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Chapter 23: Q. 59 (page 656)

In a classical model of the hydrogen atom, the electron orbits the proton in a circular orbit of radius0.053nm. What is the orbital frequency? The proton is so much more massive than the electron that you can assume the proton is at rest.

Short Answer

Expert verified

The orbital frequency is6.5脳1015Hz

Step by step solution

01

Given information and formula 

Given :

The electron orbits the proton in an orbit of radius : 0.053nm

The proton is so much more massive than the electron that we can assume the proton is at rest.

Theory used :

Orbital frequency is calculated using the formula :f=w2蟺

The electron receives centripetal force from electrostatic force. That isFe=Fc

02

Calculating the frequency value

The electron receives centripetal force from electrostatic force.

Fe=Fc鈬�14蟺蔚0脳Per2=mw虏r鈬�w2=9脳109脳10-9脳(1.6脳10-19)2(0.053脳10-9)3脳9.11脳10-31鈬�w=4.12脳1016rad/s

Now we can calculate orbital frequency using the following formula:

f=w2蟺

Replace the values in the relationship and calculate the frequency value:

f=4.12脳10162脳3.14=6.5脳1015Hz

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