Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 4, Problem 7P
To determine
The ratio of an alpha particle scattering at any angle for equal numbers of scattering nuclei per unit area.
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For aluminum (Z = 13) and gold (Z = 79) targets, what is the ratio of an alpha particle scattering at any angle for equal numbers of scattering nuclei per unit area?
In an experiment, it was observed that a backward scattered ( an angle greater or equal to 90 degrees) alpha particles formed a beam that was energetic and was directed at a piece of gold foil as thin as 6.0 * 10^-7m. Assuming that an alpha particle scatters from the foil, what is the maximum scattering angle?
Q# 4 (a) A beam of 8.3 MeV alpha particles is directed at an aluminum foil. It is found that the
Rutherford scattering formula ceases to be obeyed at scattering angles exceeding about 60°. If the
alpha-particle radius is assumed small enough to neglect here, find the radius of the aluminum
nucleus.
Chapter 4 Solutions
Modern Physics for Scientists and Engineers
Ch. 4 - Prob. 1QCh. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5QCh. 4 - Prob. 6QCh. 4 - Prob. 7QCh. 4 - Prob. 8QCh. 4 - Prob. 9QCh. 4 - Prob. 10Q
Ch. 4 - Prob. 11QCh. 4 - Prob. 12QCh. 4 - Prob. 13QCh. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 - Prob. 7PCh. 4 - What fraction of 5-MeV α particles will be...Ch. 4 - Prob. 9PCh. 4 - Prob. 10PCh. 4 - Prob. 11PCh. 4 - Prob. 12PCh. 4 - Prob. 13PCh. 4 - Prob. 14PCh. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Prob. 17PCh. 4 - Prob. 18PCh. 4 - Prob. 19PCh. 4 - Prob. 20PCh. 4 - Prob. 21PCh. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - Prob. 24PCh. 4 - Prob. 25PCh. 4 - Prob. 26PCh. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - Prob. 33PCh. 4 - Prob. 34PCh. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - Prob. 37PCh. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - Prob. 43PCh. 4 - Prob. 44PCh. 4 - Prob. 45PCh. 4 - Prob. 46PCh. 4 - Prob. 47PCh. 4 - Prob. 48PCh. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Prob. 56PCh. 4 - Prob. 57PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61P
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- In 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(b) Explain the difference between a MASER and a LASER. Who was the inventor of MASER? Explain both phenomenon in detail. Q# 4 (a) A beam of 8.3 MeV alpha particles is directed at an aluminum foil. It is found that the Rutherford scattering formula ceases to be obeyed at scattering angles exceeding about 60°. If the alpha-particle radius is assumed small enough to neglect here, find the radius of the aluminum nucleus. (b) Classical Mechanics is an approximation of Quantum Mechanics. Discuss in detail. Q# 5 (a) Derive steady state form of Schrodinger wave equations. Explain eigen values and eigenarrow_forwardIn the experiment, alpha particles follow a hyperbolic trajectory. The figure shows an alpha particle A initially approaching a gold nucleus N and being deflected at an angle 0 = 90°. N is located at a focus of the hyperbola, and the trajectory of A passes through a vertex of the hyperbola. ++► x y = x y =-x a. Determine the equation of the trajectory of the alpha particle if d = 4 x 10 14 m. Choose the correct equation below. O A. X= -. + 16 x 10 - 28 В. X= Vy + 16 ×10-28 OC. D. X= + 4x 10 - 28 X = - 4x 10-28 b. What was the minimum distance between the centers of the alpha particle and the gold nucleus? (Use scientific notation. Round to the nearest tenth as needed.)arrow_forward
- 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.arrow_forwardThe speed of the alpha particles in Rutherford experiment was 0.01c, the scattering material was gold. What was the impact parameter of the alpha particle scattered by 60°?arrow_forwardAlpha particles of kinetic energy 6.9M V are incident at a rate of 3.1x 10" per second on a copper foil of thickness 3.1 x 10-m. A circular detector of diameter 1.0cm is placed 13cm from the foil at an angle of 30° with the direction of the incident alpha particles. At what rate does the detector measure scattered alpha particles? (The molar mass of copper is 63.5 and its density is 8.9em-)arrow_forward
- In a scattering experiment, you concentrate on Alpha particles with impact parameters b=0, 1×10^-3, and 1×10^0 mm. For which b will the behavior of the Alpha particle be very different in Thomson's and Rutherford's models and for which will it be nearly similar?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_forwardIn 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_forward
- Using the principle of precision, prove the impossibility of an electron inside the nucleus, noting that the nucleus has a radius of 1x10-14 marrow_forwardIs the angular momentum of alpha-particles in Rutherford scattering conserved?arrow_forwardConsider the scattering of an alpha particle from the positively charged part of the Thomson plumpudding model. Let the kinetic energy of the∝ particle be K (nonrelativistic) and let the atomic radius be R. (a) Assuming that the maximum transverse Coulomb force acts on the ∝ particle for a time∆ t = 2R/v (where v is the initial speed of the ∝ particle), show that the largest scattering angle we can expect from a single atom is (b) Evaluate θ for an 8.0-MeV ∝ particle scattering from a gold atom of radius 0.135 nm.arrow_forward
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