electron in each second is

N = ( 4.12 * 10 ^ 16 rad /s) / 2 pi = 6.55* 10 ^ 15 rev / sec

3) electron centripetal acceleration is

a _ c = v^2 / r

= ( ( 2.18 * 10 ^ 6 m/s ) ^2 / 5.29* 10 ^ -11 m

=8.983 * 10 ^22 m/s^2

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