11.17 Show that the wave funnite square well satisfy ththat m(x)*f,(x) dx =FIGURE 11.21SECTION 11.5 (Transitions;Perturbation Theory(Problem 11.10)11.11 (a) A classical point charge q of mass m is in a cir-cular orbit of radius r around a fixed charge Q (with qand Q of opposite sign, of course). Starting fromEq. (11.1), derive a formula for the radiated power Pin terms of q, m, r, and Q. (b) By what factor is Pchanged if we double q (leaving m, r, and Q un-changed)? (c) What if we double Q (with m, r, and qunchanged)?11.12atom was that they failed to predict the correct fre-quency for the radiation emitted. According to classi-cal electromagnetic theory, the frequency of emittedradiation should equal the frequency of the orbitingelectron. (a) Calculate the orbital frequencies, forb (1)and forb (2), of a classical electron in the n=n3 2 Bohr orbits of a hydrogen atom. (b) Now findthe frequency f,(2→1) of the actual photon emittedin the 2 1 transition. Show that f,(2 1) is notequal to either forb 2) or forb 1) (or their ayerage or11.18 (a) The first excited st2.11 eV above the grounddiation can cause transitels? What sort of radiatic(b) Answer the same quein hydrogen, which are4.5 x 10 eV apart. (THting discussed in Secticquestions for the lowestwhich are 0.48 MeV apaOne of the difficulties with classical models of the11.19 The atoms of a certaingy levels: E = 0, E2Es = 12.4, all measurefrared light with wavele3200 nm shines throughcause? If the gas was seground state, would yo%3D1 and portions. The transition zone between the near and far fields necessarily con-atlial field. Whenportions of the field lines are offset from nearlanged position moves outwardportiransverse component, as shown in Fig. 11.1(b) and (c).* While the ra-dial component of the electric field falls like 1/r it can be shown that thetransverse component falls like 1/r. Consequently, at large distances it is thetransverse component that dominates and carries radiated energy away from(b)the charge.The total power P radiated by any single charge q (moving nonrelativis-tically) can be shown to bemsns2kq aP =(c)(11.1)3cFIGURE 11.1ol-(a) Electric field lines from a staticwhere a is the charge's acceleration. This formula accurately describes the charge are radial. (b) When theplyso,power radiated by any macroscopic system of moving charges. For example, in charge is given an abrupt kick tothe right, changes in its electric fieldpropagate outward at speed cdistant portions of the field stillpoint outward from the originalTV or radio broadcasting, electric charges are made to oscillate inside the rodsof an antenna, and the resulting radiated power is given by (11.1). (See Prob-n-lem 11.2.) Notice that the power (11.1) depends on the acceleration a. Thus acharge moving at constant velocity does not radiate. We should also mentionthat with an assembly of many accelerating charges, the fields produced by theuferent charges can sometimes interfere destructively, with no net radiatedpower. For example, consider a uniform ring of charge rotating at a constant(open circle) position. (c) Thetransverse disturbance linking nearand far fields continues to moveradially outward as the chargeats#.a-coasts forward.byer.steady current loop and does not radiate any power.

Question
Asked Jan 14, 2020
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How might I be able to answer Problem 11.11? This section is in a chapter named "Atomic Transitions and Radiation," and is under quantum mechanics. Also, the section that this problem resides in is called  Radiation by Classical Charges.

11.17 Show that the wave fun
nite square well satisfy th
that m(x)*f,(x) dx =
FIGURE 11.21
SECTION 11.5 (Transitions;
Perturbation Theory
(Problem 11.10)
11.11 (a) A classical point charge q of mass m is in a cir-
cular orbit of radius r around a fixed charge Q (with q
and Q of opposite sign, of course). Starting from
Eq. (11.1), derive a formula for the radiated power P
in terms of q, m, r, and Q. (b) By what factor is P
changed if we double q (leaving m, r, and Q un-
changed)? (c) What if we double Q (with m, r, and q
unchanged)?
11.12
atom was that they failed to predict the correct fre-
quency for the radiation emitted. According to classi-
cal electromagnetic theory, the frequency of emitted
radiation should equal the frequency of the orbiting
electron. (a) Calculate the orbital frequencies, forb (1)
and forb (2), of a classical electron in the n=
n3 2 Bohr orbits of a hydrogen atom. (b) Now find
the frequency f,(2→1) of the actual photon emitted
in the 2 1 transition. Show that f,(2 1) is not
equal to either forb 2) or forb 1) (or their ayerage or
11.18 (a) The first excited st
2.11 eV above the ground
diation can cause transit
els? What sort of radiatic
(b) Answer the same que
in hydrogen, which are
4.5 x 10 eV apart. (TH
ting discussed in Sectic
questions for the lowest
which are 0.48 MeV apa
One of the difficulties with classical models of the
11.19 The atoms of a certain
gy levels: E = 0, E2
Es = 12.4, all measure
frared light with wavele
3200 nm shines through
cause? If the gas was se
ground state, would yo
%3D
1 and
help_outline

Image Transcriptionclose

11.17 Show that the wave fun nite square well satisfy th that m(x)*f,(x) dx = FIGURE 11.21 SECTION 11.5 (Transitions; Perturbation Theory (Problem 11.10) 11.11 (a) A classical point charge q of mass m is in a cir- cular orbit of radius r around a fixed charge Q (with q and Q of opposite sign, of course). Starting from Eq. (11.1), derive a formula for the radiated power P in terms of q, m, r, and Q. (b) By what factor is P changed if we double q (leaving m, r, and Q un- changed)? (c) What if we double Q (with m, r, and q unchanged)? 11.12 atom was that they failed to predict the correct fre- quency for the radiation emitted. According to classi- cal electromagnetic theory, the frequency of emitted radiation should equal the frequency of the orbiting electron. (a) Calculate the orbital frequencies, forb (1) and forb (2), of a classical electron in the n= n3 2 Bohr orbits of a hydrogen atom. (b) Now find the frequency f,(2→1) of the actual photon emitted in the 2 1 transition. Show that f,(2 1) is not equal to either forb 2) or forb 1) (or their ayerage or 11.18 (a) The first excited st 2.11 eV above the ground diation can cause transit els? What sort of radiatic (b) Answer the same que in hydrogen, which are 4.5 x 10 eV apart. (TH ting discussed in Sectic questions for the lowest which are 0.48 MeV apa One of the difficulties with classical models of the 11.19 The atoms of a certain gy levels: E = 0, E2 Es = 12.4, all measure frared light with wavele 3200 nm shines through cause? If the gas was se ground state, would yo %3D 1 and

fullscreen
portions. The transition zone between the near and far fields necessarily con-
at
lial field. When
portions of the field lines are offset from near
langed position moves outward
portiransverse component, as shown in Fig. 11.1(b) and (c).* While the ra-
dial component of the electric field falls like 1/r it can be shown that the
transverse component falls like 1/r. Consequently, at large distances it is the
transverse component that dominates and carries radiated energy away from
(b)
the charge.
The total power P radiated by any single charge q (moving nonrelativis-
tically) can be shown to be
ms
ns
2kq a
P =
(c)
(11.1)
3c
FIGURE 11.1
ol-
(a) Electric field lines from a static
where a is the charge's acceleration. This formula accurately describes the charge are radial. (b) When the
ply
so,
power radiated by any macroscopic system of moving charges. For example, in charge is given an abrupt kick to
the right, changes in its electric field
propagate outward at speed c
distant portions of the field still
point outward from the original
TV or radio broadcasting, electric charges are made to oscillate inside the rods
of an antenna, and the resulting radiated power is given by (11.1). (See Prob-
n-
lem 11.2.) Notice that the power (11.1) depends on the acceleration a. Thus a
charge moving at constant velocity does not radiate. We should also mention
that with an assembly of many accelerating charges, the fields produced by the
uferent charges can sometimes interfere destructively, with no net radiated
power. For example, consider a uniform ring of charge rotating at a constant
(open circle) position. (c) The
transverse disturbance linking near
and far fields continues to move
radially outward as the charge
ats
#.
a-
coasts forward.
by
er.
steady current loop and does not radiate any power.
help_outline

Image Transcriptionclose

portions. The transition zone between the near and far fields necessarily con- at lial field. When portions of the field lines are offset from near langed position moves outward portiransverse component, as shown in Fig. 11.1(b) and (c).* While the ra- dial component of the electric field falls like 1/r it can be shown that the transverse component falls like 1/r. Consequently, at large distances it is the transverse component that dominates and carries radiated energy away from (b) the charge. The total power P radiated by any single charge q (moving nonrelativis- tically) can be shown to be ms ns 2kq a P = (c) (11.1) 3c FIGURE 11.1 ol- (a) Electric field lines from a static where a is the charge's acceleration. This formula accurately describes the charge are radial. (b) When the ply so, power radiated by any macroscopic system of moving charges. For example, in charge is given an abrupt kick to the right, changes in its electric field propagate outward at speed c distant portions of the field still point outward from the original TV or radio broadcasting, electric charges are made to oscillate inside the rods of an antenna, and the resulting radiated power is given by (11.1). (See Prob- n- lem 11.2.) Notice that the power (11.1) depends on the acceleration a. Thus a charge moving at constant velocity does not radiate. We should also mention that with an assembly of many accelerating charges, the fields produced by the uferent charges can sometimes interfere destructively, with no net radiated power. For example, consider a uniform ring of charge rotating at a constant (open circle) position. (c) The transverse disturbance linking near and far fields continues to move radially outward as the charge ats #. a- coasts forward. by er. steady current loop and does not radiate any power.

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Expert Answer

Step 1

a)

the power radiated is, 

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Step 2

the expression for acceleration, 

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Step 3

rewrite the  equation for P usin...

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