Compare a matter wav2o nrge+n0:tre $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory /k 8y 7-ud:n7mzbbkfc of the atom is not compatible with quantum mechanics, particularly the uncertainty 7-ky 8 uzmdbbc/7nkf :principle.

Explain why it is that the more massive an object is, t ysvdphbr2 j)v0;n5 h m-bfn77he easier it becomes to predict its future j-nb;b2ph fdv h nv)r77 ms05yposition.

In view of the uncertainty principle, why does a baseball seem to have a well- w8f;6a+v/ wvvr3qb )amd5s6)y8 melqaiirr 7defined position and speed whereas an electro aa 8adslwrfq 6evr5 ym;/v)8)q+3r7 miwbvi6 n does not?

  Would it ever be possible to balance a very sharp needle preciselyymai )d2: g 0vwsvc1k.7) cdih on its point? Explain.dc17 iwk:2h 0 gims ady).v)cv

  A cold thermometer is placed in a ho ikkl7 w2a,u: 5a99pqh- tgtslt bowl of soup. Will the temperature reading of the thermometer be the same as the temperature of the hot soup before the measurement was made? Expltw-s5l9 agp2,k k 9alt7: uqhiain.

  Does the uncertainty principle set a limit to how wcef-tn8(w1zk y1; ox1odwc on75w pb7ell you can make any single measurementcz w87fn 1b5ywn 1wo c; to1xe7opk-d( of position?

If you knew the positiw4 40)kndnf yl2yk ys8on of an object precisely, with no uncertainty, how well would you know i f8yn d04y sk2yn4wlk)ts momentum?

  When you check the pressure in a tire, doesn't some air io:9wae 6du la:9l9fsr nevitably escape? Is it possible to avoid this escape of air altogether? What is the relation to t99f el d oarla6::su9whe uncertainty principle?

  It has been said that the ground-state ed xq/e*c)ahfd4s,r f7nergy in the hydrogen atom can be precisely known but the excited states have some uncertainty in their values (an "energy wid/d* 4xq,rfac ehsfd)7 th"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydrogen atom,lcvi-wb/o pm4de 5o;, 6qs nl3 the Bohr model or the quantum-mechanical model, predict46ce5 nvsl/;, bipolo-qd m 3ws that the electron spends more time near the nucleus?

The size of atoms varies by only a factor ofz9g :z/ s*chsb three or so, from largest to smallest, yet czzh /b s*:gs9the number of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as they jump dow1q5us3t: bvnqq ;t, (s0p ttnf.vvf7vn to thevsvvuf0t:q fq7 q vnbt,n; t5t1(.ps 3 $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spicw o(l is.0:ken but otherwise quantum mechanics were valid? Consider the firs eo(0clwski.: t 20 elements or so.

  Which of the following ex+o 9zc g6gmw0 *ztr5nlectron 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 uranium atom z*j b;hjtm8k3(careful scrutiny across t3mzj htj* b;8khe periodic table on the inside back cover will provide useful hints).

In what column of the periodic table would you expect to find the atoms: eno7nlp-+x with each of thes+ l-:oxe7pnn following 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 exhibit similar uuw3u4hy, 6xa properties?

Explain why potassium and sodium exhibit similar properties. (qlgtd(y*b (d

The ionization energy fz7rsm ibab,cv.i7- (bor 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 wavelength in (Fig. Below) imply a photon nature for light?81w9 7ul vcunf 1c fnlvu8 u97w

Why do we not expect perfect agreement between measu60xcw )z lph3szwvm* .red values of X-ray line wavelengths and those calculated using Bohr theory?w mpv6hzx.w zs c*30)l

How would you figure out which lines in an X-ray spectrum correspond t o.iwb bpyl72)o $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron teo5bt 4 kzu0 ,b r+)7,cdog bwi7psaj9n+.afdransitions deep within an atom to produce shorter wavelengthsn.04 agre d sooauzb) bd jcw75 ,k,i+pf+t9b7 than transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary liq7+6e mdnh/ k 2koj5lmj(x/right? How is it the same?

Explain how a 0.0005-W laser beam, photojyo( dt3sqw54graphed at a distance, can seem much stronger than a 1000-W street lamp at the same distan4tq d3ysj (5owce.

  Does the intensity of l6kaybe4q,. 4v4p/, h zggyqqb ight from a laser fall off as the inverse square of the distance? 4,qe 6gah/k 4.b q4qyzpg y,bvExplain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic ene/ skabllq*f4m(c - k rh;nxx76rgy $0.40 \, \text{eV}$ 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 with a spwfrle8g+h .e(8 j2whmeed 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 to fvv2b6j l fba);vx.:ch u.d:xan 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 for typz:l7a/usqis *s6)xdn ically $10^{-8} \, \text{s}$. 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 mas-bxma ; xxh8yk.to-3o s of a muon $(m=105.7 \, \text{MeV/c}^2)$, 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 ne/a8m16l wwd gsutron contained in a typical nucleus o6mgw ldaw/1s 8f radius $1.0 \times 10^{-15} \, \text{m}$. [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 if an electron wer ajn4.8jb) njte present in the nu.ba4 tj8 nn)jjcleus $(r \approx 10^{-15} \, \text{m})$, 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 po*e6h8vunog,zwvq sl e7 33iq+sition 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 bw :c3o14q am-a*ahrroe in the $n=6, l=3$ subshell?    elections

How many different states are posk3s cg58p4p7mbfz1r a5fts8 e)2 h eiesible for an electron whose principal quantum numbersfrf) ze8e835 1 4 p5agsb2hck 7eimtp is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the ground state of ix:ood,gu j 7y605zqs
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground state of nitrogee*;y3tmluq5eo ezz22 n $(Z=7)$.

  Suppose a certain hydrog8 sv/,xnw 3n ll1-vtpgen atom 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 angular momentum of an electron k*uhsb2.5qr9rsd t h3in the $n=4, l=3$ state of hydrogen.
L =    $\times 10^{-34}\ \text{kg} \cdot \text{m}^2/\text{s}$

  If a hydrogen atom h01kp 72*zb/sl yfno djas $m_l=-3$, 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 1/* x(6ak7t yyiodthnv0q w02h8 electrons in a "g" subshell.    electrons

What is the full electron configuration in the ground state for 89fvm,c6m nylelements with $Z$ equal to (a) 27, (b) 36, (c) 38? [Hint: see the periodic table inside the back cover.]

What is the full electron conf4 gombgdhb (0i1a/a6higuration for (a) selenium (Se), (b) gold (Au), (c) radium (Ra)? h0(6h4 bbai1gao dg/m [Hint: see the periodic table inside the back cover.]

  A hydrogen atom is in thfvik2o lfarne, ak00t 7; b7ixacm 2aij-:u- 1e $6s$ 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 energyca7 od( mgnuhww(j50 * of the third electron in lithium using the Bohr theory. [Hint: This electron hasad(0o7hnmgcuw * j5(w $n=2$ and "sees" a net charge of approximately $+1e$.] The measured value is $5.36 \, \text{eV}$.    eV

Show that the total angular momentu5sm tytg0/rh nem/ -/vs h03ajm is zero for a filled subshell.

  For each of the following atomic transiti(lruks6 l o8k*ons, state whether the transition is allowed or forbidden, and if forbidden, w lk8orls6k*( uhat 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 akd*w6pk 3pdx) 5.wv tl $6d$ 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 stri+kgns9qk +t/zking the face of ak9qsn +gk z+t/ $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength saeo, 3-4dd2:ta ojrj r w3k.dbremsstrahlung X-rays emitted from an X-ray tube have oaded tj.orsr4k2d:w,3a- 3j$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelength 23k6+b3rzh gy9 n bglfzw rd*3$\lambda_0$ 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 wavela+,soh+p.84nfld p xx ength emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for an 2 oxksdqo1ft q5juxm5 :52ts0$n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength for andj5p.1 l ty z6b/um0gl+0aozj4gte3d $n=3$ 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 bom*z+:p(i z - d21j ghw* rq8szo*utvrczbarded with electrons. The wavelength of thec*: w us18hzt-zpodjg *z i r+2(zqvr* $K_\alpha$ 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 retixr z;h-1y*f*t(ggj/tj )ejj-e ky+ lznas 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 hal.iwr z51huw0k tr xhp9q6/g f; b(dl1ve 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 diffractio.af mf7yzd i7)n if the beam emerges th yfaidm7z)f 7.rough 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-:j f1ahjoqf8m-q8 (ti Ne laser?$\lambda $ =    nm

Use the uncertainty principle aef/dfo5-8k s)cgh. 1xsrw1sto estimate the position uncertainty for the electron in the ground state of the hydrogen atom. [Hissxc5rhfg w 8kf)1aeod-/ s.1nt: 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 angusoyx/sv fx.j 2kg +;9zlar 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 a - .jzbwo5:xwmn electron orbit, estimate the average distancebw ow: -zm.5xj from the nucleus 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 operateojddk1jy t /*/-c7h efs 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 of the outermost electron in boniis+ n1ev-8j8*m9 xcm3a /sd mdl(fm ron 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 shh8a f4tuw 5qjsjo;08 oow that 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 states d 2 w+sw,6f8(l lv)t6tughja jfor 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 ps)xzfa4bl jji0*v .7tossible for a given value of * .iajltjsbv)4x7f0 z $n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot throug 0:60pgkruz lrh two narrow slits in a barrier. The slits are a distanc rkzpgu06 r:0le $2.0\times10^{-6}\ \text{m}$ 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 is given both byg)pv)h /( yq ex )rm2lu/eq5eva zq h6t1r:gw5 the Bohr model and by quantum mechanics. Compare the results for v h lryq6w): xtm)ez (p5)euqhgreav q1/52/g$L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling with a i ly ri8f 7hsr, v6xh0t9+(mhqspeed 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 at 488 nm. Caref /:gkj sd 2d8c1drt0cbul b8dd20rg/dkt1jcs c : measurements show the line is really spread out between 487 and 489 nm. Estimate 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 t6qkp; q (ncte;qrc78rwo slits 0.70 mm apart. How far apart will the interference peaks be on a screep ckqr(q 8q r7nt;c;e6n 28 m away? $\Delta y$ =    nm

An electron and a proton, each init2 cp drwwn6dkbn8-8j0 ially at rest, are accelerated across the same voltage. Assumn8c-82d nw0jwrdp k6bing that the uncertainty in their 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 frh,6 qxz,r(v(vr-fe j rom 1 to 6, how many elements would we rfj( -er(vq,v,hxr z 6find in nature?   

  If your de Broglie wavelern 4g*b :;l)g2;pxrqf-v d uwrngth were 0.50 m, how fast would you be moving if your mass is q;dr *4wp-f;rbguv x:)ln2 rg75.0 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 spectrumtwbwt26(z(d+ ao* tlx vyw -)xkz/4 mz of an unknown element shows a series of lines with one out of e( t wbmxz-vy*(ww zo l4+xkt2t)daz /6very 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 *h)5z9 rec gss:4tdbc nm are emitted from the surface of a certain metal when it is bombarded with high z)tc:db 49rhg5 *scesenergy radiation. If this photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread oauk6hzi cv+;e4o*.r.xbvt ,aefv /c1f 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.]