Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 38, Problem 53GP
To determine
The kinetic energy and speed of alpha particle which is trapped in a nucleus.
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In a Rutherford scattering experiment, assume that an incident alpha particle (radius 1.80 fm) is headed directly toward a target gold nucleus (radius 6.23 fm).What energy must the alpha particle have to just barely “touch” the gold nucleus?
Alpha particles are projected toward a gold foil from a distance that is sufficiently large to consider the Coulomb force negligible. The gold nuclei have 118 neutrons and 79 protons. If a 3.60 MeV alpha particle has a scattering angle of 180° and the gold nucleus does not recoil, determine the distance of closest approach of the alpha particle.
In a Rutherford scattering experiment, an a - particle (charge = 12e) heads directly toward a gold nucleus (charge = +79e). The alpha - particle had a kinetic energy of 5.0 MeV when very far (r -> infinity`) from the nucleus. Assuming the gold nucleus to be fixed in space, determine the distance of closest approach. Hint: Use conservation of energy with PE = ke q1q2/r.
Chapter 38 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 38.3 - Prob. 1AECh. 38.8 - Prob. 1BECh. 38.8 - Prob. 1CECh. 38.9 - Prob. 1DECh. 38 - Prob. 1QCh. 38 - Prob. 2QCh. 38 - Prob. 3QCh. 38 - Prob. 4QCh. 38 - Would it ever be possible to balance a very sharp...Ch. 38 - Prob. 6Q
Ch. 38 - Prob. 7QCh. 38 - Prob. 8QCh. 38 - Prob. 9QCh. 38 - Prob. 10QCh. 38 - Prob. 11QCh. 38 - Prob. 12QCh. 38 - Prob. 13QCh. 38 - Prob. 14QCh. 38 - Prob. 15QCh. 38 - Prob. 16QCh. 38 - Prob. 17QCh. 38 - Prob. 18QCh. 38 - Prob. 1PCh. 38 - Prob. 2PCh. 38 - Prob. 3PCh. 38 - Prob. 4PCh. 38 - Prob. 5PCh. 38 - Prob. 6PCh. 38 - Prob. 7PCh. 38 - Prob. 8PCh. 38 - Prob. 9PCh. 38 - Prob. 10PCh. 38 - Prob. 11PCh. 38 - Prob. 12PCh. 38 - Prob. 13PCh. 38 - Prob. 14PCh. 38 - Prob. 15PCh. 38 - Prob. 16PCh. 38 - Prob. 17PCh. 38 - Prob. 18PCh. 38 - Prob. 19PCh. 38 - Prob. 20PCh. 38 - Prob. 21PCh. 38 - Prob. 22PCh. 38 - Prob. 23PCh. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - Prob. 27PCh. 38 - Prob. 28PCh. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Prob. 31PCh. 38 - Prob. 32PCh. 38 - Prob. 33PCh. 38 - Prob. 34PCh. 38 - Prob. 35PCh. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - Prob. 40PCh. 38 - Prob. 41PCh. 38 - Prob. 42PCh. 38 - Prob. 43PCh. 38 - Prob. 44PCh. 38 - Prob. 45PCh. 38 - Prob. 46GPCh. 38 - Prob. 47GPCh. 38 - Prob. 48GPCh. 38 - Prob. 49GPCh. 38 - Prob. 50GPCh. 38 - Prob. 51GPCh. 38 - Prob. 52GPCh. 38 - Prob. 53GPCh. 38 - Prob. 54GPCh. 38 - Prob. 55GPCh. 38 - Prob. 56GPCh. 38 - Prob. 57GPCh. 38 - Prob. 58GPCh. 38 - Prob. 59GP
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- ts) We can approximate the 232Th nucleus as a one-dimensional infinite square well with length L equal to the nuclear radius R = R₁A¹/3, where Ro = 1.2 fm and A is the atomic mass number. (a) What is the length of this infinite square well? What is the ground state energy of a proton (which has mass m₂ = 938.3 MeV/c²) in this infinite square well? (b) 232Th has 90 protons and 142 neutrons. Assume that all these protons and neutrons trapped in the infinite square well. How many energy levels of this infinite square well contain protons? How many energy levels contain neutrons?arrow_forwardA 5 MeV α particle approach a gold nucleus with an impact parameter of 2.6 ×10−13 meter. Through what angle will it be scattered.arrow_forwardIn a Rutherford scattering experiment, an a-particle (charge = +2e) heads directly toward a gold nucleus (charge = +79e). The α-particle had a kinetic energy of 5.0 MeV when very far (r→ ∞) from the nucleus. Assuming the gold nucleus to be fixed in space, determine the distance of closest approach. Hint: Use conservation of energy with PE =kq1q2/r.arrow_forward
- T1arrow_forwardIn a neutron-activation experiment, a flux of 108 neutrons/cm2sec is incident normally on a foil of area 1 cm?, density 1022 atoms/cm3 , and thickness 10-2 cm. The target nuclei have a total cross section for neutron capture of 1 barn (10-24 cm2), Find the number of b ( the light particle) per second ? 104 particle/sec 102 particle/sec 106 particle/sec 108 particle/sec Clear my choicearrow_forwardThe isotope of Nickel, 66Ni decays by β emission, has a half-life of 2.3 days. and the β particles have an average energy of 65 keV. A source consisting of this isotope has an initial number of atoms N0 = 5 x 1020 atoms. What is the power per unit area initially deposited by this source in a small target placed at 1m distance from the source? Select one: a. 1.45 W/m2 b. 7.6 MW/m2 c. 4.5 kW/m2 d. 35 W/m2arrow_forward
- In an alpha particle (42He) scattering experiment, using a thin gold (19779Au) foil, the initial kinetic energy of the alpha particle is 2.0MeV.(a.) What is the potential energy of the alpha particle/gold nucleus system at closest impact?(b.) Calculate the distance of closest approach. Compare this distance with the radius of the gold nucleus.arrow_forward2. The nuclear radius of gold is approximately r = 7.0 fm (1.0 fm = 1.0 x 10-15 m). The radii of protons and aparticles are 1.3 fm and 2.6 fm, respectively. (a) What energy a particles would be needed in head-oncollision tor the nuclear surtaces to just touch? This is about where the nuclear torce becomes etective.(b) What energy protons would be needed?arrow_forwardAlpha particles are scattered from a thin aluminum foil. At what alpha-particle kinetic energy would you expect the Rutherford formula to fail because the alpha particle enters the aluminum nucleus? Assume r = 1.9 fm for the alpha particle and 3.6 fm for the aluminum nucleus.arrow_forward
- V= 0 Vo II E X X=0 x= a Consider a neutron With Mass M And Energy E in the nucleus As Shown In The Figure. Question: (1). Write down the Schrödinger equation which applies to neutrons in regions I and II. (II). Calculate the normalized wave function neutrons in each of these regions.arrow_forwardIn a Rutherford scattering experiment, an ?-particle (charge = +2e) heads directly toward a silver nucleus (charge = +47e). The ?-particle had a kinetic energy of 4.6 MeV when very far (r → ∞) from the nucleus. Assuming the silver nucleus to be fixed in space, determine the distance of closest approach (in fm). Hint: Use conservation of energy with PE =(keq1q2 / r) _____fmarrow_forwardCalculate the distance of closest approach for a head-on collision between a 5.30 MeV alpha particle and a copper nucleus.arrow_forward
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