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 $9.0 f m$ . 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 is $4 \times 10^{7} m / s$

Step by step solution

Given information and theory used

Given :

Iron is element number : $26$

Diameter of the nucleus is : $9.0 f m$

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, $\frac{m v^{2}}{2} = k \frac{q_{1} q_{2}}{r}$

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

We get $\frac{m v^{2}}{2} = k \frac{26 \cdot 2 e^{2}}{d}$

by substituting $q_{1} = 26 e, q_{2} = e, and r = d / 2 .$

We may express the speed from here as :

$v = \sqrt{\frac{26 \times 4 e^{2} k}{m d}} = 2 e \sqrt{\frac{26 k}{m d}}$

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

v = 2 \times 1.6 10^{- 19} \sqrt{\frac{26 \times 9 . 10^{9}}{1.67 \times 10^{- 27} \times 9 \times 10^{- 15}}} = 4 \times 10^{7} m / s

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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 $9.0 f m$ . What initial speed does the proton need to just reach the surface of the nucleus? Assume the nucleus remains at rest.

Short Answer

Step by step solution

Given information and theory used

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

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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

Step by step solution

Given information and theory used

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Astrophysics

Fundamentals of Physics

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Force

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Study anywhere. Anytime. Across all devices.

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 $9.0 f m$ . What initial speed does the proton need to just reach the surface of the nucleus? Assume the nucleus remains at rest.