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Chapter 25: Q.56 (page 712)

A proton is fired from far away toward the nucleus of an iron atom. Iron is element number 26, and the diameter of the nucleus is 9.0fm. What initial speed does the proton need to just reach the surface of the nucleus? Assume the nucleus remains at rest.

Short Answer

Expert verified

The initial speed does the proton need to just reach the surface of the nucleus is4×107m/s

Step by step solution

01

Given information and theory used 

Given :

Iron is element number :26

Diameter of the nucleus is : 9.0fm

Theory used :

We can deduce from the law of conservation of energy that all kinetic energy will be converted to electric potential energy.

As a result,mv22=kq1q2r

02

Calculating the initial speed that the proton needs to just reach the surface of the nucleus 

We get mv22=k26·2e2d

by substituting q1=26e,q2=e,andr=d/2.

We may express the speed from here as :

v=26×4e2kmd=2e26kmd

We can find the speed to be v2 by substituting our numerical numbers.

v=2×1.610-1926×9.1091.67×10-27×9×10-15=4×107m/s

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Most popular questions from this chapter

Your lab assignment for the week is to measure the amount of charge on the 6.0-cm-diameter metal sphere of a Van de Graaff generator. To do so, you’re going to use a spring with a spring constant of 0.65 N/m to launch a small, 1.5 g bead horizontally toward the sphere. You can reliably charge the bead to 2.5 nC, and your plan is to use a video camera to measure the bead’s closest approach to the edge of the sphere as you change the compression of the spring. Your data is as follows:

Use an appropriate graph of the data to determine the sphere’s charge in nC. You can assume that the bead’s motion is entirely horizontal, that the spring is so far away that the bead has no interaction with the sphere as it’s launched, and that the approaching bead does not alter the charge distribution on the sphere.

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The electron gun in an old TV picture tube accelerates electrons between two parallel plates 1.2 cm apart with a 25 kV potential difference between them. The electrons enter through a small hole in the negative plate, accelerate, then exit through a small hole in the positive plate. Assume that the holes are small enough not to affect the electric field or potential.

a. What is the electric field strength between the plates?

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Note: The exit speed is so fast that we really need to use the theory of relativity to compute an accurate value.

Your answer to part b is in the right range but a little too big.
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