Compare a matter wav ouonyy9 ;,)ace $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's th so/jsawhm ;2.:lp-bzeory of the atom is not compatible with quantum mechanics, particularly the umw;- :hbj z. /assp2loncertainty principle.

Explain why it is that the more massive an object is, the easier it9 4qik pr-juz/acre*; becomes to predict its future posckpij-rz*u r; / aq49eition.

In view of the uncertainty principle, why does a baseball seem to have a vpl- *bl d )*n1y*awnun( c0gfwell-defined position and speed whereas an elecn l(*c n)yvw*f0d un*l1p-bga tron does not?

  Would it ever be possible to balance a very sharp neej o vj(yk4-t1ulaa mp8 ri(w-+/ +afwqdle precisely on its point? Expp ((-j wykwl+uo +ra-v8j/qatfm i14alain.

  A cold thermometer is placed in a hot bowl of soup. Will the temperature readiny+l9t7:)j ,bui bam hdg of the thermometer be the same as the temperature of the hot soup before the measurement wasiy,hd )u+lb7 jmb ta:9 made? Explain.

  Does the uncertainty principle set a limit to how well you can m g.e/vyxnf-k3/2j iry ake any single measurement onekxijy/-g / 3vf.y2 rf position?

If you knew the position of an object precisely, wi2nfk 93uu,pajth no uncertainty, how well would you know its ku fa93j,un2pmomentum?

  When you check the pressure in a tire, doesn'ka7 pu d3fqq;z+ju o47ev/jk(t some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relation t uj e/u4(+7zo3dqpkj;aq 7v fko the uncertainty principle?

  It has been said that the ground-state energy in the hydrogen atom can be prec (it:vh2x/np oan*2kz isely known but the excited states have some uncertainty in their values (an "energy width"). Is this consistent with the kv2h*(:pi xa t2/z nnouncertainty principle in its energy form? Explain.

Which model of the hydrogen atom, t 5qamwn9qs9st 7zh1k f1x;z u+he Bohr model or the quantum-mechanical model, predicts k57uhznf +;sx 919mtazw1q q sthat the electron spends more time near the nucleus?

The size of atoms varies by only a factor of three or so, -xqz5qp-9f vlr)n k. ifrom largest to smallest, yet the number of electrons varies from one to over 100. 5fkxl)-zriq-n .p 9q vExplain.

Excited hydrogen and excited helium atoms both radiate light as they jump xz izsj8vim 17 3bzd))1,0 h.l bkfzmbdown to tmf b.d )8h7z11 z klzivzmjb3ixbs,)0he $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron ikkv9 +vz1e7qspin but otherwise quantum mechanics were +z k9vvqik71evalid? Consider the first 20 elements or so.

  Which of the following electr*6m ob7p 6,m 3 cpmu4ugxafqs s:x2/ghon 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 con.foibltd eozawtm83- 48z; zxzi 9/:gfiguration for a uranium atom (careful scrutiny across the periodic table on the inside back cover wiiz zglz89t /:x 8wabmt 3 feodi-4;.ozll provide useful hints).

In what column of the perijvq2-+zc u tl5odic table would you expect to find the atom with each of the following configurations: zv2q-+tulj 5c
(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 prope kkt;8+ff6n, gzbr8evrties?

Explain why potassium and sodiskv+2+adm r9h um exhibit similar properties.

The ionization energy for 1svu0n 5kxpd/e sm1 4f0v6 l,qhxye- vneon $(Z=10)$ 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) irl l .,bd 0,eb:kz-uxmmply a photon nature for light? .- r0mbd:ez,xbk,lul

Why do we not expect perfect agreement between measured s *2 zddd6l0q7rr rry4values of X-ray line wavelengrdd*r46qz l7rds2yr0 ths and those calculated using Bohr theory?

How would you figure out whichh v79ria ,nm:q lines in an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect elec0r7 m 4r/obgfw xqsc76cc57l btron transitions deep within an atom to produce shorter wavelengths tha 0 bc746olcm7w rs/fbqrc5g7xn transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordox7ci wgj1-p.s g* j-8bxwv s-inary light? How is it the same?

Explain how a 0.0005-W laser beam, photogrnl h vicvvpd;g* ;-s13aphed at a distance, can seem much stronger than a 1000-W ih slg v*vc;vp;13-ndstreet lamp at the same distance.

  Does the intensity of light from a laser fall off as the inverse squ nm xkoazz888*h.rm+ lare of the distanc 8onmz*mrx lk.h88+aze? Explain. ----待选择----yesno 

  The neutrons in a parallel beamm .c : 8vcgcni9;(.h8khodc qjm/6 bev, 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 traveling with ovnzrv+s5q+fkb77)r 0 /gztr 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 accuracygdu.mb/nbiu v fpb1cg:9 x-40 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 typicallydi9)no)ixg2j-hmv ;.fz rq.d $10^{-8} \, \text{s}$. 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()x8j + z)m,0amcrhxkbmk: dqal( okl5h;:nt 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 contained ls: 8q 0 algffm(ma(r8in a typical nucleus of g lrsm :la8(f8af q(0mradius $1.0 \times 10^{-15} \, \text{m}$. [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 present4xzze0ys-f te+ a(xe6 in the nucleuey6+-4tse( xezz 0xaf 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 the position of a n0fc;i. sm(z l$3.00$-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 thg4t :(v0i n;fcxek1f pe $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whose principal quan;wi)sm ;9d ute y3-*bskfs k3sig0a0 vtum number is;ksf v ss0y9g i)mkus-w 3*e atbi3;0d $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the gro-e3l2vv, ba*n j+wm1l-g lkp jund state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for eawsccxq,hfhbbz r 7ti+na pnyp 1))5 5f7r ,a9*ch electron in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen atom ha sdowl;*e,lbc t1v* q1s $l=4$. 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 magnitudevcfx8 :l6 p(gvtj4w(;s8k;pf)hu cw v of 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*z, dd f;4atdv4)5ku frovn8p $m_l=-3$, 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"9svmy. n*top 5 subshell.    electrons

What is the full electron config;weo vfew6jgn;u7(6ezg m+ x /uration 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) 0uslkx )) iuhkb*q,. qgold (Au), (c) radium (Ra)? [Hint: see the peri ux)) q ,0suq*lkkbh.iodic table inside the back cover.]

  A hydrogen atom is in th 8d3 pjnpsi,.xe $6s$ 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 thr xb1x2,wb38wh z4kkkolex -0ird electron in lithium using the Bohr theory. [Hint: This w x4, 1xbkzk3 0wbxokhl8 -2reelectron 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 momena376u:xx juo 96/gnzy)nfeaz tum is zero for a filled subshell.

  For each of the following atomic transitions, state 93taxym/l( k.mx1 ab 3y(ljqg(dbc6mwhether the transition is allowed or forbidden, an6x(3a9l/ ( lg1tkmb3j mdycy. mx(aq bd 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 6b* rt; zw258icmyva oin 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 + k3ohfei/c:nz j5o +bX-rays emitted by electrons striking the face of+bec5/jiznoo3fhk+: a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted fr8d2*g dnc7aoz2a 0vpw7 gp w)xom an X-ray tube have zxa72dd 7 8 pg)pw2wn*vag0co$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelength x v+ g *i6e.q0dxducmd:n,rh7$\lambda_0$ 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 emi6+ ; iuvi+ 6vaokejgg-tted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength u/y:-jxjjf8lyfh6g +for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavep dkfxb 1-v/8elength 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 unkno,k:lj s(t56 m 0vrido+h5 fbxqwn material is bombarded with electrons. The wavelength of t ki:vhrom5+ l(5b 0qxf6, jsdthe $K_\alpha$ 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 ret*5iaha h. * pb5ti*rzjinas 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 have a pnd/n:/kq 4..y2tqkm dsu sj4vower 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 / vjki5ikv n9,to diffraction if the beam emerges throu,/i5nj 9 kivvkgh 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 6 w-p7 c;7jrjkwjxa2g He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to est lg;p f9/n2m0cod1qff imate the position uncertainty for 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 momentum can be anywhere between this value and zero.] How does this result compare fpqmn/0cd 21fl;o g9f 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 tec4c q3 5od)sb.wm8v 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 radiuiv00r/u p lcz:t4f/2q2 gez vgs of an electron orbit, estimate the average distance from the nucleus for an electron in the innermostgqg020v fui l 2c4//ze ztpvr: $(n=1)$ 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 a6gq i 5m*er:apt $95 \, \text{kV}$ 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 thernu5kgesn b:m2( o)84ohyx, n outermost 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 o-2mpegr,l * +no;san fh (m2pbe)gu 5the 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 differei;h87hp5kt ru nt 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 possipw(4 kw*d)4hrq fmk o-ble for a given value of 4 wwqmhd) kfpr4(ok-*$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narrow slits in a bay*vc 1n.p k/f j0.lsiwrrier. The s.jwl nki.sv 0yp1cf/*lits 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 tup zu58x.oa .bu(k7vbhe hydrogen atom is given both by the Bohr model and by quantum mechanico.b7 85ak xz uuvb.(pus. 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 j1umnmd/z1 fun 40.a gwith 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 center./ -ugrv 8xoeid m1ww2avr2)) 5nxnci ed at 488 nm. Careful measurements show the line is really spread o)vndrgv 5anii1 x u /2x.-rcewwm 2)8out 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 fh7 ec77mn im1(ix5k ozrom rest across 550 V. They are then directed at two slits 0.70 mm apart. How far apart will the interference peaks be on a screen 28 1cih k7xni7e mzmo( 75m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, are accelerae4en (sd3nn i; o)fwjej1d(:t ted across the same voltage. Assuming theed1di(j ofn(ewst;n43n) :j at 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 wcc9yt1t+1wb/4 6wq (bafna xnere limited to the range from 1 to 6, how many elements would weq4n(b t +wb9cy61ax /fntwa1c find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast wn(p,s mno9m :)(dmfqk ould you be moving if your masndf spmnkq:o( 9)(mm,s 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 shows a series ofmb;a.cz4yq k,c./gx k 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 prkzg; x,/y c4..aqkbmc otons 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 a certain metal w6 elvjnvw:m(ii3 zbog; d-ko6+d91m phen it is bombarded with high energy radiation. If this photon wavelength corresp96l: jbvdw ;z(o3 e+p mki d1imnvo6-gonds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread oiuw 1zci16dto dzlw .s+8/ lv;f 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.]