Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term
5th Edition
ISBN: 9781133422013
Author: Raymond A. Serway; John W. Jewett
Publisher: Cengage Learning
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Question
Chapter 11, Problem 39P
(a)
To determine
The orbital speed of the electron in a hydrogen atom in its ground state.
(b)
To determine
The kinetic energy of the electron in the ground state of the hydrogen atom.
(c)
To determine
The electric potential energy of the atom.
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Consider the earth-sun system as a gravitational analog to the hydrogen atom. You may need to know
that the mass of the earth is
m =
5.97219 × 1024 kg,
the mass of the sun is
the distance between the sun and the earth is
ework 08
M = 1.98847 × 1030 kg,
R = 1.49598 × 1011
m,
1
2
and the force and potential energy distribution that the earth experiences due to the gravitational field
of the sun are
GmM
F
7.2
GmM
U(r) = -
==
r
where G is the gravitation constant
G = 6.67428 × 10-11 N m²/kg².
[Some standard calculators have issues with the numbers in this problem. If you get overflow or
underflow errors, try using MATLAB]
(a) Using the fact that the centripetal force must have magnitude
mv2
F
=
r
what is the centripetal velocity of the earth at an arbitrary radius r?
(b) Using the centripetal velocity, find the total energy of this system as
E=T+U
1
= √mv² + U(r).
(c) Use Bohr's assertion that
mvr = nh,
to find the radii rn as a function of the principle quantum number n for the earth-sun…
At a very short range, the potential energy between electrons and nuclie in atoms can be expressed as U(x) = -C3/x3, C3 is a constant. What is expression for force of this energy, is it repulsive or attractive?
Determine the distance between the electron and proton in an atom if the potential energy U of the electron is 11.6eV. Give your answer in Angstrom.
Chapter 11 Solutions
Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term
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- Rank the following quantities of energy from largest to the smallest. State if any are equal. (a) the absolute value of the average potential energy of the SunEarth system (b) the average kinetic energy of the Earth in its orbital motion relative to the Sun (c) the absolute value of the total energy of the SunEarth systemarrow_forwardA system consists of five particles. How many terms appear in the expression for the total gravitational potential energy of the system? (a) 4 (b) 5 (c) 10 (d) 20 (e) 25arrow_forwardIn a simple model of a hydrogen atom, the single electron orbits the single proton (the nucleus) in a circular path. Calculate (a) the electric potential set up by the proton at the orbital radius of 52.9 pm, (b) the electric potential energy of the atom, and (c) the kinetic energy of the electron. (d) How much energy is required to ionize the atom (that is, to remove the electron to an infinite distance with no kinetic energy)? Give the energies in electron-volts.arrow_forward
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