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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 radius0.053nm.

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 is6.56脳1015Hz

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

Step by step solution

01

Given Information (Part a)

Hydrogen atom circular orbit of the radius is0.053nm.

02

Explanation (Part a)

The centripetal force is the electrostatic one, then

ke2R2=F=m蝇2R

The angular frequency is just 蝇=2蟺f,

ke2R2=F=4蟺2mf2R

Rearrange for the frequency as,

f2=ke24蟺2mR3,

The frequency will be given by

f=e2蟺kmR3

Substituting the values,

f=1.6鈰�10鈭�19C2蟺9脳1099.1脳10鈭�31kg鈰�5.3鈰�10鈭�11m3

=6.56鈰�1015Hz

03

Final Answer (Part a)

Hence, the hydrogen atom circular orbit of the radius is6.56脳1015Hz.

04

Given Information (Part b) 

Hydrogen atom circular orbit of the radius is0.053nm.

05

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,

qeff=fe=6.56脳1015Hz脳1.6脳10-19C

qeff=1.05脳10-3A.

06

Final Answer (Part b) 

The effective current of the electron is1.0mA.

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