Compare a matter wave(ke e:r1/yyx.s( .- afbegrso $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory eac ;k4z.;r z,qto/a*dzk*yqkb:l7b of the atom is not compatible with quantum mechanics, particularly the unz7 za; k*tkbzd,q;*:l ayr4qk ocb./ecertainty principle.

Explain why it is that the more massive an object is, the 1 x+7;bh/hkl2io5s 6fij xccheasier it becomes to predihx2i5cbj+ho/1sk; x 6 fcl7hi ct its future position.

In view of the uncertainty princ st)u a+ox.i-5e m j1tgify6qi w.)4adiple, why does a baseball seem to have a well-defined positionji fgtxa mqt)d -is5o 6eu) .ayw.41i+ and speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle precisely o-d +s /exlwvn0n its point? Explaxl0w n/de-+vs in.

  A cold thermometer is placed in a hot bowl of soup. Will the temp h 6lb/lcfz0i(erature reading of the thermometer be the same as the temperature of the hot soup be/il(0 6bzhl cffore the measurement was made? Explain.

  Does the uncertainty principlrc/ *3x le+ f:h0nj-9mtj xrose set a limit to how well you can make any single measrsjjx93tle*+-hf/0m rn c: xourement of position?

If you knew the position of an object precisely,.w1y p,n(tkou:cglie , 9gw/ e with no uncertainty, how well would you know itseke 9t/ogwp u.cn ,liw( 1:yg, momentum?

  When you check the pressure in a tire, doesn't some hqt * 6lzay9 kgr9ow3,air inevitably escape? Is it possible to r*q gay,9z k6owl th93avoid this escape of air altogether? What is the relation to the uncertainty principle?

  It has been said that the ground-stat/k/ mkq/bl(a idf-ztf xe0j:6e energy in the hydrogen atom can be precisely known but the excited states have some uncertainty in qf m// a/x bz6 k(-tflejdi:k0their values (an "energy width"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydrogenop 1(g/nk huxpoqdd0u v r;qb-bq )2;( atom, the Bohr model or the quantum-mechanical model, predicts that the electron sp;no (qupkqoh0)d 1bu-(rp;/ vx2b dgq ends more time near the nucleus?

The size of atoms varies by only a factor ofr7(( kp:hskqy,p ab w, three or so, from largest to smallest, yet the number of electrons varies from one to over 100. Exp qyw(,a:ph k7krp ,sb(lain.

Excited hydrogen and excited helium atoms both radiate light as they jump downkfzqrh, b pjj()u0 *u9 to th 0j )b* jfu(uzrp9q,hke $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electr7o-mv-1 *z7) 5fhwzidblgdlson spin but otherwise quantum mechanics zblh)gl1 s5*ddif-mwv o7- z7were valid? Consider the first 20 elements or so.

  Which of the following electron configurations are *uv*ob40 cl(d p2r g-gaoli:q 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 s3v78kg/ (- tkvr5 efosozww y0ca 88datom (careful scrutiny across the periodic table on the insideev o5kcaw8(r- g3vz t7yf 808dssk/ow back cover will provide useful hints).

In what column of th t)-ojtzy n9crj,2 zf7e periodic table would you expect to find the atom with each of the following c7 ,rtz f-tjc2zyjon9)onfigurations:
(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 exhib1nofd73k9 n ,m/qty*h ui,hyvy+r 1zb it similar properties?

Explain why potassium and sodium exhibit similar propertixkm* vq 1fxhlm111p2nd3v z/yes.

The ionization energy for neo*w1vxj f,e*rs n: lb5 pif(yl2n $(Z=10)$ is 21.6 eV, and that for sodium $(Z=11)$ is 5.1 eV. Explain the large difference.

Why does the cutoff wj0f1ogr fkbnu k.zj/e6mp9 ,*avelength in (Fig. Below) imply a photon nature for light? j grn*oj. fme ,6/zufk09 kpb1

Why do we not expect perfect agreement between measured qk/y)c5y rqg+ values of X-ray line wavelengths and those calculated using Bohy5k+r q y)qg/cr theory?

How would you figure out which lines in an X-ray spectrum correspondptb4vb6: uj8wc (r(m m to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atom to produce shorter wit0e zt:hm/vi / lwq;c4;ii 5uavelviw/;t/l;i 4mq05h :i ezui tcengths than transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from hw4s a7z1re/j*w8lbr ordinary light? How is it the same?

Explain how a 0.0005-W laser beam, photographed at a /+jx ldm2ygyjn0 a0m *distance, can seem much stronger than a 1000-W sy nl d0mx/+0*amjg2 yjtreet lamp at the same distance.

  Does the intensity of light from a laser fall off as the ie iqmi h0/5)xwnverse square of the dis/ehm5w0) ii xqtance? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each ha a7mxt rd zq +8ab056suj+6 i;u-ycenyving 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 a speed ofd * o/:yrnf+yz 16rynh $(6.560 \pm 0.012) \times 10^3 \, \text{m/s}$. 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 ysw7htf .f1k-3 i 67hc6mgt uf*xs;h ian 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 fxwg: ;uy1s1*fv:c ql 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 in the ma*q6a 2(di r +hhqb2hnoss 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 in a typical nucleus . zfhfr/+b,av ,a+ adhof radius f fd,,.a h+bh /zr+ava$1.0 \times 10^{-15} \, \text{m}$. [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 toe ufc3lv6+x8cfa2mxi ry+7 : s show that if an electron were present in the nucleusf 6 8ulrv:c7a2fsx +3+ myixec $(r \approx 10^{-15} \, \text{m})$, 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 positir9e;hm v7 /ry-ws9xp qon 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 bev.wd r5i+i*6dzk .rmx in the $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whose prinrcn134 yvmh7 6g1hgjo e:wbt;cipal quantum number is 1btm;r:v3 gje c7g41hhw6 ony $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the grouna hft-,m1h-rhad hiv58 z5d0bd state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum number (e7kn1icnxoe,h /nb v5q6(b ls for each electron in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogenw i ,0.4 - 4)fyuxfajqesnalv) 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 mome9o; jjoso3*wzou93 ajntum 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;o-i )-ba oyk,z(cl km $m_l=-3$, 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" subshell vh lb.x07 i2c7pbns1n.    electrons

What is the full electron configuration in t 0tqe :vp(ph hsfhn;e) /kwp--he 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 zjl zu s/b;)to,;jfr/ (Se), (b) gold (Au), (c) ra )s jtu,lz//;; rfbzojdium (Ra)? [Hint: see the periodic table inside the back cover.]

  A hydrogen atom is i5,j v)rsz( gtin 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 aj9 ..ken ay-so te-3cin lithium using the Bohr theory. [Hint: Th.3j-k tas. -n9e caeoyis 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 kamt8qgm .w :1wi:a k+);nf4 nck6 khbfor a filled subshell.

  For each of the following atomic transitionjuxt6o,9)0 gmzjf)hts, state whether the transition is allowed or forbidden, and if forbidden, 6j),gtut9 j o)0m fzxhwhat 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 in av,qmg c c7nc: 4j2:qb5xf. boj $6d$ 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 strikip qo+( jpi4o3mng the face of ai(j34mq pp oo+ $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitt- ikgq :tjm tel/a0v0/ed from an X-ray tube have aq/tg0 i:m/-v 0tklje$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelength -2r lkoyvwj k, :umh;/$\lambda_0$ 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 wavelebux2 nv-1g)0 xsofd o5phhv*im 7e(s:me 5i z2ngth emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for f/y4ls563ee dc krv8oan $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength for an azqce 57br/tzn .54* +ubyu nt$n=3$ 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. The wavs p(xk;vt 9qrms8a)gd,b/ o4relengx/gk,m; bssq9 vd r(4rapo t)8th 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 detacq/-196s 8wekf jlvh/s9 pompjhed 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 used in a phkae)wmx) u.qy t4( b(iysics 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 rwi lbn4 ;g:4h6is f2zof a laser beam due to diffraction if the beam emergng z4bfl 4 hi6r2iw;:ses 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-Ne +g9(9l7vlm ttg oert*laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the positionly;fr-zt- (xlz lv 2d3ca9v0eptxy*) 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 zeplf *ayc yd) e-x30zltv-; 9x2r(vztlro.] 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 nw uig 564kd:upossible 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, estimate the0qnk q+bd: a4u average distance from th4qabn0:qd +kue 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 operates at ft d(md;,9elu $95 \, \text{kV}$ 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 outermost electroy4d8int :;lvnsriu67 n 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. B4h nw 46e lgfmtfpf.:9elow) 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 different stateh +jiunpp*6bmpr 2y1 )s 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*0/j 2ycc1,e.gtdwm msu k*/q/omkys different electron states possible for a given value of md/eqo//mtj 2c *guw mcss* k01,y.ky$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons wi+)8qb qf xr*iyth energy 45 kV is shot through two narrow slits in a barrier. The slits are a dist bi)*rf+8 xqqyance $2.0\times10^{-6}\ \text{m}$ 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 k2;k: tq fmzsnw5c,.,nh *kphgiven both by the Bohr model and by quantum mechanics. Compare thek mkwz2:sq*nt hpf;5h,nc, .k 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 s mlflb k( t+-4g0pj,xvpeed 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. Caref( f1+o eorgh(,o6vwroul mhroo1 ov gwo,(erf 6(+easurements 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 two6.jf h 4b ;f,sg4q+hnyx(-bu tpn;ec c slits 0.70 mm apart. How far apart pnxjcn (b.y ,f+ufb - ;tg;446cshhqewill the interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, are accelerl * k56twxa1evated 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 * 65wltxk1v eatheir momentum.

  If the principal quantum numbeajlkzn q5 )xci8 q;)g)r n were limited to the range from 1 to 6, how many ej8q k;)gan5iq)) zxl clements would we find in nature?   

  If your de Broglie wavelen,udy)a+z.p6zfj c ;k ggth were 0.50 m, how fast would you be moving if your masgcd+y,6zfjazu ).; kp 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 elemenc./uy:jdf d.6 sma3z yt 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 Zuyzd3/m:jasc ..6 f dy 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 suxuqhp ky9 - 2/zzpzd:0rface of a certain metal when u:k-phzx 2/dp zzy90 qit 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 be rr;11 , lfu1 rqrj5ick.7jppgam, $$\theta \approx \lambda/D$$ , 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.]