Chapter 23: Q. 59 (page 656)

In a classical model of the hydrogen atom, the electron orbits the proton in a circular orbit of radius $0.053 n m$ . 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 is $6.5 \times 10^{15} H z$

Step by step solution

Given information and formula

Given :

The electron orbits the proton in an orbit of radius : $0.053 n m$

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 : $f = \frac{w}{2 π}$

The electron receives centripetal force from electrostatic force. That is $F_{e} = F_{c}$

Calculating the frequency value

The electron receives centripetal force from electrostatic force.

$F_{e} = F_{c} \Rightarrow \frac{1}{4 π ε_{0}} \times \frac{P_{e}}{r^{2}} = \frac{m w ²}{r} \Rightarrow w^{2} = \frac{9 \times 10^{9} \times 10^{- 9} \times {(1.6 \times 10^{- 19})}^{2}}{{(0.053 \times 10^{- 9})}^{3} \times 9.11 \times 10^{- 31}} \Rightarrow w = 4.12 \times 10^{16} r a d / s$

Now we can calculate orbital frequency using the following formula:

$f = \frac{w}{2 π}$

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

$f = \frac{4.12 \times 10^{16}}{2 \times 3.14} = 6.5 \times 10^{15} H z$

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In a classical model of the hydrogen atom, the electron orbits the proton in a circular orbit of radius $0.053 n m$ . 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

Step by step solution

Given information and formula

Calculating the frequency value

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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

Step by step solution

Given information and formula

Calculating the frequency value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Physical Quantities And Units

Further Mechanics and Thermal Physics

Electricity and Magnetism

Circular Motion and Gravitation

Conservation of Energy and Momentum

Study anywhere. Anytime. Across all devices.

In a classical model of the hydrogen atom, the electron orbits the proton in a circular orbit of radius $0.053 n m$ . What is the orbital frequency? The proton is so much more massive than the electron that you can assume the proton is at rest.