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Chapter 22: Q. 54 (page 626)

In a simple model of the hydrogen atom, the electron moves in a circular orbit of radius 0.053nmaround a stationary proton. How many revolutions per second does the electron make?

Short Answer

Expert verified

Revolutions per second for electron is6.6×1015rev/s.

Step by step solution

01

Formula for force

The two particles exert forces on each other, with the force decreasing as the distance between them grows and increasing as the size of the charges increases.

The force that exists between a proton and an electron is known as the proton-electron force.

Coulomb 's law force is,

FC=Kq1q2r2=Ke2r2

The electrostatic constant is 9.0×109N·m2/C29.0×109N·m2/C2.

Because the electron revolves around the nucleus, it has a centripetal force, which is given by

Fe=mω2r

02

Calculation for revolution per second

Angular velocity,

FC=Fe

Ke2r2=mω2r

ω=Ke2mr3

=9.0×109N·m2/C21.6×10-19C29.1×10-31kg0.053×10-9m3

=4.12×1016rad/s

We discovered the angular velocity in rad/sec, so we'll convert it to rev/s.

localid="1649151421673" ω=4.12×1016rad/srev2πrad

=6.6×1015rev/s

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Most popular questions from this chapter

Pennies today are copper-covered zinc, but older pennies are 3.1gof solid copper. What are the total positive charge and total negative charge in a solid copper penny that is electrically neutral?

You sometimes create a spark when you touch a doorknob after shuffling your feet on a carpet. Why? The air always has a few free electrons that have been kicked out of atoms by cosmic rays. If an electric field is present, a free electron is accelerated until it collides with an air molecule. Most such collisions are elastic, so the electron collides, accelerates, collides, accelerates, and so on, gradually gaining speed. But if the electron’s kinetic energy just before a collision is 2.0×10-18Jor more, it has sufficient energy to kick an electron out of the molecule it hits. Where there was one free electron, now there are two! Each of these can then accelerate, hit a molecule, and kick out another electron. Then there will be four free electrons. In other words, as FIGURE P22.61 shows, a sufficiently strong electric field causes a “chain reaction” of electron production. This is called a breakdown of the air. The current of moving electrons is what gives you the shock, and a spark is generated when the electrons recombine with the positive ions and give off excess energy as a burst of light.

  1. The average distance between ionizing collisions is 2.0μm. (The electron’s mean free path is less than this, but most collisions are elastic collisions in which the electron bounces with no loss of energy.) What acceleration must an electron have to gain of kinetic energy in this distance?
  2. What force must act on an electron to give it the acceleration found in part a?
  3. What strength electric field will exert this much force on an electron? This is the breakdown field strength. Note: The measured breakdown field strength is a little less than your calculated value because our model of the process is a bit too simple. Even so, your calculated value is close.
  4. Suppose a free electron in air is 1.0 cm away from a point charge. What minimum charge is needed to cause a breakdown and create a spark as the electron moves toward the point charge?

A 10.0nCcharge is located at position (x,y)=(1.0cm,2.0cm). At what (x,y)position(s) is the electric field

  1. localid="1648545048454" −225,000i^N/C
  2. localid="1648545057140" (161,000i^+80,500j^)N/C
  3. (21,600i^−28,800j^)N/C

Two 3.0 g point charges on 1.0-m-long threads repel each other after being equally charged, as shown in FIGURE CP22.73. What is the magnitude of the charge q?

A 0.10ghoneybee acquires a charge of +23pCwhile flying.

a. The earth’s electric field near the surface is typically (100N/C, downward). What is the ratio of the electric force on the bee to the bee’s weight?

b. What electric field (strength and direction) would allow the bee to hang suspended in the air?
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