Biomedical Engineering Reference
In-Depth Information
2
(
m
1
+
m
2
)
z
2
+
2
m
r
x
2
+
V
(
x
)
, where
m
r
,isthe
reduced mass, given by Eq. (2.20), and
x
=
dx
/
dt
. The total
energy is thus the sum of the translational kinetic energy of the
motion of the total mass along the
X
-axis and the total energy
associated with the relative motion (coordinate
x
and mass
m
r
)
.
1
Show that
E
=
32.
What is meant by the fine structure in the spectrum of
hydrogen and what is its physical origin?
33.
Calculate the momentum of an ultraviolet photon of
wavelength 1000 Å.
34.
What is the momentum of a photon of lowest energy in the
Balmer series of hydrogen?
35.
Calculate the de Broglie wavelength of the 7.69-MeV alpha
particles used in Rutherford's experiment. Use nonrelativistic
mechanics.
36.
What is the energy of a proton that has the same momentum
as a 1-MeV photon?
37.
What is the energy of an electron having a wavelength of
0.123 Å?
38.
Calculate the de Broglie wavelength of a 245-keV electron.
39.
(a)
What is the momentum of an electron with a de Broglie
wavelength of 0.02 Å?
(b)
What is the momentum of a photon with a wavelength of
0.02 Å?
40.
Calculate the kinetic energy of the electron and the energy of
the photon in the last problem.
41.
A microscope can resolve as distinct two objects or features
that are no closer than the wavelength of the light or electrons
used for the observation.
(a)
With an electron microscope, what energy is needed for a
resolution of 0.4 Å?
(b)
What photon energy would be required of an optical
microscope for the same resolution?
42.
Show that Eq. (2.29) follows from Eq. (2.22) for relativistic
electrons.
43.
Estimate the uncertainty in the momentum of an electron
whose location is uncertain by a distance of 2 Å. What is the
uncertainty in the momentum of a proton under the same
conditions?
44.
What can one conclude about the relative velocities and
energies of the electron and proton in the last problem? Are
wave phenomena apt to be more apparent for light particles
than for heavy ones?
45.
The result given after Eq. (2.36) shows that an electron
confined to nuclear dimensions,
10
-15
m, could be
x
∼
