682 15 The Principles of Quantum Mechanics. I. De Broglie Waves and the Schrödinger Equationfactor of 332958. The earth’s orbit is slightly elliptical,
but pretend that it is circular, with a radius of
1. 4967 × 1011 m.a.Find the value of the Bohr radius assuming that the
sum is stationary (as it would be if it were infinitely
massive).
b.Find the ratio of the reduced mass of the earth–sun
system to the mass of the earth.
c.Find the value of the Bohr radius using the reduced
mass of the earth and the sun.
d.Find the value of the quantum number corresponding
to the size of the earth’s actual orbit.
e.Find the kinetic energy, the potential energy, and the
total energy of the earth’s orbital motion.15.33Identify each statement as either true or false. If a
statement is true only under special circumstances, label it
as false.
a.A de Broglie wave can be identified as a transverse
wave.
b.A de Broglie wave can be identified as a longitudinal
wave.c.The oscillating quantity in a de Broglie wave cannot be
physically identified.
d.The Schrödinger equation has been rigorously derived
from first principles.
e.An eigenvalue equation can have solutions for arbitrary
values of the eigenvalue.
f.Several different eigenvalues can correspond to the
same eigenfunction.
g.Several different energy eigenfunctions can correspond
to the same energy eigenvalue.
h.Light can be identified as a wave in a pervasive
medium.
i.Light exhibits both wave-like and particle-like
properties.
j.Electrons exhibit both wave-like and particle-like
properties.
k.If the length of its box is made to approach infinity, a
particle in a box behaves like a free particle.
l.A free particle cannot be described by a standing-wave
type of wave function, but must be described by a
traveling-wave type of wave function.