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University of Washington

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Problem 80 Hard Difficulty

The diameter of the hydrogen atom is $10^{-10} \mathrm{m}$. In Bohr's model this means that the electron travels a distance of about $3 \times 10^{-10} \mathrm{m}$ in orbiting the atom once. If the orbital frequency is $7 \times 10^{15} \mathrm{Hz}$, what is the speed of the electron? How does this speed compare with that of light?

Answer

$1.43 \times 10^{2}$

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Top Physics 103 Educators
Elyse G.

Cornell University

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Farnaz M.

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Jared E.

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Video Transcript

in this question. We are having a hydrogen atom. So, uh, nucleus, Yeah. Um and then the diameter is given to be 10 to the minus 10 meters. So that's the conference. So the electron to the electron, it's going around a nucleus, and the circumference is the conference. Is she times into the negative 10 meter, Right. And then we also given that ah ah, Oh, you know, frequency is equal to seven times 10 to the 15 minutes. So this, uh, tells you that in one seconds in one second, the electron goes around the nucleus seven times, 10 to the 15 times. Okay, so we wants to find a speed off the electron, so speed to be distinct. But by time, in this case, you would just be these things times the frequency. Okay, because one over time, the distances that's the conference. That time will be the 10 take into trouble. One wrong one of the time would be the frequency. So putting in the values three times 10 to the negative, 10 meters times the frequency, which is £7.10 to the 15 hurts, and you get 2.1 times. And to the six because her second. Okay, so if you compared to speed off light, this is 0.7 times. Let's be awfully. Okay. So, um, so this is this is this is the answer, uh, for the speed up the electron.

University of Washington
Top Physics 103 Educators
Elyse G.

Cornell University

LB
Liev B.

Numerade Educator

Farnaz M.

Simon Fraser University

Jared E.

University of Winnipeg