Compare a matter wave 20cmsee7eh5 :g4u n pgkso/s( $\Psi$ 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 with quantumrxtd)() 3edyouhsc3f c(x.9c mechanics, particul9e)rcu3) .xhx(ts co(c 3yddfarly the uncertainty principle.

Explain why it is that the more2zaryy4 k emf,q:n k/kdm: 75a massive an object is, the easier it becomes to predict its fyaa5r4,k :e y/2mkdkm7qfz:nuture position.

In view of the uncertainty principle, why does a baseball seem to havzdzbwc aa, a7;65+um 6b ufem/e a well-defined position and speed ba,wamaz e z ;7b+6c6d5u/mfuwhereas an electron does not?

  Would it ever be possible to balance a very sharp needle precin .n*/ e c4lcs*g)fefisely on its point? Explain.f f*4)egec cnln/*.si

  A cold thermometer is placed in a hot bowl of soup. Will t/qk.qxh/ 6ezthe temperature reading of the thermometer be the same as the temperature of the hot soup before the 6eq/ kz.h/qxtmeasurement was made? Explain.

  Does the uncertainty principle set a limit to how well you xa)6be .1i:) cryjdanx 9ll(c can make any single measuremea)6c1ldry :x 9.iaclxjb) e n(nt of position?

If you knew the position of an object pre+05*lwade cs ucisely, with no uncertainty, how well would you know it sc+uda*w5 0els momentum?

  When you check the pressure in a tire, doesn't some air inevitably slej.-dofw0q 44 o l q;c;hx q8b8(2fjndlr:c escape? Is it possible to avoid this escape oh4;;l. j8 l:sfo0dd8eo4w cqrn j (qqlbc x-f2f air altogether? What is the relation to the uncertainty principle?

  It has been said that the ground-state energy in the hydrogen atos5t9 :cgsida0lx go6*m 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 its energy formg0t sx:9osi*5gdl6a c ? Explain.

Which model of the hydrogen ato7:ligzbh;z)o/up ;z+ 4kedf em, the Bohr model or the quantum-mechanical model, predicts that the electronbuek ; 4/hl+g:dopfze)z7i ; z spends more time near the nucleus?

The size of atoms varies by only a factor of three or so, from ladrl xv08,au5lc *b1gk rgest to smallest, yet the number of electrons varies from one to over 100. b, d grcakxv18u05ll*Explain.

Excited hydrogen and excited helium atoms both rad cj kd uo4k iq9yzziu.:q,w1*1m2k. mviate light as they jump down to q2,.z 1 zk.odcw*um:y jk9mi1 kviuq 4the $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there we-jvy z 5xbud7r ((bn/h, fom,tre no electron spin but otherwise quantum mechanics were valid? Consider the first 20 bt,fouv n5b j h/d7m(z-,xyr (elements or so.

  Which of the following electron configurg e8z8rjmg6a+ations 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 (caref+oz, i rb0id)vxsw1 ,w+ab oz+ul scrutiny across the periodic table on tw+)v o0zxbw+da1rbzos,i,+ i he inside back cover will provide useful hints).

In what column of the periodic table would you expsp q,40z zp;h(jtg* r9ghy 8uject to find the atom with each of the following cjp,zugz*;y rj q8h9gs4h0p(tonfigurations:
(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 properp ely/ssn8ix/ xlj 0+0ties?

Explain why potassium and sodium exhibit similar propertie/iie3 l:3ul t5i6:6ypktnw ges.

The ionization energy fo/q b mihxh,8 a0f7es6cr 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. Bk /8(zcwy8 l; :m8lk dda3boazelow) imply a photon nature for light? wdoylaaz kd(z8lbkcm: ;83 8/

Why do we not expect perfect agrexs6nmaw baj8k po 5t97gqo427ement between measured values of X-ray line wavelengths and those calculated using Bohr theory?t xbjk67 9soao57g4w2q8mna p

How would you figure out which lines in an X-ray spectrum -hbaq+fmnj m-*svvmz 1m*y69correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep withbkce i *au*k:w) fylvv(5ga2 .in an atom to produce shorter wavelengths than transitions by outer elekcyul* e(bfi*a 2a5wv):. kvgctrons?

Compare spontaneous emission to stimulated emission.

How does laser light dt6cdo f ql87h3)0nd4xx, ud0za /tkjoiffer from ordinary light? How is it the same?

Explain how a 0.0005-W laser beam, photographed at a distance, can seexa ko k f.n8pso(x3t0*m much stronger than a 100(8n*xsaoo03p xkkft . 0-W street lamp at the same distance.

  Does the intensity of light from ab)02jgakx++s i;me r y laser fall off as the inverse square of the disti0r2eax) mj by;+g+ks ance? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each having s:x f :)u; bdum(8eitokinetic 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 traveling with x.l vmmbo,7izz-rk02a 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 positio/o-jz r12g2p;cprfbd n can be measured 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 l qyew /v2.2atb/ kp,xof 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 marcy5 (.be9 9 ul(ubrwdwsq7m;ss 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 en22uykbm+o5 je ergy of a neutron contained in a typical nucleus of+2juo kby5e2m 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 3eaw buy1n1h3to show that if an electron were present in the nucleus13ayh1nb 3ewu $(r \approx 10^{-15} \, \text{m})$, 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 a e8, kpi6;mily $3.00$-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 cap;qf)ix)9 d fmn be in the $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whc7g7 hq;)dlp b ooaa1 4;wo-pmose principal quantum numcogmq oah7w; )o4alb;1 -dp7p ber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for eij.7sm /kk o 6t)4 6g:hhpqnhvach electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground sta ql1xfg9.:irr;8t k dkte of nitrogen $(Z=7)$.

  Suppose a certain hydrogen ato0.as:1bkkp6j uk xy+pm 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 owuu0* j5mh,zofs * qa2f 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 hasvl 7 yfyv9q9k4,v 7oqv $m_l=-3$, 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 electrons in a "g" subqrn9/ko)beg /d,n;d g r3;zivshell.    electrons

What is the full electron cqd i o 6mep/tfu gg2o-x0af.-4onfiguration 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 (Au)r u.fis*r-5 ;ywh-0env v;m kv, (c) radium (Ra)? [Hint: see the periodic table insfr0m.w;v -s;*ynk ie-h rv uv5ide the back cover.]

  A hydrogen atom is infkn:81a 9p-t 8i8y plqyb)glh the $6s$ 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 theoj5opt7 wm32(w1(mmonhzf5 x lry. [Hint: Th7((lno2mw mw55 ht 3oxjzm fp1is electron 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 is zero for a filimte 4z0/ob+f48 wy/pe0 tta k;p6dqg led subshell.

  For each of the following atomic transitions, state y 9ig7d;x- j2 oukpzdnkq60;gs6w9 rvwhether the transition is allowed or forbidde -dgd7xg;9sq6oiwjkp 6 z;9n0kvur2yn, and 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 2 i9c(pp:sumfa $6d$ 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 electron 1 5kgipjyva0-4kkp c)s striking the face ofpk5yjkk0 gc-a vp 41i) a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahtl4 w;tegsj .2lung X-rays emitted from an X-ray tube have we j.l;gtt2s4 $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelengtiuheskt4h4j2*s fn )6 8qd* j;pl)zvkh $\lambda_0$ 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 emitted when a azuyc yn:5m+g prx,/1xc )m3sCo $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for ankb5 uwyftg,c;nf+y 0/ $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the 4jkg; cec4.6ail yw 7swavelength for 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 unknown material is bombarded with elecji2gbb,3r(*v anbp5un t c8x+ trons. The wavelength of tnbcuavb *nxjpg,i+2b35 (t8 rhe $K_\alpha$ 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 deteij.rlsd;p; h2 ,- d7duj+jpiached retinas 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 lab35mxm nl-ptui. hp( 6h 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 bqcq4 7qridv-7x6 o 6eneam due to diffraction if the beam emerges thqq6-oqd4 c6xie vr7n 7rough 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-N7,lgp8 i 8w wdil ;sp1x9iwma+e laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncertainty forakc 5 4. :vkwk:8;l84y d.egkar aemij the electron in the ground state of the hydrogen atom. [Hint: Determine the momentum using the Bohr model of Section 27-12 and assume the meia:v rk mk . 5e;dg4 wkj.:ca8alk84yomentum 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 foc b c4,gr7. vxk4qbu3ar the 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 rhgqy.if yh*c0s i*5 x2adius of an electron orbit, estimate the average distance fr2i.0 s y *qfx*chhygi5om 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 operates atxf0j9 7 dwlpmzwymq 91 5le.,. xic)hd $95 \, \text{kV}$ 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 bo69jcqtm-zq 0 rron 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 toa.sewyktj;8 7 show 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 fh)mkvy5 ijg s9 v2jall :biu*w1 d2x7dv321w 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 c*e- j+kh vz m2uvalnv;10(nl a given value of v vlcn0n(2euklzva*1- + ;hjm $n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narrow slits in a barzf ,nb-cv7 uwa+(qh s,rier. The slits are a distanc, ncqv (usw+baf7h ,z-e $2.0\times10^{-6}\ \text{m}$ 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 hydrox)xkd) f:dga -ps 8;ztgen atom is given both by the Bohr model and by quantum mechanics. Compare thf d gx )8)dk-ztxspa;:e results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is tra qy7qlaednch oa -gc2..l6p*+veling 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 a5waq rtaj2. h)4cze(k line with a wavelength centered at 488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. Est twac)5a4 qhk2rej.(zimate the lifetime of the excited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated frw6dwf*8c k0i iom rest across 550 V. They are then directed at two slits 0.70 mm apaw*i f0kw6id8crt. How far apart will the interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, are acceleratej*,h im; y5cepd across the same voltage. Assuming that the uncertainty in their ,ehcy* jmp5i;position is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum number nml-srjn6 7z(r were limited to the range from 1 to 6, how many elements would we find in namzj7 rr-lns (6ture?   

  If your de Broglie wavelength were 0.50 m, how fastx h)nu*1r3f6 fph14w tqgue0t would you be moving if your mass is 75.0 kg? fxt3rh0gqfh)64up *e1nu 1tw $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 shoqv:lrck*f d cfbm1f13cp - j;/ws a series of lines with one out of every four matching b 1j 3fk/c1-dclf :prcq*v;f ma 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-wrl3o-a( -wz8da,g xkmrxq jc*0 /rb a certain metal when it is bombarded with high energy radiation. If this photon wavelength cor/-jw *a-m3(q ,brdwrl8-arxokxzg c0 responds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread o1ho;4pv5qu nl p/1xli r.v8sjf 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.]