Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
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Chapter 25, Problem 36P
To determine
The speed of protons in the solar wind.
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The proton-proton chain is the multi-step process that powers the Sun via fusion of hydrogen into
helium. In the fırst step of the proton-proton chain, a positron is produced when two protons fuse
together (with one proton converting to a neutron). The emitted positron quickly collides with its
anti-particle, the electron. (Recall that the electron and positron have exactly the same mass, but
opposite electric charges.) The electron and positron then completely annihilate, converting all of
their rest mass into two gamma-ray photons.
Given a single particle of mass m, the amount of energy E produced when all of its mass is
converted to energy is given by Einstein's famous formula, E = m c2, where c = 2.9979 x 108 m/s is
the speed of light. We also learned that the energy Ephoton of a single photon is related to its
frequency f or wavelength A via Ephoton = hf = he, where h = 6.626 x 10-34 m² kg/s is a
fundamental constant of nature called Planck's constant.
In the electron + positron…
provides some pertinent background for this problem. Suppose a single electron orbits about a nucleus containing two protons (+2e), as would be the case for a helium atom from which one of the naturally occurring electrons is removed. The radius of the orbit is 3.09 × 10-11 m. Determine the magnitude of the electron's centripetal acceleration.
of the average electric field that could accelerar
to a speed of 1,0 x 10' m/s. Ignore any relainist
effects (Chapter 26) and determine the magnitude
tor is 4.0 m long and must accelerate protons from red
killing the malignant cells. Suppose a proton acceler
ton therapy in which proton beams are accelerated o
high energies, then directed to collide into a ru
56. + e Some forms of cancer can be treated using pr
these protons
Chapter 25 Solutions
Physics for Scientists and Engineers, Vol. 1
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- (a) At what speed will a proton move in a circular path of the same radius as the electron in Exercise 22.12? (b) What would the radius of the path be it the proton had the same speed as the electron? (c) What would the radius be if the proton had the same kinetic energy as the electron? (d) The same momentum?arrow_forwardA proton is fired from very far away directly at a fixed particle with charge q = 1.28 1018 C. If the initial speed of the proton is 2.4 105 m/s, what is its distance of closest approach to the fixed particle? The mass of a proton is 1.67 1027 kg.arrow_forwardCalculate the angular velocity of an electron orbiting a proton in the hydrogen atom, given the radius of the orbit is 0.5301010 m. You may assume that the proton is stationary and the centripetal force is supplied by Coulomb attraction.arrow_forward
- (a) At what speed will a proton move in a circular path of the same radius as the electron in the previous exercise? (b) What would the radius of the path be if tlie proton had the same speed as the election? (c) What would the radius be if the proton had tlie same kinetic energy' as die electron? (d) The same momentum?arrow_forward(a) Find the potential difference VB required to stop an electron (called a slopping potential) moving with an initial speed of 2.85 107 m/s. (b) Would a proton traveling at the same speed require a greater or lesser magnitude potential difference? Explain. (c) Find a symbolic expression for the ratio of the proton stopping potential and the electron stopping potential, Vp/Ve. The answer should be in terms of the proton mass mp and electron mass me.arrow_forwardCalculate the angular velocity ω of an electron orbiting a proton in an atom, assuming the radius of the orbit is 5.02×10^-11 m. You may assume that the proton is stationary and the centripetal force is supplied by Coulomb attraction.arrow_forward
- 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%?arrow_forwardA proton is located at the origin, and a second proton is located on the x-axis at x₁ = 6.02 fm (1 fm = (a) Calculate the electric potential energy associated with this configuration. 3.827e-14 J 10-15 m). (b) An alpha particle (charge = 2e, mass = 6.64 × 10-27 kg) is now placed at (x₂, Y₂) = (3.01, 3.01) fm. Calculate the electric potential energy associated with this configuration. 2.55e-13 J (c) Starting with the three particle system, find the change in electric potential energy if the alpha particle is allowed to escape to infinity while the two protons remain fixed in place. (Throughout, neglect any radiation effects.) -2.167e-13 J (d) Use conservation of energy to calculate the speed of the alpha particle at infinity. 8.079e6 m/s (e) If the two protons are released from rest and the alpha particle remains fixed, calculate the speed of the protons at infinity. 1.1392e7 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake…arrow_forwardAn alpha particle (charge +3.20 x 10-19C, mass 6.64 x 10-27kg) is initially 5.2 cm away from a fixed gold nucleus (charge +1.26 x 10-17C, mass 3.29 x 10-25kg) and moving toward the nucleus with a speed of 8.1 x 105m/s. How close to the nucleus does the alpha particle get? (Note: The nucleus diameter is approximately 10-14m and the and alpha particle’s is 10-15m.)arrow_forward
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