Compare a matter wavejv/71txic p2z,nxg ) ;hlly3 i $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory q2btd)t f7 g8gof the atom is not compatible with quantum mechanics, particubqd)f2 8tgtg 7larly the uncertainty principle.

Explain why it is that the jl6tir4,q9n w more massive an object is, the easier it becomes to predict its future posit qw,4tn r9ji6lion.

In view of the uncertaionz-oao0ha*y6.u n:b0po q e4nty principle, why does a baseball seem to have a well-defined position and speed whereas an electron does not?4ya.ho-paun0 0o:* ebo6zqn o

  Would it ever be possihr-jm2dyn8nve3xd q ) g/jl -0ble to balance a very sharp needle precisely on its point? Expx- )my2q/e jdg3 jhr0v8ldn-nlain.

  A cold thermometer is placed in a howqdyql + 4q7l uhnc-+x1i.0thxcc) q5t bowl of soup. Will the temperature reading of the thermometer be the same as the temperature of the hot soup before the m q t.5q-ihlcwxhqyn4+cc7)x0q l1+du easurement was made? Explain.

  Does the uncertainty principle set a limit to how well68.k*v.kfeffi f. ygc you can make any single measuremenf*yf.ik.6fk gcef .v8t of position?

If you knew the position of an object precisely, with no uncertainty, hlmxe589q rlhs8upeb+1lxl2by/ hh;; o 8kv -kow well woulkl/qub 1;h hs h- ep9o+y 8k;bx2v lxre88lm5ld you know its momentum?

  When you check the pressure in a tire, fjelmq/mi+y+p:/x 8q doesn't some air inevitably escape? Is it poslfmq j:+e/i +/mp qx8ysible to avoid this escape of air altogether? What is the relation to the uncertainty principle?

  It has been said that the grwcsx)2kk,8uks3jt)nhkl v 5 0 ound-state energy in the hydrogen atom can be precisely known but the excited states have sol 8xt c0v))hnj,2uswks5k kk3 me 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 Bohr model or the quantum-mechanical m3jzdth 8 q2my6odel, predicts that the electronymd z38qht2j 6 spends more time near the nucleus?

The size of atoms varies by oz u q3ej,k*d*jnly a factor of three or so, from largest to smallest, yet the jjuke3**q , zdnumber of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as they :ek( ) e0evzro5 r0hsnjump down to th5 rk0e: v)e0hnez(rs oe $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spin but otherwise s4t2i13+ f+gncsrqor w 2j dx8quantum mechanics were valid? Consider the firs84sjgr+ 2 o321nsqr ictw +xdft 20 elements or so.

  Which of the following electron configurations are not allowed: 0fxns/ my8 o,r98y4sn9wtzgg
(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 conn; w9n:wkrd i)figuration for a uranium atom (careful scrutiny across the periodic table on the inside back cover will pr9rw wk)nd;:i novide useful hints).

In what column of the periodic table would you expect to find the ato roc/ xhc-iwx3t9 hxe7sz:: g0m with each ofx-h eow9:/hg07czsr t3ix :xc the following configurations:
(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 1et:r q s:ds;2vnimg- 29uwsmdc2+mkiodine exhibit similar properties?

Explain why potassium and sodium exhibit similar prop k:5 xc/2avggby::fqterties.

The ionization energy for ne 545wv tbj1;sbz * w2l mjy(j9jp 4,owyz/eknuon $(Z=10)$ 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 pss.q7qseb tl f*9 v0a,ue2b1e hoton nature for light? 7fb129e etsulevbqs, *0a s.q

Why do we not expect perfect agreem,2f (ose ,-xlnzswc6went between measured values of X-ray line wavelengths and those calculated using Bf s x(,-ezcw6n w2los,ohr theory?

How would you figure out which li9tulm8 oi)v dey z114tnes 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 toa9ktf, hz95 go produce shorter wavelengths than transitions by outer elea 59tk,9 hofzgctrons?

Compare spontaneous emission to stimulated emission.

How does laser light differj l-6u:, msxti from ordinary light? How is it the same?

Explain how a 0.0005-W laser beam, photographed at a distance, can seem much str.d. l7qileaztuj1v n+o5(c )bonger than a 1000-W street lamp at the same distancz(i.nv uj5clo)ad 7b+1.lt qee.

  Does the intensity of light from a laser fall off as the inverse squarevf+rh w*j/e j; of the distance? Expl*;hwf/e j+rv jain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic energy hvs8v-qr 0h7(k k3av t$0.40 \, \text{eV}$ 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 akvhmee(,xy5 muff 45e h7i/0 jg.9zhx 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 ca5ju c4.5h: gglswx.g 6q(kgr/1e3rapf b up4fn be measured to 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 -vrao tg 4;j;latom 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 uncertaintvh7n8q -ayj3my in the mass 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 possiblevl(3 t9cp 5tcs energy of a neutron contained in a typical nucleus of radisctvl 9tc5 p3(us $1.0 \times 10^{-15} \, \text{m}$. [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 princikez+ y7skd)i9y5 a/ ejple to show that if an electron were present in the nucle)j iz7ek+9y a5sdy/k eus $(r \approx 10^{-15} \, \text{m})$, 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 poslakix 3w,d nv/02( hepition 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 bsl/ t+yi5rx+ * .usz6lkg:yvse in the $n=6, l=3$ subshell?    elections

How many different states are possible f b4)va;6rsjv9yim ug 5or an electron whose principal quantum number iagy mv95;vb4jr isu)6s $n=4$? Write down the quantum numbers for each state.

List the quantum numbers rz*zpu3;p;mox j tm.v 2 bez 2s,me.5rfor each electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the groukw 0 ,tkce*pvcnk u 3/y/k1sn+nd state of nitrogen $(Z=7)$.

  Suppose a certain hy-jn,2a2 6l1bztdweyful fl 7-drogen 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 anguxq2n azf8eud ;o8:*mu lar 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 hd f3rno9zn8)c as $m_l=-3$, 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.cy8ucvub3 k782 sy3; 9zz1xv0qcow og    electrons

What is the full electron configuration in the ground state for elemgj/54dyi2es* o3yclx ents 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 6drq04wcqx - l(a) selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see thqcq rxlw 4d-60e periodic table inside the back cover.]

  A hydrogen atom is in thrhk pd) um3 rm(31dm.me $6s$ 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+i1z7x*7 qqqjyupx3;rkzb((gvdi; j lithium using the Bohr theory. [Hintx 7ijxygzrqji3+u1; (qzpbv 7(* qdk;: 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 am5(ubp h2a.(qbq g/)wemk/zis zero for a filled subshell.

  For each of the following atomic transitions, state olw.v4 y+:y+mep vyk, whether the transition is allowed or forbidden, and if + v4mvlk.+y:p ywo, yeforbidden, 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 cw-7q vy uk)b(in 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 electronv exav)nrsz p in-e:*(mwh .cwtf7h:,.j6 3fgs striking the face of a 7xvhzf fh:i.cvrs w ge na)n:w(6j t.*e,3m-p $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted from an X-ray tub0be h2j; tpv0 si/r( whm:lk4je have /t jihmphrbskj e:4( ;l00w v2$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelength 5qci5d-e p*k2vks y kbk34q+j$\lambda_0$ 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 , pq(rz ;p50 92dwu2zypvzmbk when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength iik+kj:f h0xuc)3 c3v20ptmp for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelenw(rj4jcm)blyf si 5p *ra5adv 7,wl7+gth 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 unknown material is bombarded with electrons. The wavfo/j:b 23eylh ell be2yohf3 j:/ength 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 dea/o2 0s.w3yv,oagcqr tached 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 phyhkn5j 6f3r/8y-gc4ez7unox/j( y p fnsics 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 of a laser bib(s:xgn k )jw yq;67ueam due to diffraction if the beam emergesjq yx67nsb);i kw:u(g 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 la)(u:/l-4hxtml mf axug8yvq2ser?$\lambda $ =    nm

Use the uncertainty pri8x qupx) k pc9,l,;hwsnciple to estimate the position uncertainty for the electron in the ground state of the hydrogen atom. [Hint: Determine the momen;9hskq pxc, xlup 8,w)tum 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 w32 hk4oj6 jri- 2zdqhvalues 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 av (4gsz 9q1gzn, wd2qaeerage distance from the ndze gqzasqw1 n94g(, 2ucleus 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 swz23 egmq7z wq0s. ;qat $95 \, \text{kV}$ 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 i1b ,uraqb4w)ky;q6 fermost 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) cann8 dg/i(3gi3chifd 4)bbecw ) 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 differenot2* auw1zr+4/5)gyotjdo hw2vi a y1t 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 o,bfpp,mc mx-cl)d n oifl)n;r 7;b0x)f different electron states possible for a given value of dn7b- lcx) ml;i )fx ,n0rpfc;mpb)o ,$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot tpsq5 3vru*hh ;jswqd:a*+a )bhrough two narrow slits in a barriebw) dha v*3ua :+j5qsr; spqh*r. The 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 gij,lg5flc e kj+q*2k6 cven both by the Bohr model and by quantum mechc6j kc2j*+lg lf qe,k5anics. 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 with a speed of )nz2a hwu;4q.-tp30u hs zdhr$(22 \pm 0.22)\ \text{m/s}$. 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 nmpsg2/a / qz4ohp(qeu5 . Careful measurements show the line is really spread out betwe q/ouqp s2h4z (/5egpaen 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 tw.pgt7 w/jurb0oh4+idf, o 8if o slits 0.70 mm apartw7tuir4 pg bi +jffo8.d o,0h/. How far apart will the interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each ir ja2;4ltp8ysnitially at rest, are accelerated 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 thaj2s l 84t;rypeir momentum.

  If the principal quantum number n were limited to the ranr+l1v- p udq e8c6qz*uge from 1 to 6, how many ele lpr1ucq 6ze*u8v+q-d ments would we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast would you be moving if yox 5) qr5n 6j4edqnfuu1ur mas rd4q6u)n5xfq e5nu 1js 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 s/,.nprrkrs): 4jg lfh eries 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/f) 4nj r g,sr:phlrk. one electron, determine Z and the element in question. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm a; zo,*ddxf-, .zsew o,a qwyd(re emitted from the surface of a certain metal when it is bombarded with ,dsd zo d*w,w- fx;eqy (o,za.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 beamkwml1f , hy56ip cz3zgh4e, v2, $$\theta \approx \lambda/D$$ , 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.]