Compare a matter wav;yw./v+sgzhq*7,e8mqf doi se $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory of th- pou;.k erg6tffxc; 6e atom is not compatible with quantum mechanics, particularly the uncertainty ;.;6c6e- fkg ouxfrtp principle.

Explain why it is that the more massive an object is, the easierk(a9e+l+ql+z i /a2*j,qqnqg- oiaya it becomes to predict its fua,nlgzq+ak +qel 2a+ q-*aoqj9ii (y/ture position.

In view of the uncertainty prinou,nu; 4snt6bciple, why does a baseball seem to have a well-defined position and speed whereas an electron dotu ns ,n4b6;uoes not?

  Would it ever be possibg m+i*nx)gin;le to balance a very sharp needle precisely on its point? Explaiggmx+ )ini*;nn.

  A cold thermometer is placed in a hot bowl of soup. Wilc-5)h4t /,1rbq/ti7 knfnb:ii cjejik;(thhl the temperature reading of th,(ik/4ncfitk1;7h:r j5 iecbjt -n bithqh)/e thermometer be the same as the temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well you cwgxtntbhr + + db3*r0(an make any single measurexg+rw bnd h(b+*0rtt3ment of position?

If you knew the position of an object precisely (;tr f)j--eh3+eygt zbrf5rq, with no uncertainty, how well would you know its mfzrth)q3-y-gft ;e j5 r+r( ebomentum?

  When you check the pressure in a tire, doesn't some air inevitabj+qc+b az) aifrk0pak52,*l jly escape? Is it possible to avoid this escape of air altogether? Wq2*fk)+,zi rl5j a b+cakajp0hat is the relation to the uncertainty principle?

  It has been said that t1u du g9.-x hqd3+dktlhe ground-state energy in the hydrogen atom can be precisely known but the excited states have some uncertainty in their values (an "energy width"). Is this con9 +ukudd3t.q h1l-gdxsistent with the uncertainty principle in its energy form? Explain.

Which model of the hydro gbj4cw i:.+cwgen atom, the Bohr model or the quantum-mechanical model, predicts that g w.:c wcj4b+ithe electron spends more time near the nucleus?

The size of atoms varies by only a factor of tu-t(6w3/wqlg j hikjj+6 dl8whree or so, from largest to smallest, yet th ij(-t 3+l6j6 wgw/8dh jlwqkue number of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as theyb2 j/nbj(eogct6tz ,9kdc-7n jump down to tzt( n kb6et2gjb,-97nd c o/jche $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spin but o,6x6x9eqw fratherwise qua,6x9wr6q ex fantum mechanics were valid? Consider the first 20 elements or so.

  Which of the following electron confiw *,9klblje /fsjbvjy m4b-lh*23 r,ggurations 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 (carx-qaho do- ifrpy-h2mayw: *oj;5a (5eful scrutiny across the periodic table on the inside back cover will provide useff*pw-:a;r j qm2i-yhd5oxo-ya(o ah5ul hints).

In what column of the periodic table would you expect to find the atom with7n2*0ngpyk(g q 8k(vq5lwjv b each of the follo 0vl27 *p8 nkg bjkw5vqyg(qn(wing 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 tn*8x05s4 qu ( vun(:ascz;o0b pmhxde, u5kjexhibit similar properties?

Explain why potassium and sodium exhibit si+ p 9gkck+8hg83oqvnqmilar properties.

The ionization energrnqb ,f3nr(+-i tbz: ly 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 wavelength in (Fig. Below) imp8:jb c;;/i pkjjx ewj3ly a photon nature for light? xe ;jw/ij: cjp k8bj3;

Why do we not expect perfect agreement between measuref4 ,qryd- ; 6+vzhc:sz 6zzgzsd values of X-ray line waveleng ;:zvg+h4-dy s6q zz6rzc zs,fths and those calculated using Bohr theory?

How would you figure out whichnmjx 6 qd-.k;r lines in an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep wit j bsreim.g,9ev bw38+hin an atom to produce shorter wavelengths than transitions by o3vig8sb,bw m.r +je9e uter electrons?

Compare spontaneous emission to stimulated emission.

How does laser light divlh ()do9 q)t::yipk mffer from ordinary light? How is it the same?

Explain how a 0.0005-W laser jg ++mv-tvdcpaun0c*619 x tc beam, photographed at a distance, can seem much stronger than a 1000-W street lamp at the same d9vcj+vp x6c-gcan+u0 mt td* 1istance.

  Does the intensity of light from a laser fall off as the i ctd(bhhs0 w53nverse square of the distance? Explatch3 (hsw d0b5in. ----待选择----yesno 

  The neutrons in a parallel beam, each ha/ b fz0- b4c/akhiy7 kz9u6axlving kinetic 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 wip gw l)n* psn1 le*ok+ 7r(*zosebl7d-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 to an awg3 ,lr(n;zy0rc5m w fccuracy 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:8 m0ayyygj0 b1c mgc0 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 i:hen0bn )e 1lrrgy2q/dj 5zc2n the mass 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 neutron containedvo-u80 azv:-pe mzjf+tia(.n in a typical nucleus of r avenizvfp -:zu(o+-.j m80taadius $1.0 \times 10^{-15} \, \text{m}$. [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 were preu dnc r:w/ut-sphlcd44u5; l5 sent in the nucleus wddu cpl- :/l hnsr;t4uu5c45 $(r \approx 10^{-15} \, \text{m})$, 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 t;wxle 6b 8+xathe 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 the 8ba/ s;)dwmi( er/jih v:b20wikbdb7$n=6, l=3$ subshell?    elections

How many different states are possibleoy( z aab-;p1 vs,pcy9 for an electron whose principal quantum numb (1 a;bsy9oa-pzcy v,per is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the j b5(uqclj)9mground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground state of nitrogen -cii e7v, u6ko$(Z=7)$.

  Suppose a certain hydrogen atom has vx ny;8nyf yov9c97o)$l=4$. 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 moment)k4zhahhw1 bspc/ 1c 0t+hs eg n72l4xum 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 hf z//tf gfv5)/g3vs naas $m_l=-3$, 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 iuu5cakerw: k fy 4y-40n a "g" subshell.    electrons

What is the full electron configuration in thercy 8 jm-+9sw.oy derw,v: r9a 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), ramo//ugzwaam:qg /x,u)(afe;g+e selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the periodic table inside thw: gefoau/aa+,m()gm,a/ rxuq;e /gz e back cover.]

  A hydrogen atom is in ths qyh4m9z3w)ne dn;b- tpk4t ;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 third electron in e,rq4 0 zvqj5c.**h1he lyixd lithium using the Bohr theo hd h1. *4,5crlqy* zviqeex0jry. [Hint: This 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 foh6 l44q,bt trlr a filled subshell.

  For each of the following atomic transitions, state whether the transition ur ;tlxrs;*)nw)0hmn is allowed or fo;0)s nnurht* wlr;)xmrbidden, 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 inomp2+ q91d b6 gjf)nxg 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 strikinm5 kf6hvn) bs7g the face of f7 hv)65mbknsa $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rp )i j:a1foe3jays emitted from an X-ray tube have j pi3eafjo1:)$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff w06y4p lx k.4d8/b vbv ntgi7pqavelength $\lambda_0$ 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 wavelengt5f62x 0uw3mv aga3pt czu6lx: k 2t;ajp kn31xh emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for o1oh. sng 16qean $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength for (7s 2fgynwz)rtm5i7 r 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 bombarda .ix:k*y+h .hy n+zqted with electrons. The wavelen ikt+y .+xh zaq:.*nhygth of 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 retinar k;rzux js+v)u(po68s 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 physic5 szv7e0r+n xvs 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 spreat1y tbq)4 p9xt4uhez9d of a laser beam due to diffraction if the beam emerges tht pb)e1zt94 qtu9hxy4rough 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 i sjj7*vh *;byh jd(ftvmd28;m d*ue3He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle towwg: tdkm/wk.dn au *bmzp jz2-;9 3n5 estimate the position uncertainty for the electron in the ground state of the hydrogen atom. [Hint: Dez z- db;knad3m95wwju :mkwpg2/.n*t termine 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 anyn+ pofw0w6c l7*jwu5gular 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, estimate t;wq t5lmrcmaqh,).5npsk,i6 he average distance from the nucleus for an electron in the innermo5l;m),rtkwqp6m i s.n5a chq,st $(n=1)$ 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 operate.)dv vxe1-u /3anuue7.uf pb js 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 outermh,e-v wxdk ;:1lm v/laost 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 -sy.vux(fl -96sy mac 3q:w :yjed:hrplot(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 numn8lsot(a;qsn q7 s;c-ber of different states 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 possm* u.mh2hkht9 .ek 2vsible for a given value of 2 9. t2usevk.k*hhmhm$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot througheuohg0vo8ruc:m2;essm7 )t-x+c /m i2 c +ncr two narrow slits in a barrier. The slitsur0cr ig28v/:oxssc em;uh2+ )m t+nm-7oce c 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 hydrogen atom is given b ju4k gasw0m6;oth by the Bohr model and by quantum mechanics. Compare the r k4j;g0am6wsu esults for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is tra s19 ;hq1w1nbip:i nmmveling 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 at 488 nm. Careful;o/s6 bsx sm.yf 2c0c3nxzp j, measurements show the line is really spread out between 487 and 489 nm. Estimate ths 2 ,szncc.3s 6y/0 jxmxpob;fe lifetime of the excited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated from re :v6wtr yjnxfs .0m3a5st across 550 V. They are then directed at two slits 0.70 mm apart. How far apart will the interference peaky5an t0vr f6m:3.wsxjs be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, are aj vzb5zg30lr8al :wk-ccelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentumbg 3z l8:kz5vlaj0w-r .

  If the principal quantum number n were limited to th8xif(a fa);v/nhh2luzp;l 08.e khf ze range from 1 to 6, how many elements fezvah. 0fka);8ln hfxu /2zi;p(l8h would we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast would you be moving if y5i (ha/rmr i g8;tg lxl6e-emh:h.w-uour masm (ir;thieh5g mxua8-le: w g/.rh-l6s 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 unknx n mjy7y.sik2*:izp:own element shows a series of lines with one out 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 qu . kiym2 :*i:y7snjzpxestion. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm bevl,ain, .*v*vy) pgare emitted from the surface of a certain metal when it is bombarded with high e*geba, *,vn .v v)piylnergy radiation. If this photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractivel2+axshj fso r2.71ou spread 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.]