Compare a matter wave l siw3rle:76c $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory of the atobw,ikcrw.b f8ve cr4 i:)*;zfm is not compatible with quantum mechanics, particularly the v;fb 4,fzcrw:ie*b) k iwc8.r uncertainty principle.

Explain why it is that the more massive an object is, the easier :a.ks /0 xdfj z.tekl1di 9kf b/4o;mxit becomes to predict its;e0ibzd famtkx ./kx .1l4odkf /:s9j future position.

In view of the uncertainty principle, why does a baseball seem to hznot mda. btps:w phug-*g/xh 2g050 *ave a well-defined position and speed wherea:5./gpgw*0tt2ma0-h gxnb s p*dzuoh s an electron does not?

  Would it ever be possible to balance a very sharp needl52shf t-wfk jnjj8;w 3h5 2wg )sjud6ye precisely on its point? Explai3 2fj2ys hu8tw5jk;jgw f- wh)5jnsd6n.

  A cold thermometer is placed in a hot bowl of soup. Will the temperature zt/tjjln l04t;h zxk- 2:g9 lureading of the thermometer be the same as the temperature of th xt:t4gkt9jl0l-n l;2u hjz/ ze hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well you can make a7kv4 zad 6rup r2rg3+cny single measurement ra c7p2 dgkruv 346+rzof position?

If you knew the position of an object precisely, with no uncertainty, how wel* 8 0i(xltresil would you know its mome* xs8lriei(t0ntum?

  When you check the pressure in a pi t8tb7ivhng+lt k,9(kz -2 htire, doesn't some air inevitably escape? Is it possible to avoid this escape of air altogethphk-gtk 7+ zt9,in 8lv( 2ibther? What is the relation to the uncertainty principle?

  It has been said that the ground-state energy in the hydrogen atom can be ypd2ea :3p8unf,r2s oprecisely known but the excouy3r,pa 2:f sp8de2nited 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 atom, the Boh-xr5rf8,fs( o09xs y osxplj*r model or the quantum-mechanical model, predicts thatplfx9s (8rfy0jxs, x *5-soor the electron spends more time near the nucleus?

The size of atoms varnvr lc t.3l 7w6 8j+vnhthu7c*ies by only a factor of three or so, from largest to smallest, yet the number of electrons varies from one to over 7wuc+8rnll3*nv ht7v tjch.6 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as they jump 21zdmg4.bq zd down to the 2zmz4dg qd.1 b$n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spx7cbaa+eu/ 2oin but otherwise qu2ceax/au +o7bantum mechanics were valid? Consider the first 20 elements or so.

  Which of the following elect.c)th,kbmw 3 hron 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 configuratio3r+iyvq+oy xm m:- navt;dp; ue; al04n for a uranium atom (careful scrutiny across the periodic table on the inside backq+vy4n:d ty;a0;m+malo3 i; x-up rve cover will provide useful hints).

In what column of the periodic table,wpzui s .5y)xy 6-w 8ascuu2u would you expect to find the atom with each of the following configuraucx2, za yu58-6w py)usw.s uitions:
(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 qf5:q a 1-uxl5:ptxccsimilar properties?

Explain why potassium and sodium exhibit similar g0s+.yd cw wdob;)r)1s+hzvcp -lnu, properties.

The ionization energy for jk (who ewpl6l.43h/ dneon $(Z=10)$ 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) imp 8zjd;z4r bts.ly a photon nature for light? .dbsrtz;z8 4 j

Why do we not expect perfect agreement between measured th .9d5le7 -vm:-y gd.f siuhvvalues of X-ray line wavelengths and those calculated using Bohr theorh-m.dve5.:d9 -f yutli s7g vhy?

How would you figure out which vd8my5s rg/o rq,9s u8lines in an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atom to ua39 bkwi)c o2produce shorter wavelengck 3bw2 aoiu)9ths than transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary lightzvn((b/t5da0g9 oicy ? How is it the same?

Explain how a 0.0005-W laser beam, photographed at a distance, can seem mucb mo mt(9uyh0+ xsvoxfv). z g71uy8n+h stronger than a 1000-W street lamp at the same dgv7.+0oy1+sbvxym xm zf8o 9( uh)tun istance.

  Does the intensity of light from a laser fall off fyxg05d52h1 5yg lbtb1/cx0dmwk :avas the inverse square of the distance? Eg1x:v5yb d g5t y/dk105f0whxcalb2mxplain. ----待选择----yesno 

  The neutrons in a parallel beam, each ha rxhqx,.* g/*z y)*iivnb8g laving 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 aksz amt0.n9w3sk/: br 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 accurqrd/z aag4h( mye)0.en 0aav0 acy 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 typicm:p/3 jypsv(98 r s4b u jp1n6hmze5avally $10^{-8} \, \text{s}$. 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 u(r 6 u/v6nblamass 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 poss++sej3g 2 bm-ad1qk cv6jqj7iible energy of a neutron contained in a typical nucleus ofjqejvb3s d+km1 iq g-2caj+67 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 electron were present ij5rpf,b467h i 0ddglcn the nucleur,bp7lc4 i65hdj 0gfds $(r \approx 10^{-15} \, \text{m})$, 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 the5y8e( vj8 z7hakmv*x i 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 y*1jn g qv+bq,dnt6 y2$n=6, l=3$ subshell?    elections

How many different states are 6y7n :mp+1ff yoizpd ac-n*+kpossible for an electron whose principal quantum number i+f:my*pic-+1a onp6ydz fnk 7s $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each gm1bpm+xjs-e)3v 1fb 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 ni+ sdcld9p0v ;jtrogen $(Z=7)$.

  Suppose a certain hydrogen a8i5gpx-err1 .k0j lu vtom 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 magnitudeg) udi rua7o(oz2.y 6i4g w+rc 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 ha kgou v iu.kjs48q:l6:8ao xo-s $m_l=-3$, 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 bebf/ 4g6k y/bt,ig qsf) 18 electrons in a "g" subshell.    electrons

What is the full electron configuration in the ground statu/6o,iwbi+ fkrd (dh 8e 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) seleni,1 nrmj;scj:-ic fy4;rvmbw-um (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the perioj;m cis-;1r-vbrj w,fymn 4c:dic table inside the back cover.]

  A hydrogen atom is i p.)ax 1p.izpwn 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 elec4p 5-)/dxnatt0pegl o tron in lithium using the Bohr theory. [Hint: T0a l4 tt5p gdx-n)oep/his 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 r0d 9.v bcbx 6a;3vi+woer2dbis zero for a filled subshell.

  For each of the followingcmf:, ijz(+q2t gc-plzb)hm y su-50f atomic transitions, state whether the transition is allowed or forbidden, and if fy2,hubl ifm: czp0zc)5(s -qg+tjm f-orbidden, 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 ,)indfz*9ew zin 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 strik7 uomrucc; x/m60g fi/ing the face of a7 mcucgo0x;6mrf/u i/ $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelen6 yao0w9fj1f ugth bremsstrahlung X-rays emitted from an X-ray tube havey6uf1a9 0jofw $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavele :+bomnx +ik2q ggo:4zngth $\lambda_0$ 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; b.usx5lu1kc a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for anpd1-bsue w ;2y-xcl2 t $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength for an4 p6q- (ypz: b7qygn;b9xkx+lyie c: s $n=3$ 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 d7k bc2sd. 8n mdbrj6)electrons. The wavelength of km) 87d6cd2bsj.dbnr 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 retinyf / (hs8-yjyn 7 y*ls.em fk0tpq7ybh*e:q /las 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 power of +xpwq(uw .tvzj;9 )vs$0.50 \, \text{mW}$ 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 bea 5p1xy lwx7r215n epzxm emerges th21 e5ywxnx7r p1l5xp zrough 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 H4i g15a jlm5fne-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimatbdad9 gr3hiq k*p cyooahw+4)( ,qg53 e 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 tqo ,9k dpa cdh34a*g(+ri5ygo)bq3 whhis 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 pz)n83 uagaxy) ossible 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 rky 6cou y9- vsp /dgo(-qx,e*ladius of an electron orbit, estimate the average distance from the nucleus for an electron in the invd-k ye(y*o6qc- 9 pusxl ,g/onermost $(n=1)$ 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 operatev 9nmy)6gij -9ail0r xs 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 o2ryi* v e+hcrf70d -*fy/nbdof 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 wh;o8 vkh, )mup0lj h,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 dlv6jwif 1e:u f dzuw.3p78g3xifferent 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 fz8-v nnqh57 vgor a given value of 7n v qgz-5hn8v$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narro lrguigu0g+ck)g rp( i- k6p*/w slits in a barrier. Tr)gkc+pgrl 0/gpi6(ugk i *u-he 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 atom is given both by the Boh4qm ,ol9 z51+j3ldytsozgu t-r model and by quantum mechanics. Compare t,dq4gtol3s ym5 jz+1-9ouzt l he results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling with a gah . 3mv6n2sfhtk ;cu)fht74speed 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//ex-hhyks41igll5 p . Careful measurements show the line is really spread out between 487 and 48k1/pe4 x yighl- /5lhs9 nm. Estimate the lifetime of the excited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated frx0k1w za; oofb k o*e*i.xlr1(om rest across 550 V. They are then directed at two slitsa *o;x1.lix (bk1oo0* wfze rk 0.70 mm apart. How far apart will the interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each ind 8.hh.gx b/ljcn s,nil(v9,uitially at rest, are accelerated across the same voltage. Assuming that the uncertainty in their gh(/lni9 .cnsj. xd8,bhvu,lposition is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum number n were liq93ar r/ j-elfmited to the range from 1 to 6, how many elements would we find in natulq/ a3f-errj 9re?   

  If your de Broglie waveymq /x r oz7f(w;xvu(fc2j4 q0length were 0.50 m, how fast would you be moving if your massxmf yw(uvco r02(z; xq jq74f/ 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 unknownl-kook rdlz,lv3 d :+l+q;vn/ element shows a series of lines with one out of every four m/dkl l+od;-n lrl, k 3oq:vz+vatching 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 question. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm are emitted from the surface of a certaiu2uwwoda/++ m8f qqo1 n metal when it is bombarded with high energy radiation. If this photon wavelen u/w1fqu++2oq dw8moa gth corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread of a lasoy b8sta4+u*.;jcl xh er 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.]