Chapter 11 Atomic Transitions and Radiation and 11.30, For reference, we have collected together some of the more impor- this possibility to amplify lig acronym for "Light Amplific In stimulated emission tant selection rules in Table 11.1. each atom is in lockstep wi emitted radiation is exactly as suggested in Fig. 11.6. E the resulting light wave is with the incoherent light atom's radiation is rando- that this coherence meam direction in space. Some of the selection rules that apply to transitions of electrons in an atom. Each rule TABLE 11.1 is stated in the form of a condition that must be met if a transition is to be allowed (that is, occur with significant probability). For example, the first rule, Al = only transitions for which Al = l - 1, = ±1 are allowed. The quantum numbers +1, means that SuR identifies the magnitude of the total spin of all the electrons; similarly jot gives the magnitude of the total angular momentum 2(L+ S). Selection Rule Reference We have described Quantum Number Eq. (11.46) Al = ±1 0 or ulated emission from E their ground state, and absorbed, not amplifie jority of the atoms are tion of the levels is cal means to achieve po counts of some impo light, while others pr of these two types a with the pulsed lases /(magnitude of L) Problem 11.30 Am = 0 or ±1 %3D m (z component of L) Problem 11.25 AStot = 0 %3D Stot (total spin s) Jrot [total spin + orbital (L+ S)] Problem 11.27 Ajtot = 0 or ±1 %3D Metastable States Looking back at Fig. 11.5, you can see that the 2s level of hydrogen has no al. lowed downward transitions because there is no 1 This would seem to imply that the 2s state is perfectly stable. In fact, there exists other processes that de-excite the 2s state, such as a collision with other atoms. * However, these processes all occur very slowly, and the lifetime of the 1 level below the 2s level. %3D Pulsed Lasers The first suoo00of SECTION 11.8 (Atomic Selection Rules) 11.26 Theg 11.23 When a quantum wave function ¥ is complex (with hoth real and imaginary parts), its probability density beyond cial casa ie lv2 where V is the absolute value of V, defined by Eq. (6.12) as |V| = Vv? V2 = ¥*¥, where V* is the complex conjugate of V. (The complex conjugate z* of any complex number z =x + iy, where x and y are real, is defined as z* = x - iy.) cal + Va. Prove that real imag· [This p %3D wave f functic wave f of a ra by (11 11.24 The outermost (valence) electron of sodium is in a 3s state when the atom is in its ground state (To
Chapter 11 Atomic Transitions and Radiation and 11.30, For reference, we have collected together some of the more impor- this possibility to amplify lig acronym for "Light Amplific In stimulated emission tant selection rules in Table 11.1. each atom is in lockstep wi emitted radiation is exactly as suggested in Fig. 11.6. E the resulting light wave is with the incoherent light atom's radiation is rando- that this coherence meam direction in space. Some of the selection rules that apply to transitions of electrons in an atom. Each rule TABLE 11.1 is stated in the form of a condition that must be met if a transition is to be allowed (that is, occur with significant probability). For example, the first rule, Al = only transitions for which Al = l - 1, = ±1 are allowed. The quantum numbers +1, means that SuR identifies the magnitude of the total spin of all the electrons; similarly jot gives the magnitude of the total angular momentum 2(L+ S). Selection Rule Reference We have described Quantum Number Eq. (11.46) Al = ±1 0 or ulated emission from E their ground state, and absorbed, not amplifie jority of the atoms are tion of the levels is cal means to achieve po counts of some impo light, while others pr of these two types a with the pulsed lases /(magnitude of L) Problem 11.30 Am = 0 or ±1 %3D m (z component of L) Problem 11.25 AStot = 0 %3D Stot (total spin s) Jrot [total spin + orbital (L+ S)] Problem 11.27 Ajtot = 0 or ±1 %3D Metastable States Looking back at Fig. 11.5, you can see that the 2s level of hydrogen has no al. lowed downward transitions because there is no 1 This would seem to imply that the 2s state is perfectly stable. In fact, there exists other processes that de-excite the 2s state, such as a collision with other atoms. * However, these processes all occur very slowly, and the lifetime of the 1 level below the 2s level. %3D Pulsed Lasers The first suoo00of SECTION 11.8 (Atomic Selection Rules) 11.26 Theg 11.23 When a quantum wave function ¥ is complex (with hoth real and imaginary parts), its probability density beyond cial casa ie lv2 where V is the absolute value of V, defined by Eq. (6.12) as |V| = Vv? V2 = ¥*¥, where V* is the complex conjugate of V. (The complex conjugate z* of any complex number z =x + iy, where x and y are real, is defined as z* = x - iy.) cal + Va. Prove that real imag· [This p %3D wave f functic wave f of a ra by (11 11.24 The outermost (valence) electron of sodium is in a 3s state when the atom is in its ground state (To
Related questions
Question
For Problem 11.23, how do I prove the following? This problem is in a chapter titled, "Atomic transitions and Radiation." It is also in
![Chapter 11 Atomic Transitions and Radiation
and 11.30, For reference, we have collected together some of the more impor-
this possibility to amplify lig
acronym for "Light Amplific
In stimulated emission
tant selection rules in Table 11.1.
each atom is in lockstep wi
emitted radiation is exactly
as suggested in Fig. 11.6. E
the resulting light wave is
with the incoherent light
atom's radiation is rando-
that this coherence meam
direction in space.
Some of the selection rules that apply to transitions of electrons in an atom. Each rule
TABLE 11.1
is stated in the form of a condition that must be met if a transition is to be allowed (that
is, occur with significant probability). For example, the first rule, Al =
only transitions for which Al = l - 1, = ±1 are allowed. The quantum numbers
+1, means that
SuR
identifies the magnitude of the total spin of all the electrons; similarly jot gives the
magnitude of the total angular momentum 2(L+ S).
Selection Rule
Reference
We have described
Quantum Number
Eq. (11.46)
Al = ±1
0 or
ulated emission from E
their ground state, and
absorbed, not amplifie
jority of the atoms are
tion of the levels is cal
means to achieve po
counts of some impo
light, while others pr
of these two types a
with the pulsed lases
/(magnitude of L)
Problem 11.30
Am = 0 or ±1
%3D
m (z component of L)
Problem 11.25
AStot = 0
%3D
Stot (total spin s)
Jrot [total spin + orbital (L+ S)]
Problem 11.27
Ajtot = 0 or ±1
%3D
Metastable States
Looking back at Fig. 11.5, you can see that the 2s level of hydrogen has no al.
lowed downward transitions because there is no 1
This would seem to imply that the 2s state is perfectly stable. In fact, there
exists other processes that de-excite the 2s state, such as a collision with other
atoms. * However, these processes all occur very slowly, and the lifetime of the
1 level below the 2s level.
%3D
Pulsed Lasers
The first
suoo00of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81ed2a7d-ef58-4ac0-a29f-af1e2992bb8e%2F39590d49-90eb-468f-99e1-4ed6ce23dbc2%2Foayaspx.jpeg&w=3840&q=75)
Transcribed Image Text:Chapter 11 Atomic Transitions and Radiation
and 11.30, For reference, we have collected together some of the more impor-
this possibility to amplify lig
acronym for "Light Amplific
In stimulated emission
tant selection rules in Table 11.1.
each atom is in lockstep wi
emitted radiation is exactly
as suggested in Fig. 11.6. E
the resulting light wave is
with the incoherent light
atom's radiation is rando-
that this coherence meam
direction in space.
Some of the selection rules that apply to transitions of electrons in an atom. Each rule
TABLE 11.1
is stated in the form of a condition that must be met if a transition is to be allowed (that
is, occur with significant probability). For example, the first rule, Al =
only transitions for which Al = l - 1, = ±1 are allowed. The quantum numbers
+1, means that
SuR
identifies the magnitude of the total spin of all the electrons; similarly jot gives the
magnitude of the total angular momentum 2(L+ S).
Selection Rule
Reference
We have described
Quantum Number
Eq. (11.46)
Al = ±1
0 or
ulated emission from E
their ground state, and
absorbed, not amplifie
jority of the atoms are
tion of the levels is cal
means to achieve po
counts of some impo
light, while others pr
of these two types a
with the pulsed lases
/(magnitude of L)
Problem 11.30
Am = 0 or ±1
%3D
m (z component of L)
Problem 11.25
AStot = 0
%3D
Stot (total spin s)
Jrot [total spin + orbital (L+ S)]
Problem 11.27
Ajtot = 0 or ±1
%3D
Metastable States
Looking back at Fig. 11.5, you can see that the 2s level of hydrogen has no al.
lowed downward transitions because there is no 1
This would seem to imply that the 2s state is perfectly stable. In fact, there
exists other processes that de-excite the 2s state, such as a collision with other
atoms. * However, these processes all occur very slowly, and the lifetime of the
1 level below the 2s level.
%3D
Pulsed Lasers
The first
suoo00of
Transcribed Image Text:SECTION 11.8 (Atomic Selection Rules)
11.26 Theg
11.23 When a quantum wave function ¥ is complex (with
hoth real and imaginary parts), its probability density
beyond
cial casa
ie lv2 where V is the absolute value of V, defined
by Eq. (6.12) as |V| = Vv?
V2 = ¥*¥, where V* is the complex conjugate of
V. (The complex conjugate z* of any complex
number z =x + iy, where x and y are real, is
defined as z* = x - iy.)
cal
+ Va. Prove that
real
imag·
[This p
%3D
wave f
functic
wave f
of a ra
by (11
11.24 The outermost (valence) electron of sodium is in a
3s state when the atom is in its ground state
(To
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