College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 28, Problem 6P
To determine
The distance of closest approach.
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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.
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, 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?
Chapter 28 Solutions
College Physics
Ch. 28.3 - Prob. 28.1QQCh. 28.4 - Prob. 28.2QQCh. 28.5 - Prob. 28.3QQCh. 28 - Prob. 1CQCh. 28 - Prob. 2CQCh. 28 - Prob. 3CQCh. 28 - Prob. 4CQCh. 28 - Prob. 5CQCh. 28 - Prob. 6CQCh. 28 - Prob. 7CQ
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- (a) An aspiring physicist wants to build a scale model of a hydrogen atom for her science fair project. If the atom is 1.00 m in diameter, how big should she try to make the nucleus? (b) How easy will this be to do?arrow_forward(a) Show that if you assume the average nucleus is spherical with a radius r=r0A1/3, and with a mass at A u, then its density is independent at A. (b) Calculate that density in u/fm3 and kg/m3, and compare your results with those found in Example 31.1 for 56Fe.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_forward
- When an alpha particle collides elastically with a nucleus, the nucleus recoils. Suppose a 5.00 MeV alpha particle has a headon elastic collision with a gold nucleus that is initially at rest.What is the kinetic energy of (a) the recoiling nucleus and (b) the rebounding alpha particle?arrow_forwardIn 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.arrow_forwardUse the below values for this problem. Please note that the mass for H is for the entire atom (proton & electron). Neutron: m,= 1.67493x1027 kg= 1.008665 u = 939.57 MeVIC H: my = 1.67353x10 27 kg = 1.007825 u = 938.78 MeVic 1u= 1.6605x10-27 kg = 931.5 MeVic? Consider the following decay: 211 At 207 Bi + a. 211 At has a mass of 210.9874963 u, 207 Bi has a mass of 206.981593 u, and a has a mass of 4.002603 u. 85 83 85 83 Determine the disintegration energy (Q-value) in MeV. Determine the binding energy (in MeV) for 211 At. 85 EB =arrow_forward
- In 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_forwardStarting from the Clasius-Clapeyron equation, Lo + constant kBT log p and assuming the latent heat of evaporation per gram of water to be constant, and equal to L= 2260 J/g , find the boiling temperature of water in degrees Celcius at a pressure of 50.0 atm. Each oxygen atom has 8 protons and 8 neutrons in its nucleus. The boiling temperature of water at a pressure of 50.0 atm is around 250 °C. How do you account for the difference? R = 8.31 //(mol · K) , m,-1.67x1027 kg , NA=6.02x1023 mol-1arrow_forwardIn Rutherford’s original experiment, alpha particles (α) were shot toward a gold foil. Gold has an atomic number of 79. An α had initial kinetic energy of about 6 MeV. When an α was closest to a gold nucleus, it stopped completely by the electric repulsive force between the two nuclei. Assume all the α kinetic energy was converted to electric potential energy. The closest distance (center to center) between the two nuclei is _____ x 10-15 meter.arrow_forward
- In a high-energy electron scattering experiment on the nucleus, a scientist has scientist has possibilities to use energies of 200, 2000 and 20000 MeV. Which energy should the scientist use? Do the calculations and give the necessary arguments to show why the scientist makes the right decision.arrow_forwardnucleus emits an alpha particle with kinetic evergy = 4.20 MeV. What is the daughter nucleus, and what is the approximate atomic mass (in u) of the daughter atom? ignore recoil of the daughter nucleus. if the image doesnt come up properly it is 92^238 Uarrow_forwardThe figure provided shows the potential energy of a proton, q = +e, and a lead nucleus, q = +82e. If a proton is fired toward a lead nucleus from very far away with kinetic energy K = 3.00×10-12 J, how much kinetic energy does it have when it is 20.0 fm from the nucleus and moving toward it, before the collision? 5.00×10-12 J 4.00×10-12 J 3.00×10-12 J 2.00×10-12 Jarrow_forward
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