Compare a matter wavni5,kwi k-vr ,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 with quantum mechaniego kgys*4h9ddj4-r:h (+pxz cs, partr zop4*e4kj +gxhh( dsg9:yd-icularly the uncertainty principle.

Explain why it is that the more massive an object is, y /lg.h ou u+6r wjsqncx07;i2the easier it becomes to predic+.u2 yq su;cirjg hlw 7x6o/n0t its future position.

In view of the uncertainty principle, why7m6koxmp+ d k+ does a baseball seem to have a well-defined position and speed wkkdpm +m o6x+7hereas an electron does not?

  Would it ever be possible to balance a very sharp needle precisely ac6.te7uw3tg( f-fj v s8jxn+on its point?u-jj7s nv(x.ft+ fe w 68ca3gt Explain.

  A cold thermometer is placed in a hot bowl of soup. Will the gk ca w10x9r.bg0m j3ytemperature reading of the tgr0j. kmyc1 g wb3xa09hermometer 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 caq 0qkma x,rz21n make any single measurement of 210mar zxkqq,position?

If you knew the position of an oc p*7iju s,h*tq*h1xb.uscj; bject precisely, with no uncertainty, how well would you know its momentucc*uss *ux;*it,h71. jpj hqbm?

  When you check the pressure in a tire, doesn't-z3ios69p2 zej :tormm)f 3dc some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relation to the uncertain-oic sm69:fpo m3z32)jer ztdty principle?

  It has been said that the ground-state energy ih1g r8aqbs 30j9b/84w ym ivpzn the hydrogen atom can be precisely known but the excited states have some uncvi1 r/ 83 bm9pgyazwjhs 0b84qertainty in their values (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-mechanicalt/lj 3db u)a 0sipn5ja301 oap model, predicts la5 tbn)1psi0jj u o3a0da/ p3that the electron spends more time near the nucleus?

The size of atoms varies by only a factor of three or so, from lxy*1e f+wmda j68a /exrd3c (sargest to smallest, yet the number of electrons varies from one to over 100. Explainaxd3rywe *x+ f6dsm( c8eaj/ 1.

Excited hydrogen and excited helium atoms both radiate light as they jump down n*r/1hny*w q*k 0jaz4 vxsn6 0 hgp2yzto t0nzx6q0vwky g1yn4 * sjn2*ah/zhr* phe $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spin buli1h nh(jui85t otherwise quantum mechanics were valid? Consider the first 20 15j( nhuiih8 lelements or so.

  Which of the following electron configurations are not allowed: 6a*lvydc 6r 3s
(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 conztc;po v2n:x ;figuration for a uranium atom (careful scrutiny across the periodic table on the inside back cover will provide useful hintx;p;2:cn tzv os).

In what column of the periodic table would:hgp4ks z/;zpy,rp -v you expect to find the atom with each of the following configurat4 z gv-zhyp/pks r,:;pions:
(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 exhj)y;l tdbn3dvp--,mz ibit similar properties?

Explain why potassium and sodium exhibit similar proper9i, h zd1 8blfm :hxj9oiyq99sties.

The ionization energy foo1vlcv :uw fdzh3.b *v:/c b+ir 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 photg 744ssarxi- svm5 v0 ky3w*cton nature for light? w 07 v x3 a4c4sgms*skvti5yr-

Why do we not expect perfect agreeme vuobrg/l hzp*yps*su( lawu g110 ,w9o, s8u:nt between measured values of X-ray line wavelengths and those calculated using Bohr theou: wwuupps1r9o,8hg vg/ (azs1oy*l,ul0 *b sry?

How would you figure out which lines in an X-ray spectrum co:p4)ou:1-h zmvsn * sa;7 arl;uynibipb, el5rrespond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atom to p)lwjat-i2gndn :fnn93 u w;:nroduce shorter wavelengths than transitions by outer enl-;nwi un nn 9)d3 w:atg:f2jlectrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? bqy9*u u u)8ocHow is it the same?

Explain how a 0.0005-W laser beam, photographed at a dista.l8: 4kq9gdqnjtn z7xnce, can seem much stronger than a 1000-W street lamp atqz87jk:.xqnd9l n 4 gt the same distance.

  Does the intensity of light from a laser fall off as the inverse square of tvv3kr9d6rha) f ov( x,he distance? Expla9(,v hofvxr3)akd v6 rin. ----待选择----yesno 

  The neutrons in a paralle+ gc7 *c ipi-2yy2pouol beam, each having 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 travelingmv b+two w-1-+j)uegr 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 posit kaq6 unvqbnx9x,0.i4 ik+p-n ion 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 of an atom for typically 2 v8m2okla3la $10^{-8} \, \text{s}$. 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 muon (u0r+k8yjmr g7kax .; 6wqkyf$(m=105.7 \, \text{MeV/c}^2)$, 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 v.. p87jbx9(ybof wt g*ae3g uenergy of a neutron contained in a typical nucleus of radi . vwgoxb(b e7t p39u8jfga*y.us $1.0 \times 10^{-15} \, \text{m}$. [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 iwxx9wo+s*0*- wue fsd f an electron were present in the nucls*wx-0o9fe+suww d* x eus $(r \approx 10^{-15} \, \text{m})$, 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 rv ;7o+:fym0n q7lyw 7lu*arqa $3.00$-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 cog- (,eny5hz4 fobno 2an be in the $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whoiawkx p-p 2tl6g;/zz,se principal quantum nu,lixakgz/twp;-p6z 2mber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbr()a1 wj8kjm,t 2gaeeers for each electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground state of nth0i)( a4qbfmitrogen $(Z=7)$.

  Suppose a certain hydrogen qct-764ot(b )os1l z7/mxgym4 kfvruatom 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 oi; j;c +or tkr8,kg6akf the angular 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()v.(goh;t+wrx sw qh-skmo9 $m_l=-3$, 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 ele7j1)eary f;f6) b1tgv 9 eyczactrons in a "g" subshell.    electrons

What is the full electron configuration in the ground state for elements w(+fm pbid3jbn v) gf,)ith $Z$ 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)ot5f(kqcd* f4;e2 l-l j*: (xl jsfdnh selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the periodh* f :e( ts*cfq;l5k-jodf l 2lx(jnd4ic table inside the back cover.]

  A hydrogen atom is indr,580,gd/ ryqa .wvps e+p vomp 8q1u 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 usiv+d 9 x;xe/ex gu)yp1wnq zvqu x8/q66ng the Bohr theory. [Hint: This electron hau/1yv 6qx +6xgn);zexpu8 qewq9/vdxs $n=2$ 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 fillff)oy55qge+ led subshell.

  For each of the following atomic transitions, state whether the transitiod cr gt8vcj0z.v o;+3pda0 .qrn is allo gc38p..d jdaz; vtr+q v00corwed or forbidden, 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 inr) phw 1a..a aoxrad(( 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 electron) bos *m,v;bcgr.dz*qs striking the face of sz*;*rb,d. bgmq )ovca $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays e .ygywn6jltk: 8 +g 5ul0n xkyima33:amitted from an X-ray tube havetg053l wmk8 uaj::yl6iy.akg yn+3xn $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelengthy; hposcq:l8/ $\lambda_0$ 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 whyz) vfr.i xg2tyzd wk*ai1;8j.*i8 f uen a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for a1bj(- loi0( bm1b3slv 0ydn bmn $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory tzr zc8a4c/tffg zat/b*0i, p:o estimate the wavelength 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 electrons.d tn g8p;6-pp,6m:ovo1 dxqqo The wavelength of the xn;6vp - qp1o:6pqmtd, o8dog$K_\alpha$ 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 detacl/blsg/js h)2yxgw nf77oos 9: ,;t euhed 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 usiik 3)hc1 s-wonp7r j9ed 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 diffra sb5umsy) xd(-ction if the beam emerges thro)5bs (us mx-ydugh 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-th+baj .bwy,h 7h j8d He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the positzy,wt/lk/x/.qob vm *iahp: 4ion uncertainty for the electron in the ground state of the hydrogen atom. [Hint: Determine the momentum using4z,p/y:lhv *mi axkqo./w b t/ 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 possle7buc v; l:acv25*qxible values for 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 radius of an electron orbit, estimate7l/ mrsek;meh7c4e igqgxm sf9)0t5 . the average distance from the nucleus for an electrog5mkcm)emqi leehsx . 4gt9 r 7;f7/s0n 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 2voniii5v4kulj;1u n9b* ( ya 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 oute7 3k kgwmm,ia:rmost 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 Moser eiod8u8zd9 +1dz9 sud(nu 2hley 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 numbp:: +u6ec/ 2ubt cd-ly xpsd.;gq/xyter 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 possible i:yv,xmehd2) for a given value of deh):2i xm,vy $n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot thrbaos,6 (t(lgnuy )a0 en3.ekaough two narrow slits in a barrier. .0a)ky(tl3a n(ean ou6 s ,begThe 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 hydrogen atvb dbty:65u j6pd0u,uom is given both by the Bohr model and by quantum mechanics. Compare the results f, 5y jb6u:d0 6tvupudbor $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling with a speed of5kfg u/lm9c:95 wm(vl ) rghfe $(22 \pm 0.22)\ \text{m/s}$. With what maximum accuracy can its position be determined? $\Delta x =$    $\times 10^{-37}\ \text{m}$

  An atomic spectrum contains a line w a7)2qpiryy.b ith a wavelength centered at 488 nm. Careful measurements show the line is really spread out betw b27qpr y.)aiyeen 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 direkb ;0:d qbem3gcted at two slits 0.70 mm apart. How far apart will the interference pdgbq:bk; m e03eaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest3 xqul/f0x3a l, are accelerated across the same voltage. Assuming that the uncertainty in their position is givenlx3x/u 3 0lafq 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, howxwn0 few54 xa: many elements a5e0wxwfn x4:would we find in nature?   

  If your de Broglie wavelength were 0.50 m, how/wg d,rpk6ttyyxlfd xg1- 2): fast would you be moving if your mass l/6yx) d:kf2 pgyxtw1,gtr- d 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 el0zbo 2tg6knyn cv*uh/+ ;upm* ement shows a series of lines with one out of every four matching a line from the Lyman serz /umg60kyt 2 *+bn*;hvopuc nies 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 surpgl-r dmo7j 9/pu.j( mkk7d/ aface of a certain metal when ia 7kujpok(rj-d.gd/l /7p mm9t is 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 beam, i7lvmk w7-g(dq pw0 a,$$\theta \approx \lambda/D$$ , 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.]