Chapter 27: Q. 44 (page 763)

In a classic model of the hydrogen atom, the electron moves around the proton in a circular orbit of radius $0.053 n m .$
a. What is the electron's orbital frequency?
b. What is the effective current of the electron?

Short Answer

Expert verified

a. The electron's orbital frequency is $6.56 \times 10^{15} Hz$

b. The effective current of the electron is $1.05 mA .$

Step by step solution

Given Information (Part a)

Hydrogen atom circular orbit of the radius is $0.053 n m$ .

Explanation (Part a)

The centripetal force is the electrostatic one, then

$\frac{k e^{2}}{R^{2}} = F = m ω^{2} R$

The angular frequency is just $ω = 2 π f$ ,

$\frac{k e^{2}}{R^{2}} = F = 4 π^{2} m f^{2} R$

Rearrange for the frequency as,

$f^{2} = \frac{k e^{2}}{4 π^{2} m R^{3}},$

The frequency will be given by

$f = \frac{e}{2 π} \sqrt{\frac{k}{m R^{3}}}$

Substituting the values,

$f = (\frac{1.6 \cdot 10^{- 19} C}{2 π} \sqrt{\frac{9 \times 10^{9}}{9.1 \times 10^{- 31} k g \cdot {(5.3 \cdot 10^{- 11} m)}^{3}}})$

$= 6.56 \cdot 10^{15} Hz$

Final Answer (Part a)

Hence, the hydrogen atom circular orbit of the radius is $6.56 \times 10^{15} Hz$ .

Given Information (Part b)

Hydrogen atom circular orbit of the radius is $0.053 n m .$

Explanation (Part b)

In one second, the effective current is equal to the frequency times the elementary charge, and this is the total charge that is passed.

That is,

$q_{e f f} = f e = (6.56 \times 10^{15} H z \times 1.6 \times 10^{- 19} C)$

$q_{e f f} = 1.05 \times 10^{- 3} A .$

Final Answer (Part b)

The effective current of the electron is $1.0 m A .$

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In a classic model of the hydrogen atom, the electron moves around the proton in a circular orbit of radius $0.053 n m .$
a. What is the electron's orbital frequency?
b. What is the effective current of the electron?

Short Answer

Step by step solution

Given Information (Part a)

Explanation (Part a)

Final Answer (Part a)

Given Information (Part b)

Explanation (Part b)

Final Answer (Part b)

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In a classic model of the hydrogen atom, the electron moves around the proton in a circular orbit of radius0.053nm.a. What is the electron's orbital frequency?b. What is the effective current of the electron?

Short Answer

Step by step solution

Given Information (Part a)

Explanation (Part a)

Final Answer (Part a)

Given Information (Part b)

Explanation (Part b)

Final Answer (Part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

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Waves Physics

Study anywhere. Anytime. Across all devices.

In a classic model of the hydrogen atom, the electron moves around the proton in a circular orbit of radius $0.053 n m .$
a. What is the electron's orbital frequency?
b. What is the effective current of the electron?