UNIVERSITY PHYSICS UCI PKG
11th Edition
ISBN: 9781323575208
Author: YOUNG
Publisher: PEARSON C
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Chapter 23, Problem 23.51P
Determining the Size of the Nucleus. When radium-226 decays radioactively, it emits an alpha particle (the nucleus of helium), and the end product is radon-222. We can model this decay by thinking of the radium-226 as consisting of an alpha particle emitted from the surface of the spherically symmetric radon-222 nucleus, and we can treat the alpha particle as a point charge. The energy of the alpha particle has been measured in the laboratory and has been found to be 4.79 MeV when the alpha particle is essentially infinitely far from the nucleus. Since radon is much heavier than the alpha particle, we can assume that there is no appreciable recoil of the radon after the decay. The radon nucleus contains 86 protons, while the alpha particle has 2 protons and the radium nucleus has 88 protons, (a) What was the electric potential energy of the alpha–radon combination just before the decay, in MeV and in joules? (b) Use your result from part (a) to calculate the radius of the radon nucleus.
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Problem 1: White dwarf star
A white dwarf star is essentially a degenerate electron gas, with a bunch of nuclei mixed
in to balance the charge and to provide the gravitational attraction that holds the star
together. White dwarf stars tend to be extremely hot by our standards; nevertheless, it is
an excellent approximation in this problem to set T=0. The gravitational potential energy
inside a star of uniform density is Ugrav =
3 см2
a) Assuming that the star contains one proton and one neutron for each electron, and
that the electrons are nonrelativistic, show that the total (kinetic) energy of the
degenerate electrons equals
h²M³
Ukinetic = (0.0088)-
męm R?
b) The equilibrium radius of the white dwarf is that which minimize the total energy
Ugrav + Ukinetie: Sketch the total energy as a function of R, and find a formula for
the equilibrium radius in terms of the mass. As the mass increases, does the radius
increase or decrease? Does this make sense?
c) Evaluate the equilibrium radius…
8) The nucleus of a silver atom has a charge +47 e and is fixed at the origin of a cartesian coordinate system. An alpha particle of mass 6.68 × 10^−27 kg and charge +4 e is fired along the x-axis from infinity with an initial kinetic energy of 7.00 × 10^−13 J. At what distance from the silver nucleus will the alpha particle come (momentarily) to rest?
Chapter 23 Solutions
UNIVERSITY PHYSICS UCI PKG
Ch. 23.1 - Consider the system of three point charges in...Ch. 23.2 - If the electric potential at a certain point is...Ch. 23.3 - If the electric field at a certain point is zero,...Ch. 23.4 - Would the shapes of the equipotential surfaces in...Ch. 23.5 - In a certain region of space the potential is...Ch. 23 - A student asked. Since electrical potential is...Ch. 23 - The potential (relative to a point at infinity)...Ch. 23 - Is it possible to have an arrangement of two point...Ch. 23 - Since potential can have any value you want...Ch. 23 - If E is zero everywhere along a certain path that...
Ch. 23 - If E is zero throughout a certain region of space,...Ch. 23 - Which way do electric field lines point, from high...Ch. 23 - (a) If the potential (relative to infinity) is...Ch. 23 - If you carry out the integral of the electric...Ch. 23 - The potential difference between the two terminals...Ch. 23 - It is easy to produce a potential difference of...Ch. 23 - If the electric potential at a single point is...Ch. 23 - Because electric field lines and equipotential...Ch. 23 - A uniform electric field is directed due east....Ch. 23 - We often say that if point A is at a higher...Ch. 23 - A conducting sphere is to be charged by bringing...Ch. 23 - In electronics it is customary to define the...Ch. 23 - A conducting sphere is placed between two charged...Ch. 23 - A conductor that carries a net charge Q has a...Ch. 23 - A high-voltage dc power line falls on a car, so...Ch. 23 - When a thunderstorm is approaching, sailors at sea...Ch. 23 - A positive point charge is placed near a very...Ch. 23 - A point charge q1 = +2.40 C is held stationary at...Ch. 23 - A point charge q1 is held stationary at the...Ch. 23 - Energy of the Nucleus. How much work is needed to...Ch. 23 - (a) How much work would it take to push two...Ch. 23 - A small metal sphere, carrying a net charge of q1...Ch. 23 - BIO Energy of DNA Base Pairing. (See Exercise...Ch. 23 - Two protons, starting several meters apart, are...Ch. 23 - Three equal 1.20-C point charges are placed at the...Ch. 23 - Two protons are released from rest when they are...Ch. 23 - Four electrons are located at the corners of a...Ch. 23 - Three point charges, which initially are...Ch. 23 - An object with charge q = 6.00 109 C is placed in...Ch. 23 - A small particle has charge 5.00 C and mass 2.00 ...Ch. 23 - A particle with charge +4.20 nC is in a uniform...Ch. 23 - A charge of 28.0 nC is placed in a uniform...Ch. 23 - Two stationary point charges +3.00 nC and +2.00 nC...Ch. 23 - Point charges q1 = + 2.00 C and q2 = 2.00 C are...Ch. 23 - Two point charges of equal magnitude Q are held a...Ch. 23 - Two point charges q1 = +2.40 nC and q2 = 6.50 nC...Ch. 23 - (a) An electron is to be accelerated from 3.00 ...Ch. 23 - A positive charge q is fixed at the point x = 0, y...Ch. 23 - At a certain distance from a point charge, the...Ch. 23 - A uniform electric field has magnitude E and is...Ch. 23 - For each of the following arrangements of two...Ch. 23 - A thin spherical shell with radius R1 = 3.00 cm is...Ch. 23 - A total electric charge of 3.50 nC is distributed...Ch. 23 - A uniformly charged, thin ring has radius 15.0 cm...Ch. 23 - A solid conducting sphere has net positive charge...Ch. 23 - Charge Q = 5.00 C is distributed uniformly over...Ch. 23 - An infinitely long line of charge has linear...Ch. 23 - A very long wire carries a uniform linear charge...Ch. 23 - A very long insulating cylinder of charge of...Ch. 23 - A very long insulating cylindrical shell of radius...Ch. 23 - A ring of diameter 8.00 cm is fixed in place and...Ch. 23 - A very small sphere with positive charge q = +...Ch. 23 - CP Two large, parallel conducting plates carrying...Ch. 23 - Two large, parallel, metal plates carry opposite...Ch. 23 - BIO Electrical Sensitivity of Sharks. Certain...Ch. 23 - The electric field at the surface of a charged,...Ch. 23 - (a) How much excess charge must be placed on a...Ch. 23 - CALC A metal sphere with radius ra is supported on...Ch. 23 - A very large plastic sheet carries a uniform...Ch. 23 - CALC In a certain region of space, the electric...Ch. 23 - CALC In a certain region of space the electric...Ch. 23 - A metal sphere with radius ra = 1.20 cm is...Ch. 23 - CP A point charge q1, = +5.00 C is held fixed in...Ch. 23 - A point charge q1 = 4.00 nC is placed at the...Ch. 23 - A positive point charge q1 = +5.00 104 C is held...Ch. 23 - A gold nucleus has a radius of 7.3 1015 m and a...Ch. 23 - A small sphere with mass 5.00 107 kg and charge...Ch. 23 - Determining the Size of the Nucleus. When...Ch. 23 - CP A proton and an alpha particle are released...Ch. 23 - A particle with charge +7.60 nC is in a uniform...Ch. 23 - Identical charges q = +5.00 C are placed at...Ch. 23 - CALC A vacuum tube diode consists of concentric...Ch. 23 - Two oppositely charged, identical insulating...Ch. 23 - An Ionic Crystal. Figure P23.57 shows eight point...Ch. 23 - (a) Calculate the potential energy of a system of...Ch. 23 - CP A small sphere with mass 1.50 g hangs by a...Ch. 23 - Two spherical shells have a common center. The...Ch. 23 - CALC Coaxial Cylinders. A long metal cylinder with...Ch. 23 - A Geiger counter detects radiation such as alpha...Ch. 23 - CP Deflection in a CRT. Cathode-ray tubes (CRTs)...Ch. 23 - CP Deflecting Plates of an Oscilloscope. The...Ch. 23 - Electrostatic precipitators use electric forces to...Ch. 23 - CALC A disk with radius R has uniform surface...Ch. 23 - CALC Self-Energy of a Sphere of Charge. A solid...Ch. 23 - CALC A thin insulating rod is bent into a...Ch. 23 - Charge Q = +4.00 C is distributed uniformly over...Ch. 23 - An insulating spherical shell with inner radius...Ch. 23 - CP Two plastic spheres, each carrying charge...Ch. 23 - (a) If a spherical raindrop of radius 0.650 mm...Ch. 23 - CALC Electric charge is distributed uniformly...Ch. 23 - An alpha particle with kinetic energy 9.50 MeV...Ch. 23 - Two metal spheres of different sizes are charged...Ch. 23 - A metal sphere with radius R1 has a charge Q1....Ch. 23 - Prob. 23.77PCh. 23 - CALC The electric potential V in a region of space...Ch. 23 - DATA The electric potential in a region that is...Ch. 23 - DATA A small, stationary sphere carries a net...Ch. 23 - DATA The Millikan Oil-Drop Experiment. The charge...Ch. 23 - CALC A hollow, thin-walled insulating cylinder of...Ch. 23 - CP In experiments in which atomic nuclei collide,...Ch. 23 - For a particular experiment, helium ions are to be...Ch. 23 - A helium ion (He++) that comes within about 10 fm...Ch. 23 - The maximum voltage at the center of a typical...
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