Explanation 1) Concept: We are given the final energy of the deuteron. We know that it is accelerated twice in each cycle, and energy it gained when it is accelerated. From this, we can find the number of revolutions made by the deuteron. From this number, we can find the velocity of the deuteron and the radius of the path. Using the radius of the path and number of revolutions made, we can find the total distance traveled. 2) Formula: i) n = F i n a l e n e r g y E n e r g y g a i n e d p e r r e v o l u t i o n ii) r = m v q B iii) K = 1 2 m v 2 3) Given: i) r c y c l t r o n = 53 c m = 0.53 m ii) Operating frequency f = 12 M H z iii) Accelerating potential between dees 80 k e V . 4) Calculation: We know that n = F i n a l e n e r g y E n e r g y g a i n e d p e r r e v o l u t i o n The deuteron accelerates twice in each cycle; each time, it receives an energy of 80 × 10 3 e V . We are given the final energy as 16.6 × 10 6 e V n = 16.6 × 10 6 e V 2 × 80 × 10 3 e V n = 103

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ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Chapter 28, Problem 37P

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Total path length traveled by deuteron

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Chapter 28, Problem 36P

Chapter 28, Problem 38P

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Estimate the total path length traveled by a deuteron in a cyclotron of radius 53 cm and operating frequency 12 MHz during the (entire) acceleration process. Assume that the accelerating potential between the dees is 80 kV.

A proton circulates in a cyclotron, beginning approximatelyat rest at the center.Whenever it passes through the gap betweendees, the electric potential difference between the dees is 200 V.(a) By how much does its kinetic energy increase with each passagethrough the gap? (b) What is its kinetic energy as it completes100 passes through the gap? Let r100 be the radius of the proton’scircular path as it completes those 100 passes and enters a dee,and let r101 be its next radius, as it enters a dee the next time. (c) Bywhat percentage does the radius increase when it changes fromr100 to r101? That is, what is percentage increase r101 - r100/r100 100%?

A cyclotron designed to accelerate protons has an outer radius of 0.350 m. The protons are emitted nearly at rest from a source at the center and are accelerated through 600 V each time they cross the gap between the dees. The dees are between the poles of an electromagnet where the field is 0.800 T. (a) Find the cyclotron frequency for the protons in this cyclotron. Find (b) the speed at which protons exit the cyclotron and (c) their maximum kinetic energy. (d) How many revolutions does a proton make in the cyclotron? (e) For what time interval does the proton accelerate?

Chapter 28 Solutions

Fundamentals of Physics Extended

Ch. 28 - Prob. 1Q Ch. 28 - Prob. 2Q Ch. 28 - Prob. 3Q Ch. 28 - Prob. 4Q Ch. 28 - In Module 28-2, we discussed a charged particle...Ch. 28 - Figure 28-26 shows crossed uniform electic and...Ch. 28 - Figure 28-27 shows the path of an electron that...Ch. 28 - Figure 28-28 shows the path of an electron in a...Ch. 28 - a In Checkpoint 5, if the dipole moment is rotated...Ch. 28 - Particle round about. Figure 28-29 shows 11 paths...

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Total path length traveled by deuteron

Solution Summary: The author calculates the total path length traveled by a deuteron.

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Total path length traveled by deuteron