Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 43, Problem 66CP
To determine
To show that the electrical electrostatic potential energy of the nucleus is
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In Rutherford's famous scattering experiments that led
to the planetary model of the atom, alpha particles (having
charges of +2e and masses of 6.64 x 10-27 kg) were fired
toward a gold nucleus with charge +79e. An alpha particle,
Consider a model of the nucleus in which the positive charge (Ze) is uniformly distributed throughout a sphere of radius R. By integrating the energy density 1/2∈0E2 over all space, show that the electric potential energy may be written U = (3Z2e2)/(20π∈0R) = (3keZ2e2)/(5R)
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Chapter 43 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 43.1 - Prob. 43.1QQCh. 43.5 - Prob. 43.3QQCh. 43.5 - Which of the following is the correct daughter...Ch. 43.8 - When a nucleus undergoes fission, the two daughter...Ch. 43.8 - Prob. 43.6QQCh. 43.10 - Prob. 43.7QQCh. 43 - Prob. 1PCh. 43 - Prob. 2PCh. 43 - Prob. 3PCh. 43 - Prob. 4P
Ch. 43 - Prob. 5PCh. 43 - Prob. 7PCh. 43 - Prob. 8PCh. 43 - Prob. 9PCh. 43 - Prob. 10PCh. 43 - Prob. 11PCh. 43 - Prob. 13PCh. 43 - Prob. 15PCh. 43 - Prob. 17PCh. 43 - Prob. 18PCh. 43 - Prob. 19PCh. 43 - Prob. 20PCh. 43 - Prob. 21PCh. 43 - Prob. 22PCh. 43 - Prob. 23PCh. 43 - Prob. 24PCh. 43 - Enter the correct nuclide symbol in each open tan...Ch. 43 - Prob. 26PCh. 43 - Prob. 27PCh. 43 - Prob. 28PCh. 43 - Prob. 29PCh. 43 - Prob. 30PCh. 43 - Prob. 32PCh. 43 - Prob. 33PCh. 43 - Prob. 35PCh. 43 - Prob. 37PCh. 43 - Prob. 39PCh. 43 - Prob. 41PCh. 43 - Prob. 42PCh. 43 - Prob. 44PCh. 43 - Prob. 45APCh. 43 - Prob. 46APCh. 43 - Prob. 47APCh. 43 - Prob. 48APCh. 43 - Prob. 49APCh. 43 - Prob. 50APCh. 43 - Prob. 51APCh. 43 - Prob. 52APCh. 43 - As part of his discovery of the neutron in 1932,...Ch. 43 - Prob. 55APCh. 43 - Prob. 56APCh. 43 - Prob. 58APCh. 43 - Prob. 59APCh. 43 - Prob. 60APCh. 43 - Prob. 62APCh. 43 - Prob. 63APCh. 43 - Prob. 64APCh. 43 - Prob. 65APCh. 43 - Prob. 66CP
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- (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_forwardNow you have a nucleus with 7 protons at x = 3.5 Angstroms on the x-axis. How much work would it take to bring in ANOTHER nucleus with 5 protons from 1 m away and place it at y = 7.3 Angstroms on the y-axis? 52.3 eV -9.9 eV 62.2 eV 41.8 eVarrow_forwardc. Write the mathematical expression for the radial probability function. The radial probability function for any orbital is zero at the nucleus, it also approaches zero at long distance from the nucleus. Explain why.arrow_forward
- Don't Use Chat GPT Will Upvotearrow_forwardSuppose 8.5x10−19 J of work is done to bring the nucleus of an atom from some infinite distance away to a particular location near a fixed positive charge. What would the electric potential energy of the nucleus be? The nucleus is released an returns to the very far original position. Considering the kinetic energy of the nucleus and a mass of 6.6x10−27 kg, which is closest to the velocity of the nucleus? Make sure to answer both parts of the question and show all work.arrow_forwardYou are working as a nuclear physicist and are performing research on mirror isobars. Mirror isobars are pairs of nuclei for which Z1 = N2 and Z2 = N1 (the atomic and neutron numbers are interchanged). You wish to investigate the independence of nuclear forces on charge by comparing binding-energy measurements in the laboratory on mirror isobars against a theoretical value for the difference in binding energies. You first find the theoretical difference in binding energies for the two mirror isobars 15/8O and 15/7N.arrow_forward
- A. Direction: Complete the table by filling up the missing particle, nucleus or name of decay. Write your answers on the spaces provided. Just write alpha, beta or gamma on the 3rd column. Number 1 serves as an example. 1. 210 84 → He + 206 82 Alpha 2. 3. 4. 5. 6. 1³N → 144 Nd→ ¹³N - 41 Ar + _je + 130 140 Ce CLarrow_forwardA neutron in a star makes an elastic head-on collision with a carb on nucleus initially at rest. The mass of the carbon nucleus is 12 times the mass of the neutron mn = 1.7 ×10^−27kg. The initial kinetic energy of the neutron is 1.6 × 10^−13J. a) Show that the final speed of the carbon nucleus, Vc, is given by (see image) where vn is the initial speed of the neutron.arrow_forwardWhen a bound electron moves to location further from the nucleus, which of the following are true? energy of electron increases because it takes energy input to separate positive and negative charges, and there is a decrease in the electrostatic potential energy of the electron energy of electron increases because it takes energy input to separate positive and negative charges, and there is an increase in the electrostatic potential energy of the electron energy of electron decreases because energy is released as positive and negative charges are separated, and there is a decrease in electrostatic potential energy of electron since it is now further awayarrow_forward
- One of the following is considered as a mirror nucleus to O (A=18, z=8): Ne (A=19, z=10) b. Mg (A=21, z=12) c. Ne (A=23, z=10) С. d. O (A=19, z=8) Ne (A=18, z=10) е.arrow_forwardAn α-particle moving with initial kinetic energy K towards a nucleus of atomic number z approaches a distance ‘d’ at which it reverses its direction. Obtain the expression for the distance of closest approach ‘d’ in terms of the kinetic energy of α-particle K.arrow_forwardAn alpha particle (charge +3.20 x 10^-19C, mass 6.64 x10^-27kg) is initially 5.2cm away from a fixed golden nucleus (charge +1.36 x10^-17C, mass 3.29x10^-25kg), and moving toward the nucleus with a speed of 8.1x10^5m/s. How close to the nucleus does te alpha particle get? Note: the nucleus diameter is approximately 10^-14m and the alpha particles's is 10^-15marrow_forward
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