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Chapter 22: Q. 37 (page 625)

The nucleus of a125Xeatom (an isotope of the element xenon with mass 125u) is 6.0fmin diameter. It has 54protons and charge q=+54e.

a. What is the electric force on a proton 2.0fmfrom the surface of the nucleus?

b. What is the proton’s acceleration?

Hint: Treat the spherical nucleus as a point charge

Short Answer

Expert verified

(a) The electric force of proton F=497.6N.

(b) The acceleration of the protona=2.99×1029ms2.

Step by step solution

01

Find electric force (part a)

Because a proton is 2.0fmfrom the SURFACE of the Xenon atom, you must add the 2.0fmto the radius of the Xeatom, resulting in a distance of 5.0fmbetween neutron and the centre of the Xeatom.

2fm+3fm=5fm=5×10−15m

We must now determine the number of currently operates by the Xeatom. Because there are 54protons in the problem, we must increase it by the charge of a proton, which is 1×10−19C.

541×10−19C=8.64×10−18C

Substitute F=kq1q2r2in equation andk=9×109Nm2C2

F=kq1q2r2

F=k8.64×10−18C1.6×−19C5×10−15m2

F=497.6N

02

Find the acceleration of proton (part b)

To find the proton's force, use Newton's F=maequation. In the equation, use the charge of a proton.

F=m×a

a=Fm

a=497.6N1.661×10−27Kg

a=2.99×1029ms2

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Most popular questions from this chapter

Three 1.0 nC charges are placed as shown in FIGURE P22.66. Each of these charges creates an electric field E→at a point 3.0 cm in front of the middle charge.

  1. What are the three fields E1→, E2→, and E3→created by the three charges? Write your answer for each as a vector in component form.
  2. Do you think that electric fields obey a principle of superposition? That is, is there a “net field” at this point given by E→net=E1→+E2→+E3→? Use what you learned in this chapter and previously in our study of forces to argue why this is or is not true.
  3. If it is true, what is E→net?

Two 1.0 kg masses are 1.0 m apart (center to center) on a frictionless table. Each has +10 mC of charge.

a. What is the magnitude of the electric force on one of the masses?

b. What is the initial acceleration of this mass if it is released and allowed to move?

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 +12 nC charge is located at the origin.

a. What are the electric fields at the positions (x, y) = (5.0 cm, 0 cm), (-5.0 cm, 5.0 cm), and (-5.0 cm, -5.0 cm)? Write each electric field vector in component form.

b. Draw a field diagram showing the electric field vectors at these points.

You have two neutral metal spheres on wood stands. Devise a procedure for charging the spheres so that they will have opposite charges of exactly equal magnitude. Use charge diagrams to explain your procedure.
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