Compare a matter wavtoke*46tw /5ta33ijqtordko 4*lr-w e $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory of the atom is not compatible wdd 7e0/k - 5ojmju*vhgith quantum mechanics, particularly the uncertainty p d vo5keh7d*mg0u-jj/rinciple.

Explain why it is thvmh 8g :c lch2:qdogc 76-rp/pat the more massive an object is, the easier it becomes to predr/gh :2:6 mo-c cpq cgpd8lvh7ict its future position.

In view of the uncertxb08v)uwt9 bw ainty principle, why does a baseball seem to have a well-defined positiot vuw)b98bxw 0n and speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle :mp.wary 4ob e7 37jwcprecisely on its point? :3 a.p77re jcowwb4myExplain.

  A cold thermometer is placed in a h 2vzcf hgx9b)+ hsl*6ubpv 74yot bowl of soup. Will the temperature reading of the thermometer be the same as the temperature of the hot soup before the measurement* 6shfyl+7hpv9)4u2 vx gc zbb was made? Explain.

  Does the uncertainty principle set a limit to how b /ck7qjngkr ; *tz4 caf*fo2(well you can make any single measurement of positncf;kr4/tac zf7* bqk*ogj2( ion?

If you knew the position of an object precisely, with no uncertai 0a0bpn:iu3am:vbzo i2k(ez7nty, how well would you knu o:epim2zkz ba(003 7iban :vow its momentum?

  When you check the pressure in a tire, doesn't some air inevitad,1;knh:o a :pezfw i3bly escape? Is it possible to avoid this esca1 eof3hzawnp k;,: :dipe of air altogether? What is the relation to the uncertainty principle?

  It has been said that the ground-state energsti)o cqs 8(o,y in the hydrogen atom can be precisely known but the excited states have some uncertainty in their ,8 i)q(co stosvalues (an "energy width"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydrogen atom, the Bohr model or the quantum-mechanic:g)aqnsrmtrehb 8 -cl;ll9*3al model, predicts that the electron spends more time near thnq) -9;mrsgre:b8l3cl h*alte nucleus?

The size of atoms varies by+i:r 9ko-:h ms qcf)zs only a factor of three or so, from largest to smallest, yet the number of electrons varies from one to ove+r :h-iz9kqfm :ssco)r 100. Explain.

Excited hydrogen and excited helium atoms both r7/kd 5*u1 r mzjjih7fzadiate light as they jump down to 7 z1d5r*jizufj/ mkh7the $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there weref stb- .w5a3wc no electron spin but otherwise quantum mechanics were valid? Consider the first 20 eb5 a swcf.3wt-lements or so.

  Which of the following electrofrw9r3*+9f sf9 mdab0l;hh kxn configurations 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 uraniu q9hb+)wkj8;br.vjjy/gxl) w4dr1as m atom (careful scrutiny across the periodic table on the inside back cover will provide useful hints)+wsj.hkg jrj9)yql 41v;d bxa)/b r 8w.

In what column of the pe 6 ;pynd,bp8nbriodic table would you expect to find the atom with each of the following ;,nd6pnbbp8y configurations:
(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 exhiwr; /;v w:qptmbit similar properties?

Explain why potassium and sslex-0+p , sxlul1v wexh g:dj.r7+p+odium exhibit similar properties.

The ionization energyw0;8v xu .bxaz for neon $(Z=10)$ is 21.6 eV, and that for sodium $(Z=11)$ is 5.1 eV. Explain the large difference.

Why does the cutoff wav-kd2f3- +y9oe6t/it agpaouh elength in (Fig. Below) imply a photon nature for light? p9e-u/-gdtfho2atk o+6 yi 3a

Why do we not expect perfect agreement between measured values of X8 d p(9)vaqkkx 7rn1v k r6k*d ;m:grb2)dpwem-ray line wavelengths and those calculated using Bohr thar) 7 k*:6dr9qn1) p2kv8 ddvxwp k gk(m;embreory?

How would you figure out which lines in an X-ray s5-4l hd;y:zsgl zx4nxp 2(iua pectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron9bdif gybkjs.vb0k 7l x8..x2 transitions deep within an atom to produce shorter wavelengths than transitions by oulb2i9k v fksbbg. 0x7jxy8 ..dter electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary lw3 7 i*l.s qsqxrp7+kq;t)ze right? How is it the same?

Explain how a 0.0005-W laser bea4tsk j.ua5cy0 oh49gfm, photographed at a distance, can seem much stronger than a 1000-W street lamp at tu4f h.c4o9 gs0kjy ta5he same distance.

  Does the intensity of light froucl+p,x/v (z,arw kx 0m a laser fall off as the inverse square of the dixa rlk,u ,+(x0w /vpczstance? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic energy y4iu- i10p j/psiodhraiw * 8-$0.40 \, \text{eV}$ 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 traveling wiv(flq xx 7vek)3q 5kb(th 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 measured to2f ydds u2sg0aig g5g0n.sr-1 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 i bzr e + -oov+2rowp nr1:bpefss.2(a-n an excited state of an atom 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 mum*.x5j : tiboxon $(m=105.7 \, \text{MeV/c}^2)$, 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 neutron contained mw*l5 y7w qax5in a typical nucleus of ra5 a57y*mw lqxwdius $1.0 \times 10^{-15} \, \text{m}$. [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 sho,6wpg xdvt*qqg . dp;xw)v+3c w that if an electron were present in the nucleu3w vvg6xq , );d.c+ wpxptqgd*s $(r \approx 10^{-15} \, \text{m})$, 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 to9 l/bd6,pqz phe position of a $3.00$-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 twnfwculh)s7-d(v43 vo 5nc:jhe $n=6, l=3$ subshell?    elections

How many different states are possib 8+j k44vzqidvle for an electron whose principal quantum number+vkijzv8q4 4 d is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in th nxcd dt54y,2se ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers ;y..9sswiji oag5kuozcd: jb a55-v 7for each electron in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen atom hk4(qm( n/ wxl mmi9j c4s)phu.mpkpsg* 6n(7las $l=4$. 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 angular momentum of an electroy + cw ;27qdho/efskyn)fp-l- n 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 e8 9z-zt 7kosl$m_l=-3$, 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 elec)3vsctb 7/w bitrons in a "g" subshell.    electrons

What is the full electron configur*of: wamjvb9 3ation in the ground state for elements with $Z$ 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 (Se), (b) gold (Au2w wx8nnmqabxlw 1 k9c7j 4k+ khzc;66), (c) rad; +kzm7lx61 cqc2x 9w6kwnka j bw4h8nium (Ra)? [Hint: see the periodic table inside the back cover.]

  A hydrogen atom is in the b xjgchx3 z)iq9 ,4oc*$6s$ 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 third electron in lithium using the Bohr*or.j l-2g ybj theory. [Hint: This eleg-y2.bo*rj lj ctron has $n=2$ and "sees" a net charge of approximately $+1e$.] The measured value is $5.36 \, \text{eV}$.    eV

Show that the total angular momentum i 0 ai.w3we/ydtvkc-x 5s zero for a filled subshell.

  For each of the following atof*0mps 5.t.x.ss jo immic transitions, state whether the transition is allowed or forbidden, and if forbidden, what rule is being viol.5ss.m jmio0sxtpf.* ated:
(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 igwhb;h/j: x ,jsbh/o/n 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 electrons striking t f:ab.:wxrd m.h:+xmj he face ofa::.jxmr xh. fb+wm: d a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted from an X-ray 9u7 jr +0z /4* ugf)xasietfqmtube have 0if*g)q9urzax7 4j ems+ tu /f$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wa kl3ki48b.ng xvelength $\lambda_0$ 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 plpi ;n5-.;d9-zrhlzgd rl t/emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength f7f;v1 m3 jw4lpyii wo)or an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength for a3gl2afv+hl+f3n y u8hn $n=3$ 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 unknown material is bombarded with al3 i ;5yl/*qcjp ig*gelectrons. The wavelength of theij*pagi/q5 3l* y;gcl $K_\alpha$ 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 retyu 1s q/mh:1wz-(( uw/* (tflnqvwzmrinas 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 used6.i yvai ) ,ra 4nz34b rant8tkw6ju.j in a physics lab might have a power of $0.50 \, \text{mW}$ 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 diffraction if the beam emerc4e k f)rm:j:w kz9s8 g(qg2zzges through asq(4ze jzr28g :g)kz k:cm9f w $3.0$-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 ofn+j 67ww+ltze the He-Ne laser?$\lambda $ =    nm

Use the uncertainty princj9ds8/j8ukxpohkr; ,;o y+p f7b;mt z iple to estimate the position uncertainty for the electron in the ground state of the hydrogen atom. [Hint: Determine the momentum us,btroxzd7py k9mk;po h 88 uj;/+fj;sing 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 anoaxro0 rwwzmx-*)h *xd(p2i 0gular 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 hu jr0 nct3a98the radius of an electron orbit, estimate the average distance from the nucleus for an electron in the it 9j08a3hcrn unnermost $(n=1)$ 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 operates at8 *bomq,in w,j $95 \, \text{kV}$ 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 of the outermost electron in n7m-gn91uu lt no+oo/ 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 ho8elxrp qj93w d(7jkkzt333that the Moseley plot(Fig. Below) 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 sxzuhm:d ypp1oi4,rc ** yj/h/ tates 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 different electron states possible for a gi1 hz m7 5bz1wd7x7x l8osyn,fwo)r;yiven value of l8)xfn7b7z;1y ,zhr1wsy o x 5wdmoi7$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narrow slits in a/j91zk l gnspnq)( 1ojdo, py2 barrier. Thoy k2 g) l,n 91po(np/dsj1qjze slits are a 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 h: y za5e2re9rhydrogen atom is given both by the Bohr model and by quantum mechanicha5 2:rz 9eyres. Compare the results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling with wcu-x(kns.2i aycu w+du2b+ - 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 contai+nta 9 or,8w/fspxz6 xb dgr,4ns a line with a wavelength centered at 488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. E bsoxpxrdzw,,r64a +gft/ 9n8stimate the lifetime of the excited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated from rest across 550 V. They are then directed at twc. bdnpjw.5v 9o slits 0.70 mm apart. How far apart will the inte pj9nw vcb.d5.rference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton,pme uv* 317kmj. 0m1tmad4gbo each initially at rest, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by theiromtbk*e1m3g 1.mvu7j0m4 adp de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum number n werei, ko n-8+e qn2g: x1)ud8glnpt gw;gq limited to the range from 1 to 6, how many elements , n 8goggnn2qtd;+igqpw1) :-e8lk uxwould we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast woul8fwcgwlm*3 inr my:74d you be moving if your lmfwn8: yg4 m*wrc73imass is 75.0 kg? $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 show,oro5r 7+i syys a series of lines with one out of every four matching a line from the Lyman serirys oo +y,57ries 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 emitte + :bng-tpmao3d from the surface of a certain metal when it is tna b:o mgp3-+bombarded with high energy radiation. If this photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread of a laser b 0;oua lpm/)+jntvli v.zn6-deam, $$\theta \approx \lambda/D$$ , 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.]