Compare a matter waveh1 ct/fa -qd4t $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theo(xik /a97si7ud3w pu(qmqhn)ry of the atom is not compatible with quantum mechanics, particularly the uncertaaku uqqwi pn9h )7(/7xdi3sm(inty principle.

Explain why it is that the more massive an object is, the easizs-.ct dz- 7gatqyfekd; (6m (er it becomes to predict its fut((gsk7 --ta.dzy td f6 mcqz;eure position.

In view of the uncertainty prin drva1; k8+ cqbc*:dkmciple, why does a baseball seem to have a well-def d*c:;qk+rcdbvk1m 8a ined position and speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle preccox/0u/:s yfbx(uy/ aisely on its point? Explaiscfua bx/:/u x0 /(oyyn.

  A cold thermometer is placed in a hot bowl of soup. Will the i3dsuep710j rtemperature reading of the thermometer be the same as the u3jsd i7p0 e1rtemperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well you can make pe+yd5h f ovw0f0z 34bany single measuzf4y0w+p0e 5 fodh v3brement of position?

If you knew the position of an object precisely, witfnfjj -a/ cr n0dsm)6)h no uncertainty, how well would you know its mo)j/fm0jasrdnc 6n) - fmentum?

  When you check the pressure in a tire, doerwcx9)33gh6r1p3m fg4 t,qaxuf 5t g ssn't some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relation to the uncertainty qa g5cfr,xw3 3ft u)6tx1mhg93sg rp4principle?

  It has been said that the ground-state energy in the hhh6rrf rf ).0 y1;orxfydrogen atom can be precisely known but the excited states have some uncertainty in their values (an "energy width"). Is this consistent with the uncertainty principle in itshyf .6;1rr rhfof x)0r energy form? Explain.

Which model of the hydrogen atom, the Bohr molcn,(j04llzs ,m y9o tw 5k5utdel or the quantum-mechanical model, predicts that the electl4ksy0 l5m9lt jcunzw,( ,5t oron spends more time near the nucleus?

The size of atoms varies by only a factor of threx y2/4.r nwvhee or so, from largest to smallestvy2/4 wx .enrh, yet the number of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as they . upz(s/,i clmd 8 oktb8u:sf)jump down to the ,istzl puu8 bc8o)fk(s m/.:d$n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spin bu9j : x h6kkbjz,g7qy j.42keewt otherwise quantum mechanics were vy.j q hjk,k g972e4jkbzxe6:w alid? Consider the first 20 elements or so.

  Which of the following electron g 4+z6xze ygwhjt)6.dconfigurations are not allowed:
(a) $1s^2\,2s^2\,2p^4\,3s^2\,4p^2$;  ----待选择----allowednot allowed 
(b) $1s^2\,2s^2\,2p^3\,3s^1$;  ----待选择----allowednot allowed 
(c) $1s^2\,2s^2\,2p^6\,3s^2\,3p^3\,4s^2\,4d^3\,4f^1$? ----待选择----allowednot allowed 
If not allowed, explain why.

Give the complete electron configuration for a uranium atom (careful scrutinyt: .7bm gi:spr acrsmt:7gb p:ri. oss the periodic table on the inside back cover will provide useful hints).

In what column of the periodic tablet 7rx8.1o3i+fe1 vbzrpj) evd nc51lp would you expect to find the atom with each of the following cer)t jf3l+ed57cvpnv. 1 1zoi pxr 18bonfigurations:
(a) $1s^22s^22p^63s^2$;
(b) $1s^22s^22p^63s^23p^6$;
(c) $1s^22s^22p^63s^23p^64s^1$;
(d) $1s^22s^22p^5$?

Why do chlorine and iodine exhibit similarld/2 r pq73lvy+z g+wg properties?

Explain why potassium and sodium exhibit similar properties.6 -pp *d/s9cdz7 na8ffbmrw 2l

The ionization energy for nwz(zexf/ ys 1)a1 pkh;eon $(Z=10)$ is 21.6 eV, and that for sodium $(Z=11)$ is 5.1 eV. Explain the large difference.

Why does the cutoff wavelev kluak 4ff*523p9srp ngth in (Fig. Below) imply a photon nature for light? 94kuf32kp 5 *favlsr p

Why do we not expect perfect agreement between measured values of X-rav28jd3r kxcn4 y line wavelengths and those calv2k84dj cnx3 rculated using Bohr theory?

How would you figure out which lines in an X-ray spectrum correspontq.vj xmw x suy0qm,l*ep0b 0h *t.-c,t.rh;xd to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transi9q sr38f:dgve x4ly f:g t4ct7tions deep within an atom to produce shorter wavelengths than transitions by outer electrons? q3 e7fs4g9: :y84f vtdtlxgcr

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How is it the same?2 q-hxdo540sv.eq-9ed+fewcqh/m wu

Explain how a 0.0005-W laser beam, photographed at cv2xpng2-pis73kv 3la distance, can seem much stronger than a 1000-W street lamp ag xk7n2lc v23s3vp -ipt the same distance.

  Does the intensity of light from a laser fall off as the inverse squarggu 2j l tggjz+cpfw7+c*74l,e of the distance * 2pjl4+flcgju,w7g7zgt+gc ? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kineti sljsas ac u:/sj8j-bnm.;4.y c energy $0.40 \, \text{eV}$ are directed through two slits $0.50 \, \text{mm}$ apart. How far apart will the interference peaks be on a screen $1.0 \, \text{m}$ away? [Hint: First find the wavelength of the neutron.]
$\Delta y$ =    $ \times 10^{-7}\ \text{m}$

  Bullets of mass $3.0 \, \text{g}$ are fired in parallel paths with speeds of $220 \, \text{m/s}$ through a hole $3.0 \, \text{mm}$ in diameter. How far from the hole must you be to detect a $1.0 \, \text{cm}$-diameter spread in the beam of bullets? L =    $ \times 10^{28}\ \text{m}$

  A proton is travelingorvzpb5p7zh1 7-bz /g1ro; vg with a speed of $(6.560 \pm 0.012) \times 10^3 \, \text{m/s}$. With what maximum accuracy can its position be ascertained? [Hint: $\Delta p \approx m \Delta v$]
$\pm$    $ \times 10^{-11}\ \text{m}$

  If an electron’s position can be measr-;oykev u 8otkjgvq/l jb41 ;q 0li/.ured to an accuracy of $1.0 \times 10^{-8} \, \text{m}$, how accurately can its speed be known?
$\Delta v $=    $\times 10^{3}\ \text{m/s}$

  An electron remains in an excited state of an atom vw lmh.1iv..m( zwyc )for typically $10^{-8} \, \text{s}$. What is the minimum uncertainty in the energy of the state (in eV)?
$\frac{\hbar}{\Delta t}$ =    $ \times 10^{-8}\ \text{eV}$

  The $Z^0$ boson, discovered in 1985, is the mediator of the weak nuclear force, and it typically decays very quickly. Its average rest energy is $91.19 \, \text{GeV}$, but its short lifetime shows up as an intrinsic width of $2.5 \, \text{GeV}$ (rest energy uncertainty). What is the lifetime of this particle?
$\frac{\hbar}{\Delta t}$=    $ \times 10^{-25}\ \text{s}$

  What is the uncertainty in the mass of a muon5r +rs3y tlwy) $(m=105.7 \, \text{MeV/c}^2)$, specified in $\text{eV/c}^2$, given its lifetime of $2.20 \times 10^{-6} \, \text{s}$? [Hint: $\Delta E \approx \hbar / \Delta t$ and $\Delta m = \Delta E / c^2$]
$\frac{\hbar}{\Delta t}$=    $ \times 10^{-10}\ \text{eV}$
${\Delta m}$ =    = $\times 10^{-10}\ \text{eV}$

  A free neutron $(m=1.67 \times 10^{-27} \, \text{kg})$ has a mean life of $900 \, \text{s}$. What is the uncertainty in its mass (in kg)?
${\Delta m}$=    $\times 10^{-54}\ \text{kg}$

  An electron and a $140$-g baseball are each traveling $150 \, \text{m/s}$ measured to an accuracy of $0.055\%$. Calculate and compare the uncertainty in position of each.
For the electron $\frac{\hbar}{m\Delta v}$=    $\times 10^{-3}\ \text{m}$
For the baseball $\frac{\hbar}{m\Delta v}$ =    $ \times 10^{-33}\ \text{m}$

  Estimate the lowest possible energy of a neut;55d j)/k m+ zokt/khyz +yiyhron contained in a typical nucleus of radiy+y//kht +kh ozdm;j5)5z ky ius $1.0 \times 10^{-15} \, \text{m}$. [Hint: A particle can have an energy at least as large as its uncertainty.]
$\frac{\hbar}{\Delta x} $=    $\times 10^{-19}\ \text{kg} \cdot \text{m/s}$
E =    Mev

  Use the uncertainty principle to show that i:eq 0kj5;70cl cke qvcf an electron were present in the nucleu5e v0jel0q k7;cqk:ccs $(r \approx 10^{-15} \, \text{m})$, its kinetic energy (use relativity) would be hundreds of MeV. (Since such electron energies are not observed, we conclude that electrons are not present in the nucleus.) [Hint: A particle can have an energy at least as large as its uncertainty.]
E $\approx$    Mev

  How accurately can the position of a6wkrb sv vt u(un*+m;) $3.00$-keV electron be measured assuming its energy is known to $1.00\%$?
$\frac{\hbar}{\Delta p} =$    $ \times 10^{-10}\ \text{m}$

  For $n=6$, what values can $l$ have?
$\ell$ =    or    or    or    or    or   

  For $n=5, l=3$, what are the possible values of $m_l$ and $m_s$?
$n_\ell$ = $\pm $    or $\pm $    or $\pm $    or $\pm $   
$m_s$ = $\pm $ 1/  

  How many electrons can be in t5 e6t gh7nby,z0roxtn9jh 5 )bhe $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whose principal quantuailpl.c3n( o80 yj*g vm number* nlc(8l.ap0y g3o jiv is $n=4$? Write down the quantum numbers for each state.

List the quantum numberq 0zc)-qben 9b3qir1iu( m6rcs for each electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in thez7u,yhp z-w rz+c na07x 7v.yo ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen atom sgg9dtv9c mfyy) uz .;90heb- has $l=4$. What are the possible values for $n, m_l$, and $m_s$?
n $\ge $   
$m_\ell$ =    $\pm$    $\pm$    $\pm$    $\pm$   
$m_s$ = $\pm$   

  Calculate the magnitude of the an3sk z(. u2t-2gprp ncagular momentum of an electron in the $n=4, l=3$ state of hydrogen.
L =    $\times 10^{-34}\ \text{kg} \cdot \text{m}^2/\text{s}$

  If a hydrogen atom has t1ai2ih yr(7s$m_l=-3$, what are the possible values of $n, l$, and $m_s$?
$\ell \ge $   
n$\ge \ell$ +    (minimum 4)
$m_s$ = $\pm $   

  Show that there can be 18 fn nn.(r4se; kelectrons in a "g" subshell.    electrons

What is the full electron configuration in the ground state for elements witvqqxm13th2fq ig,8e.( eu rj;h $Z$ equal to (a) 27, (b) 36, (c) 38? [Hint: see the periodic table inside the back cover.]

What is the full electron configuration for (a) selenium (Sv dk,o8ubqor01e5r d2e), (b) gold (Au), (c) radium (Ra)? [Hint:d8vr0 5ou2,bdqoe1 rk see the periodic table inside the back cover.]

  A hydrogen atom is in thgb8ldwvmf +r 7mx4obn y/4o6: e $6s$ state. Determine
(a) the principal quantum number, n =   
(b) the energy of the state, $E_6$ =    Mev
(c) the orbital angular momentum and its quantum number $l$ L =   
(d) the possible values for the magnetic quantum number.$m_\ell$ =   

  Estimate the binding energy of the thd( e:cxg:c 9pvird electron in lithium using the Bohr theory. [Hint: This electron has evc: px:9c dg($n=2$ and "sees" a net charge of approximately $+1e$.] The measured value is $5.36 \, \text{eV}$.    eV

Show that the total angular momentum is zy c-cb,5fm8u l:zh)dll :yc,lero for a filled subshell.

  For each of the following atomic transitions, state wheth -ews,ful4 ,xwer the transition is allowed or forbidden, x -s l,wwe4,ufand if forbidden, what rule is being violated:
(a) $3p \to 4p$  ----待选择----forbiddenallowed 
(b) $1s \to 2p$  ----待选择----forbiddenallowed 
(c) $3d \to 2d$;  ----待选择----forbiddenallowed 
(d) $4d \to 2p$;  ----待选择----forbiddenallowed 
(e) $4s \to 2p$. ----待选择----forbiddenallowed 

  An excited H atom is in o 7-;n *lqe.zwxjj1wdd egooyekx )pa8*. +6b a $6d$ state.
(a) Name all the states $(n, l)$ to which the atom is "allowed" to jump with the emission of a photon.
(b) How many different wavelengths are there (ignoring fine structure)?   

  What are the shortest-wavelength X-rays emitted by ele0,u c ikh; eulgu0z ju;3w3*cictrons striking the face of a *hcwug u,3 ;03;u0 kui ceijzl$33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitte1/ o7jk5 vgcbtd from an X-ray tube have jtb5v/g1 o k7c$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelengthstd76qfceb(5 i1 c9rm $\lambda_0$ is given by $\lambda_0 = \frac{1240 \, \text{nm} \cdot \text{V}}{V}$ where $V$ is the X-ray tube voltage in volts.

  Estimate the X-ray wavelength emitsf v2ju(3xgz*u .wkk1ted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength fg)4if4mk h s : keg55dftc**ntor an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength t9x3gl/nyf +qe38p ijfor an $n=3$ to $n=1$ transition in molybdenum $(Z=42)$. The measured value is $0.063 \, \text{nm}$. Why do we not expect perfect agreement?
$\lambda $ =    nm
n =   

  A mixture of iron and an unkno vx0 2cai,zvf*1h;9qx; tpuj pwn material is bombarded with electrons. The wavelength ofvzuqpf;c2avjipt0 ,1h* 9x ;x the $K_\alpha$ lines are $194 \, \text{pm}$ for iron and $229 \, \text{pm}$ for the unknown. What is the unknown material?
 ----待选择----copperironmagnesiumvanadiumchromiummanganese 

  A laser used to weld detached re 9h d:j*sq*b7yaww p3ftinas puts out $28$-ms-long pulses of $640$-nm light which average $0.68$-W output during a pulse. How much energy can be deposited per pulse and how many photons does each pulse contain?
E =    J
N =    $\times 10^{16}\ \text{photons}$

  A low-power laser used in a physics lab might have a power ox* spxha :8f1 vzz,,nq0:f 6ly5jgbk bf $0.50 \, \text{mW}$ and a beam diameter of $3.0 \, \text{mm}$. Calculate
(a) the average light intensity of the laser beam, I =    $W/m^2$
(b) compare it to the intensity of a lightbulb producing $40$-W light viewed from $2.0 \, \text{m}$.I =    $W/m^2$ The laser beam is more intense by a factor of   

  Estimate the angular spread of a laser beam due to diffrs 3fm jfmi6orl+lkjyo2 .,4u. action if the beam emerges thrmfyom l+jlo6 .4kr2.,ui 3fsj ough a $3.0$-mm-diameter mirror. Assume that $\lambda = 694 \, \text{nm}$. What would be the diameter of this beam if it struck
$\theta$ =    $ \times 10^{-4}\ \text{rad}$
(a) a satellite $300 \, \text{km}$ above the Earth, D =   $ \times 10^{2}\ \text{m}$
(b) the Moon?D =   $ \times 10^{5}\ \text{m}$

  What is the wavelength of the He-Ne laserqv ntw.x0gkg+j 3,: g -a6ersoo p5je.?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncertainty for thewcmdlw. q-m mq 0m3n8+ electron l0 nc mq8w.m3dqw+mm-in the ground state of the hydrogen atom. [Hint: Determine the momentum using the Bohr model of Section 27-12 and assume the momentum can be anywhere between this value and zero.] How does this result compare to the Bohr radius?

  An electron in the $n=2$ state of hydrogen remains there on average about $10^{-8} \, \text{s}$ before jumping to the $n=1$ state.
(a) Estimate the uncertainty in the energy of the $n=2$ state. $\frac{\hbar}{\Delta t} =$    $ \times 10^{-8}\ \text{eV}$
(b) What fraction of the transition energy is this? $\frac{\Delta E}{E} =$    $ \times 10^{-9}$
(c) What is the wavelength, and width (in nm), of this line in the spectrum of hydrogen?
$\lambda$ =    nm
$\Delta \lambda =$    $ \times 10^{-7}\ \text{nm}$

  What are the largest and smallest possible values for the (e21/uctax+ xlt- l)eo up xu,angular momentum $L$ of an electron in the $n=5$ shell?
$\text{The smallest value of } L \text{ is}$ =   
$\text{The largest value of } L \text{ is}$ =    $\times 10^{-34}\ \text{kg} \cdot \text{m}^2/\text{s}$

  Estimate
(a) the quantum number $l$ for the orbital angular momentum of the Earth about the Sun, $\ell$ =    $ \times 10^{74}$
(b) the number of possible orientations for the plane of Earth's orbit. N =    $ \times 10^{74}$

  A $12$-g bullet leaves a rifle at a speed of $180 \, \text{m/s}$.
(a) What is the wavelength of this bullet? $\lambda $ =    $ \times 10^{-34}\ \text{m}$
(b) If the position of the bullet is known to an accuracy of $0.60 \, \text{cm}$ (radius of the barrel), what is the minimum uncertainty in its momentum? $\frac{\hbar}{\Delta y}$ =    $\times 10^{-32}\ \text{kg} \cdot \text{m/s}$

  Using the Bohr formula for the radius of an electron orbit, esti8mli n0ag9 m;vmate the average distance from the nucle;m80 gn9mal ivus for an electron in the innermost $(n=1)$ orbit of a uranium atom $(Z=92)$. Approximately how much energy would be required to remove this innermost electron?
$r_{\text{uranium}} =$    $ \times 10^{-13}\ \text{m}$
$\text{the binding energy is }$    $ \ \text{keV}$

  An X-ray tube operat u6q*(hb5g mfl5nyp1m es at $95 \, \text{kV}$ with a current of $25 \, \text{mA}$ and nearly all the electron energy goes into heat. If the specific heat of the $0.085$-kg plate is $0.11 \, \text{kcal/kg} \cdot ^\circ \text{C}$, what will be the temperature rise per minute if no cooling water is used?
$\frac{\Delta T}{t} =$    $ \times 10^{3}\ ^\circ\text{C}/\text{min}$

  The ionization (binding) energy ofm 0dbg5 p/bu;q7b.h *m (eejzi the outermost electron in boron is $8.26 \, \text{eV}$.
(a) Use the Bohr model to estimate the "effective charge," $Z_{\text{eff}}$, seen by this electron. $Z_{\text{eff}} $=   
(b) Estimate the average orbital radius. z =    $ \times 10^{-10}\ \text{m}$

  Use the Bohr theory to show that the Moseley plot(Fig. B-6.zjlbu k m;delow) can be written $\sqrt{\frac{1}{\lambda}} = a(Z - b)$, where $b \approx 1$, and evaluate $a$. a =    $\ \text{m}^{-\frac{1}{2}}$

(a) Show that the number of different d,b8 a;n c,+h)yx kxlxstates for a given value of $l$ is equal to $2(2l + 1)$.
(b) What is this number for $l=0, 1, 2, 3, 4, 5,$ and $6$?

Show that the number of dins/hn 14ugq(rpddxrpj;z8c8 f(g7h 7 fferent electron states possible for a given value of 8qdpzpn7 7j(;8 4( xgshc /nuhrgfd1r$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons withgp d/a 54 -9v k5bs(plgnl)xti energy 45 kV is shot through two narrow slits in a barrier. The slits are ak 5dallnpvxb s4pg( 5- )ig9t/ distance $2.0\times10^{-6}\ \text{m}$ apart. If a screen is placed 35.0 cm behind the barrier, calculate the spacing between the "bright" fringes of the interference pattern produced on the screen. $\Delta y =$    $\ \mu\text{m}$

  The angular momentum in the hydrogen atom iirfhi q+4 n542std2obs given both by the Bohr model and by quantum4ribh 2 o5 nqsd2t+i4f mechanics. Compare the results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is travelinf5 m0p.vq ha-n.9gepp4dmohn,in6t* g with a speed of $(22 \pm 0.22)\ \text{m/s}$. With what maximum accuracy can its position be determined? $\Delta x =$    $\times 10^{-37}\ \text{m}$

  An atomic spectrum contains a line with a wavelength centered*-q9yumq rp:d at 488 nm. Careful measurements show the line is really spread out between 487:mr- 9du*ypqq and 489 nm. Estimate the lifetime of the excited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are acceleratedq,pzib 7*d*pv from rest across 550 V. They are then directed at two slits 0.70 mm apart. How far apart will the interfe q*7v,*z ppdbirence peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at recm4 ib5 ctwbnn6.)o s5st, are accelerated across the same voltage. Assuming that the uncertainty in the 4.56wno)n cb5 mscibtir position is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum number n were limited to the range from 1 to 6, ) .r 4nn(xhwcy;v rau5how many elements wo4nu nx c;y)hr vw5(.rauld we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast would you be moving wetfaq:25 fg.e7qdv1if your mass is 75.0 gta1weqfd v.:75 2e fqkg? $v = $    $ \times 10^{-35}\ \text{m/s}$
Would you notice diffraction effects as you walk through a doorway?  ----待选择----yesno 
Approximately how long would it take you to walk through the doorway?$\Delta t \approx $    $ \times 10^{34}\ \text{s}$

  Suppose that the spectrum of an unknown element shows a series of lkyi fw00.(npxines with one ou n.pfx(iyk00w t of every four matching a line from the Lyman series of hydrogen. Assuming that the unknown element is an ion with Z protons and one electron, determine Z and the element in question. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm are emitted from the surface of a certain metalpcqkr7 ;f6z, y when it is bombarded with high energy radiaz6ckyrp,q 7;ftion. If this photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spreap/ocfa:nuj6d 2 w5ml*d of a laser beam, $$\theta \approx \lambda/D$$ , is precisely what you might expect from the uncertainty principle. [Hint: Since the beam's width is constrained by the dimension of the aperture D, the component of the light's momentum perpendicular to the laser axis is uncertain.]