Compare a matter wavhviofj(hv*w7k2 uw nou*u/ 8 e;9, szqe $\Psi$ 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 mk)-7 3k9.(h5j r3czln, m wzhwdos kehechanics, particularly the u7 -e.3(cohkmjhzk ns)3zwrhk5lw 9d, ncertainty principle.

Explain why it is that the moxf0o 6t g(hquc h 1rry.;9gsm2re massive an object is, the easier it becomes to pre0fg 1o(s xhrgu2q;yrmhc.6 9t dict its future position.

In view of the uncertaintr (s5bsw1w/cm1dtz x 2y principle, why does a baseball seem to have a well-defined por/btw1s2smd 51c z w(xsition and speed whereas an electron does not?

  Would it ever be possible to balance aai6 70uvsedafhb7:g v 4vdd21lys,y: very sharp needle precisely on its point? Expdsv h4: , a0aldfg62y sveu1d7vb:iy 7lain.

  A cold thermometer is placed in a hot bowl of soup. un60vg7hd a0mba03a9gg cj, i Will the temperature reading of the thermometer be the same as the temperature of the hot soup before the measurement was mabmn au00dv7,a hg gj i09cg36ade? Explain.

  Does the uncertainty principle set a limit to how well you can make any sin..ma/) *5- efw ndfzld jp1uirgle measurement of po.i nlruw-z.d1 / m5fefpjda)*sition?

If you knew the position of an object precisely, wit- 2maehk1( 0a5l mlbdgh no uncertainty, how well would you know itsl- bm125dg(aaehmlk 0 momentum?

  When you check the pressure in a tire, doesn't some air inevitably escape?0mjqm68rm :rq Is it possible to avoid this escape of air altogether? What is the relation to the uncertaintymj:0q8rrm 6qm principle?

  It has been said that the ground-state energy in the hydf0fs5blynn-fry aj7e.q21lo l 9 5- lyrogen atom can be precisely known but the excybfl2fl-n57r of5 ls-y 1an9 ye.qj0lited states have some uncertainty in their values (an "energy width"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydrogen atl2. gni5nm 0g e dk92obma+la,om, the Bohr model or the quantum-mechanical model, predicts that tbmlk09,dn.ngl2eg5 maaio2+ he electron spends more time near the nucleus?

The size of atoms varies by only a fq8y3k-yk h h)a o,sd.bactor of three or so, from largest to smallest, hobk8dykq)y. a,-s3hyet the number of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as they aqir)*ar-b i:h qgg6ddm *53fjump down to the rha*rqda qf gi-d)b im:5g3*6$n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic cv bxesmqq 2i4j4z6igpa(,)-t54 u8rjat5qu table look if there were no electron spin but otherwise quantum mechanics were va5q r4tue,gtjsu z -4aqi4pc6 bji(q)2x 5avm8lid? Consider the first 20 elements or so.

  Which of the following electron confg.va(t )imb:cedv8:x igurations 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 at )j4rwbgk .mm;nfj2;h om (careful scrutiny across the periodic table on the inside back cover will provide useful hi 4jwm)2gr;b fnjh.m;knts).

In what column of the periodic table would you expect to find the at6n /u;p5j8 zl.cjxdw jct( mh(om with each of the following configurations: j(;j /5n6c (wtd u jh.m8czlxp
(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 exhia4 5thf a79f:mkc2z3x/lq pu(mq6na pbit similar properties?

Explain why potassiu 7jsqt;h1,lb dm and sodium exhibit similar properties.

The ionization energy for n5jih 4fd :p1( qxai)qheon $(Z=10)$ 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 na-fa(04razhoc ture for light? o-f0 rac( za4h

Why do we not expect perfect agreemen +bb:fl6(sdhayirfsw m)2s4*gpr2 )gt between measured values of X-ray line wavelss(s:drw 2m)6 bg2a)f fg *pbhi rl4+yengths and those calculated using Bohr theory?

How would you figure out which lines in an X-ray spectrum corresponw 8hpl7 n4m,n7 b5fjvq+y4y3bs 4 klaqd to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep wi; kq,: leazrx3 lc3vg3 ;3pjbwthin an atom to produce shorter wavelengths : b3rp3 ;lc3xe; qvlzk3g, jawthan transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from or l7 q59mk*cbzo h9o -zli hk;5ft6u.iedinary light? How is it the same?

Explain how a 0.0005-W laser beam, photographed at a distance, can seem much wd3z9a-a:k2 fo joutn (4fnu 4ir3ntb ,s7j*vstron oartn3: ff-4*zdu s i3w7uo29t njb(4ajk,nvger than a 1000-W street lamp at the same distance.

  Does the intensity of light from a laser fall off as the inverse squ vpx m9ubdl5 )wh;/qg )/i0ewdare of the distance?b;p/w5dqu/ h0 vwlmxgdi 9e) ) Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each 3xoio37s3 )u6q*dtyly 9kwu nhaving 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 withug*4 b rrq7:/b1z ek6 ozt)nrq 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 3i*- f yx4 5vkyqkdxk7to 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 typicdk2+v;.n se a2ac((uv6 zftl eally $10^{-8} \, \text{s}$. 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 muonj7nl baaqj-h*; u2,y 1dxb( jo $(m=105.7 \, \text{MeV/c}^2)$, 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 cq073b4gyxddhd n; 1maontained in a typical nucleus of dnb03 d1q7amxdg;yh4 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 elecbc 9 v yqti:d3ld-ez-0tron were present in the nuclede -vqz dcb0:9liy -t3us $(r \approx 10^{-15} \, \text{m})$, 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 ofc.d r zvc65l5r 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 /utwuu90ktg 4in the $n=6, l=3$ subshell?    elections

How many different states are possible for an electron wh/wm vv*1,znw cose principal quantum num cm/vv*1z w,nwber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the gro.+hgl*htxx-3 om 2da tund state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electronik,0h+zbf zbv*l.6kk g c4z8m in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogec u613/i 1c qxts:mzglf.f4bq n 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 momentuma b*(( 1pckyjb 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 has8 tt0wlmt. t*e $m_l=-3$, 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" s43b tnnykt,2e ubshell.    electrons

What is the full electron configuration in the ground state for elemen l*o;wb 5pjo mzh,65gxts 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)h; y0w2dta i/;o g92qrmwy ,bi, (b) gold (Au), (c) radium (Ra)? mwyt 0idwo ;2bqahg; y,ri9/2 [Hint: see the periodic table inside the back cover.]

  A hydrogen atom is in swb+u)z5z;ac -fzk6 x 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 u y0f/yxie)5k9 kht e ungj5 y/a7d8nk2sing the Bohr theory. [Hint: This electron ht55 jgnyyiuhed27k ) 0 /x9k8afkyn /eas $n=2$ and "sees" a net charge of approximately $+1e$.] The measured value is $5.36 \, \text{eV}$.    eV

Show that the total angular momentjo c2 ;kmx;3olum is zero for a filled subshell.

  For each of the following atomic transitions, state whether the transition is y/okzprf8 8try4 32b wmev(s6 allowed or forbiddenwf438tkors6e m p8/zb 2 ry(yv, 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 i5x,,k3h:: lyc e cxohcn 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 e:cjmb zxu69 r:mitted by electrons striking the face of amc 9uzx:j:br6 $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted from an X-ray tu f(n:rcn ;z 70.bvayljbe have b7r .c(vn0nz;:ajf ly$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelekzhrix5q)qmob 16m/44s mjd 6ngth $\lambda_0$ 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 :77kqlvl;qlhs+pkyt5 z-+t 2+r vboo when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelen j2fk57mmqu n6h4wy i-gth for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength fv +2z2(jem s7j4svh ckor 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 bombark--8sleuaseu e n *x*)ded with electrons. The wavelength *x8-na skuse*)le e-u 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 retinas put:ju.;gw tc x:* hqm/cms 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 ,zx 0j 5kdg3dmmh(d4 nhave 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 diffraction if the beam emerguxn8)pjq* -x1 xh3gyoes h*gyxo8)u 3-xxnq1pj through 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-th infd dak. etr0934 yf0s id92r5j3vNe laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncertai p6a;j9u*w d*aru rs /xa3.ijpnty for the electr6audwaa*9 jxj. 3;ui/ rp*rspon 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 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 va1(c62pu0 jicaf8 o, yhvd5v irlues 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, estimate the 7. h(omijo5qu average distance7m 5ouj(. hoiq 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 operat1nxr:ljlj7q ;:twu,d167i:h y ycy w rnf;u6yes 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) ener-uol8 ocz v) (.s aqi(rfsi0h.gy of the 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 the Moseley plot(Fig. Below) can be writt-r gnw)rygi f0m2:i8h en $\sqrt{\frac{1}{\lambda}} = a(Z - b)$, where $b \approx 1$, and evaluate $a$. a =    $\ \text{m}^{-\frac{1}{2}}$

(a) Show that the number of different states for a gik5az5ni/pf12 : f lkz1nos8 pgl7p/ebven 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 statk,0u8 clk fxdnhd;-+y es possible for a given value of l kcd,fk 0-ux+yd8;nh$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons 26 s jp1y58pljfg5kazwith energy 45 kV is shot through two narrow slits in a barrier. The slits6ks58 a jjl52pf1yg pz 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 both by the Bohrt4 614he rvmas model and by quantum mechanics1 e44arhv6 stm. 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 ;1t xszj6 a9ceh0mod: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 r+d*zztw; 39etu - ckbnm. Careful measu9wte*b zk u+cz;-3tdrrements 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 twiicdn ,q; *fv8o slits 0.70 mm apart. How far apqicnd;8 vf*i,art will the interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a prokqj/jge*.j mn x6caivn a.8* 8ton, each initially at rest, are accelerated across the same voltage. Assuming that the uncertainty in th*.ja gave i/xcnq* .8 jmkn6j8eir 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 froe 7*r v3tfl80kw;( lvlw0qxrlm 1 to 6, how many elements would we find in e8 w*7xrr twl;f0(0lk3 lvqlvnature?   

  If your de Broglie wavelength were 0.50 m, how fast would youde u:wcx)uyo1gu): .a be moving if your mass is 75.0 :) ue.y)ux:c1ou dga wkg? $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 unkn)jg h,ps,1i kzown 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 electronzihjp1g,, )sk , determine Z and the element in question. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm are emitted from the 1;qv uy+yv u)nsurface of a certain metal when it is bombarded with high energy radiation. If this+yy1u nvq )v;u photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread of a lasejnp- (tbm)uvy/oej: .r 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.]