Compare a matter wavidu;hm r13* ;kz 1ogrzgu+ 2vae $\Psi$ 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 hk6 wj*u z) p* 8hwsqf:;al4hqquantum mechanics, particularly thehzh pk a8*fls;qw:6 h4jqw)u* uncertainty principle.

Explain why it is that the more massive an obgc r snj3n7+:u(t whhv4xaize9+- tq3ject is, the easier it becomes to predict itsvi9qa-s3 n+g:tr 7u4th (+j hcxzwn3e future position.

In view of the uncertainty principle, why do 6nl*jjm6cq7li nt)uh+w3b n:es a baseball seem to have a well-defined position and speed whereas an elect6 nq bj: +mi7)3uwnlht *lcnj6ron does not?

  Would it ever be possible to balance a very sharp needle pre fq u.sy8r .)cwg1on-bcisely on its point? Explain cr1f.)u-ogn8y qsbw..

  A cold thermometer is placed in a hot bowl of soup. Will the temperature rec78)t:u r nbl2omc, ltading of the ,:u72otlbncm8 ) tcrl thermometer 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 y 1j;t8rvcosm:+v)z .okwuf 8 oou can make any single measurement 1fuosw8.;rt vo+z k) mc8v :joof position?

If you knew the position of an objec6mu,klw3xditn y8:7y 3,e ce oiz5fv.t precisely, with no uncertainty, how well would you know its moe8klyn,t.5vm :e 3 fo3z7,wdyc6xuiimentum?

  When you check the pressure in a tire, doesn't.y)0b t8-qy8deierv pmqr.r *f v5b,f some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relation to the uncertaintyr.-.db8vb8 fp i yvee5f qrtq)r0,m* y principle?

  It has been said that the grouyjt(s p)t wy,.g;ff- *wzfst -nd-state energy in the hydrogen atom can be precisely known but the excited states have some uncertainty in their values (an "energy width"). Is this consistent with the uncertainty principle in its energy form? Exp- tfpw sjz f* wtfs;t,.)-(ygylain.

Which model of the hydrogen atom, the Bohr model or the quantum-mechanicaqs.ejj 1 96eq z,tdjxuu9*m( bl model, predicts t ,jq1ju6uq.9ds*m btje9(z x ehat the electron spends more time near the nucleus?

The size of atoms varies by only a fact -29si )n,janscq8qao or of three or so, from largest to smallest, yet ths- aaiq,snc 9o2n8)qje number of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate lilk8s j cxud01-ght as they jump down to thel u0kd-s1x8jc $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table loorsh+ .ua +:gxgk if there were no electron spin but otherwise quantum mechanics were ra+.+:h ggsux valid? Consider the first 20 elements or so.

  Which of the following dx)uq 0q j*y*9iw4xmielectron 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 electro)p-,( ecf abvqv3yyn+ n configuration for a uranium atom (careful scrutiny across the periodic table on the inside back copyynbfv3av+ ) -e cq(,ver will provide useful hints).

In what column of the periodic t.a9qa,sa+j) d tdlq6z 5fn( jyable would you expect to find the atom with each of the following co) d+,yq(5tj anjzad. f69 aslqnfigurations:
(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 elu(l/ fkthyk 7e0fhb 20*k .ywxhibit similar properties?

Explain why potassium and sodium;kl3jp6rb 1r :ld p ksajl.+5c exhibit similar properties.

The ionization energy for neonh95 cdh :5,uemsw*jg a $(Z=10)$ 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 nature fo b qja4a0z-ux-r light? ba u qx-04-zja

Why do we not expect perfect agreement between measured values of X-ray gguw5wme7t: * r )i4ahline wavelengths 4ag5:)gw uiw ehrmt*7 and those calculated using Bohr theory?

How would you figure out which lines in an X-ray spectrum correspond to dd.g+ dslys/ dy,)v5r$K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within 1arels(0t;b0ov k t0ean atom to produce shorter wavelengths than transitions bytls 01 b ;0avorket(e0 outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from4df2/lrgxy4 r + zw0g+aevm-m ordinary light? How is it the same?

Explain how a 0.0005-W laser beam, photographed at a distance, can seem m3 jw q9:vswg(juch stronger than: gj93qsw j(wv a 1000-W street lamp at the same distance.

  Does the intensity of light from a laser fall off as the iwh; ht*c3x l,nnverse square of the dhh l3 ;,cxn*twistance? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic energdh1jcr74q31,j7 y nvgmho .s hy $0.40 \, \text{eV}$ 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 :8jt de1sxec/ 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 accuracs qkzkhufg)m9)r6 nbs 3q ,j:,y 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 sc(u :3 f7ol0;p o 4,mgxlhhucan 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 mass of ahy+--g; *om ioun v;l/ynwk 0 h48jgxa 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 neutr)5 nw.w8nhu p0k b,m zxldrnp,8xkff1fg2 9*bon contained in a typical nucleus of radiuw 8pw0n8*xnlk,15 , hpgunk)9bfb.x 2 zdmr ffs $1.0 \times 10^{-15} \, \text{m}$. [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+72ppwf88 s sdydk :pe if an electron were present in the nucleuspdpw s kps d:2f+88ye7 $(r \approx 10^{-15} \, \text{m})$, 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 tr1d, 7jhr m5ria4okrg h7 zu42he 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 canz 3b+ + 9ndwex7v. jb5zjbrbeku6 c7(t be in the $n=6, l=3$ subshell?    elections

How many different states are dzci),;hea5 f-y./zo xssh,q b czq8 g7jy:u4possible for an electron whose principal quantum n o f 847-zuzdaze/.gc), hys5;,iq:xhbcqy jsumber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers pafw2ep8w;(clx 39z n l:lfhz -bu-5dfor 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 stat- --ka y5tmtcx6jpfe7e of nitrogen $(Z=7)$.

  Suppose a certain hyd1qe8a jsm q,q+rogen 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 magnitud7pwun pz61j 4z m,gca+e 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 w:jqzls1 9qmo*i h 7r)$m_l=-3$, 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 xd4,la8k qesgo/y *j1 "g" subshell.    electrons

What is the full electron cna--pbj.1 rogees 9 )xonfiguration 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) selyfiyz7v2t2b/zr p- 3lenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the/i z3ltbp-v2 fyr yz27 periodic table inside the back cover.]

  A hydrogen atom is iw f yi;a))epm224 ,xgyalf ,jln 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 lithium2 -;x)dp , md.hzolgqk using the Bohr theory. [l)gdz-q2 kho ;,x.pmdHint: This 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 fps5rx:7qfcqc+;x)a th ,uc u 1or a filled subshell.

  For each of the following atomic transi6+ cui2xenu bg;cy2 q9tions, state whether the transition is allowed or forbid 2 enc69u +xgu;bci2qyden, 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 ze-6d br0*se,k6 .rphd oo*uyin 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 shortes wqbw;ofbz (qmi;vx 8 -y)d2x2t-wavelength X-rays emitted by electrons striking the face of x;wzqfby2 wmov(d ) biq- 8;2xa $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelekvu97 ( 3t :r7mlzbkfwngth bremsstrahlung X-rays emitted from an X-ray tube have b:tukr3(mvw7 fl97 zk$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff w. hmv1+n:j6c 8 )alzz fhwb,aaavelength $\lambda_0$ 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 waasa u;dq;)w )7i vd u+hut+yt6velength emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength foaruf(12nyt;cnp5 qn(g2 1d *tg0 cxomr an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimatey*;.l yp(r o1vc s1,2 uxherih 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 unkn8q.aab fjtq(n 1h+ 3d/fchnj5vy2y z/ own material is bombarded with electrons. The wavelength of tnny/8+chaq 3/ybf hqd 2z vj5(1.fjathe $K_\alpha$ 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 de 71-bg.8lfv;vwg nnfbtached 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 physics lab might have a pow meh5ofn))c852 ipzider 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 4ykkwf:-b2fv to diffraction if the beam emerges throughvf: b 2wkkf-4y 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 ofyl,m tktr0+f+/lj.b b the He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the p9 lq+ kheg1dz,osition uncertainty for the electron in the gr9kze hql1d g,+ound 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 possi()gl8 m ajcm1s9ml (icble 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 forbsklwiwx 1 r)-.q-;rx the radius of an electron orbit, estimate the average distance from the nucleus for an electron in the l )bs --wr1kxr wxqi;.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 operatesus+a5c dna 01o 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 out for j;6 l+iz 0qbj3.2xsfuit(ermost 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 plsa mf-;ipm395tl)9m tgmg +mv ot(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 sbsd7* e h-qf:t.+k-+i-y cny ffhn3idifferent 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 difw1 ynq+c b66udferent electron states possible for a given value of ucqy6bwnd+61 $n$ is $2n^2$. (See Problem 50.)

  A beam of electrons .d 8tv5cdr m7:im) szbwith energy 45 kV is shot through two narrow slits in a barrier. The slits are a dr.smb7vt dz )id: mc85istance $2.0\times10^{-6}\ \text{m}$ 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 hyb,(ptacv*dy3kk : e( ndrogen atom is given both by the Bohr model and by quantum mechanics. Compare the results fory bcn3at(,pe (*d:k kv $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling with a5ywc92vcd t ggs2 /z(jor(ho, 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 auxto ,(k /mi8sm+;txqp* :iht line with a wavelength centered at 488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. Estimate the lifetime of theiottmk+q im/,sh;:txup*x( 8 excited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated from rest acrossle+q- kpzn 1 cbe99:mw 550 V. They are then directed at two slits 0.70m lwz+p9ekbc-e 91nq: 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 initiallya zoxoa6h z/ r/78k6eq at rest, are accelerated across the samkqr oa/z h8/ze6o67xae voltage. Assuming that 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 w-b5)acsh pab (ere limited to the range from 1 to 6, how many elements hp )-5 bc(sbaawould we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast would you be moving if yof/szi2 5x/e .qs.x zppv*j6y sur mass izxi.2sjvsp fq. 5zs6pxe /*/ys 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 spens((ba ,ty eg/ctrum of an unknown element shows a series of lines with one out of every four matching a line from the Lyman serien (bay,s/(t ges 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 certain mep ),msvag y3/stal when it is bombarded with high energy radiation. If this photon wavelength corresponds tp), svag mys/3o the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread of oe/k2r0:ocmwv)u9 e nwl7z8w g(,; ul+ vj chha 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.]