Hamiltonian (11.11) is linear. 11.17.. Show that the wave functions (11.21) for sh those transitions for which dicate on this energy-level tions among the levels sho Asional numbe - Ar nite square well satisfy the orthogonality property that m(x)*/n(x) dx = 0 for m # n. %3D 5s 4p 4s SECTION 11.5 (Transitions; Time-Dependent Perturbation Theory *) 11.18 (a) The first excited state of the sodium atom is 2.11 eV above the ground state. What wavelength ra- diation can cause transitions between these two lev. els? What sort of radiation is this? (visible, UV, etc.?) (b) Answer the same questions for the two 2p levels in hydrogen, which are shown in Fig. 9.7 and are 4.5 x 10 eV apart. (This is the fine-structure split- ting discussed in Section 9.7.) (c) Answer the same questions for the lowest two levels of the 'Li nucleus, which are 0.48 MeV apart. Зр sm is in a cir- rge Q (with q tarting from ated power P t factor is P and Q un- a m, r, and q 3s FIGURE 11.22 Some low-lying levels of any one e odels of the 11.25 Figure 11.23 shows sor of the He atom. They are (for example, 1s2p mea tron in the 1s level and depends somewhat on trons' spins: If the spins zero (quantum number correct fre- ng to classi- of emitted he orbiting cies, forb(1) n = 1 and O Now find 11.19 The atoms of a certain monatomic gas have five ener- gy levels: E = 0, E, = 5.4, E = 8.2, E4 = 8.6, and E5 = 12.4, all measured up from E, in eV. (a) I - frared light with wavelengths in the range from 3000 to %3D %3D %3D %3D ldit
Hamiltonian (11.11) is linear. 11.17.. Show that the wave functions (11.21) for sh those transitions for which dicate on this energy-level tions among the levels sho Asional numbe - Ar nite square well satisfy the orthogonality property that m(x)*/n(x) dx = 0 for m # n. %3D 5s 4p 4s SECTION 11.5 (Transitions; Time-Dependent Perturbation Theory *) 11.18 (a) The first excited state of the sodium atom is 2.11 eV above the ground state. What wavelength ra- diation can cause transitions between these two lev. els? What sort of radiation is this? (visible, UV, etc.?) (b) Answer the same questions for the two 2p levels in hydrogen, which are shown in Fig. 9.7 and are 4.5 x 10 eV apart. (This is the fine-structure split- ting discussed in Section 9.7.) (c) Answer the same questions for the lowest two levels of the 'Li nucleus, which are 0.48 MeV apart. Зр sm is in a cir- rge Q (with q tarting from ated power P t factor is P and Q un- a m, r, and q 3s FIGURE 11.22 Some low-lying levels of any one e odels of the 11.25 Figure 11.23 shows sor of the He atom. They are (for example, 1s2p mea tron in the 1s level and depends somewhat on trons' spins: If the spins zero (quantum number correct fre- ng to classi- of emitted he orbiting cies, forb(1) n = 1 and O Now find 11.19 The atoms of a certain monatomic gas have five ener- gy levels: E = 0, E, = 5.4, E = 8.2, E4 = 8.6, and E5 = 12.4, all measured up from E, in eV. (a) I - frared light with wavelengths in the range from 3000 to %3D %3D %3D %3D ldit
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How might I be able to solve problem 11.18? This problem is in a chapter called "Atomic Transitions and Radiation." The chapter is part of
Transcribed Image Text:Hamiltonian (11.11) is linear.
11.17.. Show that the wave functions (11.21) for
sh
those transitions for which
dicate on this energy-level
tions among the levels sho
Asional
numbe
- Ar
nite square well satisfy the orthogonality property
that m(x)*/n(x) dx = 0 for m # n.
%3D
5s
4p
4s
SECTION 11.5 (Transitions; Time-Dependent
Perturbation Theory *)
11.18 (a) The first excited state of the sodium atom is
2.11 eV above the ground state. What wavelength ra-
diation can cause transitions between these two lev.
els? What sort of radiation is this? (visible, UV, etc.?)
(b) Answer the same questions for the two 2p levels
in hydrogen, which are shown in Fig. 9.7 and are
4.5 x 10 eV apart. (This is the fine-structure split-
ting discussed in Section 9.7.) (c) Answer the same
questions for the lowest two levels of the 'Li nucleus,
which are 0.48 MeV apart.
Зр
sm is in a cir-
rge Q (with q
tarting from
ated power P
t factor is P
and Q un-
a m, r, and q
3s
FIGURE 11.22
Some low-lying levels of any one e
odels of the
11.25 Figure 11.23 shows sor
of the He atom. They are
(for example, 1s2p mea
tron in the 1s level and
depends somewhat on
trons' spins: If the spins
zero (quantum number
correct fre-
ng to classi-
of emitted
he orbiting
cies, forb(1)
n = 1 and
O Now find
11.19 The atoms of a certain monatomic gas have five ener-
gy levels: E = 0, E, = 5.4, E = 8.2, E4 = 8.6, and
E5 = 12.4, all measured up from E, in eV. (a) I -
frared light with wavelengths in the range from 3000 to
%3D
%3D
%3D
%3D
ldit
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