Biomedical Engineering Reference
In-Depth Information
Fig. 2.14
See Problem 31.
23.
What is the lowest quantum number of an H-atom electron
orbit with a radius of at least 1 cm?
24.
According to Bohr theory, how many bound states of He
+
have
energies equal to bound-state energies in H?
25.
How much energy is needed to remove an electron from the
n
5 state of He
+
?
=
26.
(a)
In the Balmer series of the hydrogen atom, what is the
smallest value of the principal quantum number of the
initial state for emission of a photon of wavelength less
than 4200 Å?
(b)
What is the change in the angular momentum of the
electron for this transition?
Calculate the reduced mass for the He
+
system.
27.
28.
What percentage error is made in the Rydberg constant for
hydrogen if the electron mass is used instead of the reduced
mass?
29.
The negative muon is an elementary particle with a charge
equal to that of the electron and a mass 207 times as large. A
proton can capture a negative muon to form a hydrogen-like
“mesic” atom. (The muon was formerly called the mu meson.)
For such a system, calculate
(a)
the radius of the first Bohr orbit
(b)
the ionization potential.
Do not assume a stationary nucleus.
30.
What is the reduced mass for a system of two particles of equal
mass, such as an electron and positron, orbiting about their
center of mass?
31.
Figure 2.14 shows two interacting particles, having masses
m
1
and
m
2
and positions
x
1
and
x
2
. The particles are free to move
only along the
X
-axis. Their total energy is
E
1
2
m
1
˙
x
1
+
2
m
2
˙
x
2
+
V
(
x
)
, where
˙
dx
2
/
dt
are the velocities, and the potential energy
V
(
x
)
depends only
on the separation
x
=
x
1
=
dx
1
/
dt
and
˙
x
2
=
x
2
-
x
1
of the particles. Let
z
be the
coordinate of the center of mass
C
:
m
1
(
z
-
x
1
)
=
=
m
2
(
x
2
-
z
)
.
