Compare a matter wav; l cosvt /o9m;tz:yv8e $\Psi$ 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 wr/ * yqa/f1qtth,uj a5ith quantum mechanics, particularly the una5j,trqf1 /h qa */tuycertainty principle.

Explain why it is that the more massive an object is, the errr06g cqd2wxcc*;+;5e6 e9thm osku asier it becomes to predict its future positiou d+ rs;* 0h92eoecqcc6rt;g 56rmk xwn.

In view of the uncertainty princip. r*rn ;3upgds8qbv e2le, why does a baseball seem to have a well-deu*v bqre;823 gp.drs nfined position and speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle precisely on cdy e75 1m4t2vcfevl k4: 8t iyw5fqkm94gng*its point? Expla9:q*vfk c4gyc7kmd1l 5met42t54 wgin 8fv eyin.

  A cold thermometer is placed in a hot bowl of soup. Will the tempeyv*m i, u;7r.gm (wcrbrature reading of the thermometer be the same as the temperature of the hot soup before the measurementrmb;mw .(*7i yc gruv, was made? Explain.

  Does the uncertainty principle se(l3tb 234qrm zr+9:j paufhbx t a limit to how well you can make any single measurem 3h9al3xfrjr 2zb+ (tpmq:u4bent of position?

If you knew the position of an object precisely,(4h0 ptso-bj c with no uncertainty, how well would you know its0 ho-tjcs bp4( momentum?

  When you check the pressure in a tire, doesn't some air inevitably escape? Is dk70)vg.ddrk x) iby;0 -mmo , hz;xsjit possible to avoid this escape of airko),vd 7s0)jg;m0dxr-hz bdm;ykx.i altogether? What is the relation to the uncertainty principle?

  It has been said that the ground-state energy in the hydrogen atom ca1cnb22 ds js :h2ri3w+v uw;dtqo;w 0tn be precisely known but the excited states have some uncertainty in th; tv2;jr2:21twcsd+ 0dno qi swhw3 ubeir values (an "energy width"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydrogen atom, t8tm;ld jp ifbf+8 ba2tymwjy; u7 )/;iq. dr1ohe Bohr model or the quantum-mechanical model, predicts that the electron spendsq1+obl pt a;2dfjiu/ym 8ir. ;t7yb )j mw8df; more time near the nucleus?

The size of atoms variesr foz4e,1q9*y.e ikzb by only a factor of three or so, from largest to smallest, yet the number of electrons va eb9f. 1rioez ,y4q*zkries from one to over 100. Explain.

Excited hydrogen and excited helium atoms both ra)n+ bbg m5zbr8diate light as they jump down to n 5bmb+b rzg8)the $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if the) roh1iegc4w cpd3.(vre were no electron spin but otherwise quantum mechanics were v1(ch.vr )ec 4id3owpg alid? Consider the first 20 elements or so.

  Which of the following electrou9oe*b)vtngp -4 v 6ayn 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 configuration for a uranium atom (ca ib95 bo/tb j8;sx3zfjok d0f3reful scrutiny across the periodic table on the inside back cover will provide u0/odsjxb bftizb ;o353kf89j seful hints).

In what column of the perio eh 7ae/d3tc0kdic table would you expect to find the atom with each of the followi 0hk3ac 7e/edtng 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 iodine exhibit 9rm 1qf5hc)dq1fven3 similar properties?

Explain why potassium awfltecm5b x/fgv 4(k 484ruv(nd sodium exhibit similar properties.

The ionization energy fozq. a-bl; t/8:xarn2jwe . y1sae lpx7r neon $(Z=10)$ 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 phoe0a0oly8 f 0d6bvp whz(dbu2 6y1ihb; ton nature for light? 8uabv(6 0021y60zbephlidb y ;df hw o

Why do we not expect perfect agreement between measured values of X-ray line wavgzhp+p h0(: 5ing+ khielengthpng+ g 5ihk0h(z+i p:hs and those calculated using Bohr theory?

How would you figure out which lines in an X-ray spectrum corr x-,rn;tf/ v7v.wxssm espond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atomutpk-zlq188 69diwf e to produce shorter wavelengths than transitions b dw-fu1l8869qpi zk tey outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How is it the sam+xlphxuv8k6a 1).j*li z .zsfe?

Explain how a 0.0005-W laser beam, photographed at an bi -+4ufjaf z7bw2j+ distance, can seem much stronger than a 10002ni+b74+ a -jjfbw zuf-W street lamp at the same distance.

  Does the intensity of light from a laser v by59o nd; k09ljdgv-fall off as the inverse square of the distance? Explaivl 9kjdgv ;yo5d 09nb-n. ----待选择----yesno 

  The neutrons in a parallell*ce5(m6 j x*;v(llti * pezhm beam, each having 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 w+k5t g p08ewuxith 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 ;hwu6lst9 er lm(0, rfcan 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 eddsr vu1aqp4x ;f y70fo o-,(excited state of an 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 x ,9.(bbp*jxol/a-z djwc n ,hmass 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 nxx p:.kfgld-rn)2 8 + ;vfberweutron contained in a typical nucleus of+ : ff -2rv;.edkln8)bxp wxrg 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 4 .hoss(4ur 3t 9mwbqzprinciple to show that if an electron were present in the nuclto 4hb4z9s. rqw(u3sm 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 position ofsv6 f6,i/ekl7+gmnb w 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 il e)i5th443.nx qdnbfn the $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whoa8zbvoi nh.oftw((o00:h 23zkp vyl4;q.pse se principal quantum nin2hhk0syzv3bowl.fo v;z (o 40 (.pat8qe:p umber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in thedxv ,p qzlzv-+4aqa46 ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in,o-,o dxw: dlk the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen atom h3844h zpf2lsq* a rsrfas $l=4$. 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 momentum of an electron in th40ax, e;ecm rcszn++ae $n=4, l=3$ state of hydrogen.
L =    $\times 10^{-34}\ \text{kg} \cdot \text{m}^2/\text{s}$

  If a hydrogen atom hasdho- /lzknl rq26g:r) $m_l=-3$, 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 electronsa eh0lwk01 tnoivj(nw 4e,-- u in a "g" subshell.    electrons

What is the full eled :ijn+jzx48bu b888fn g7rqk ctron configuration 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) selenium (Se), (b) gold (Au), -t+rc,fab c;lon69zu7il v+vc 9 zs7m(c) rb++ a6 o9 nvt ,-czlu;f9lsv 7mc7zricadium (Ra)? [Hint: see the periodic table inside the back cover.]

  A hydrogen atom is in tl0k:ms/: qujbhe $6s$ 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 .icu9bs,2rp2n b*vkilithium using the Bohr theory. [Hint:v2p2isbiu*, 9kcr n.b 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 for a filled subshell6x e s *lii4v3 o*4b3(s qcrucux0b8rr.

  For each of the following atomic transitionaqt0y 2/ l /sf,pstq3ms, state whether the transition is allowed or forbidden, and if forbidden, what rule is bp2s/0f mqs t,3lyaq/ teing 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 i -y.d7vxqwt/mwglg5 :n 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 strp/irn ahg((7 mbye (3uiking the face of a a(pubr(m37(en y/ih g$33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelw 2qqjef5h08(e;otlb-enxj0 rrbx0+ength bremsstrahlung X-rays emitted from an X-ray tube have rwb0h058jb 0-ojrqf + xeq lx;e(nte2$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelengg w3x98t(x w8;c6dsnhvuu r+lth $\lambda_0$ 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 wavd.y x 96 r5alahk n9ag/4vt3ojelength emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for an 1 fucyl5ytg 22/lmu8m$n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength for av4z6y1/k bkil, vfdn1nn1om 0n $n=3$ 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.b zl5yg k */yw-srh,k is bombarded with electrons. The wavelr, y h*-kzbky 5ls.gw/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 detached retina33 fuu2wvmlo1geo 3w ;/1 tnaas 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 l(mr3 a 0e*xcawab 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 azgo io6+kby,,umn pv0x;9 w-c8pu-ds laser beam due to diffraction if the beam emerges through pw 8ugkm -,6u-y0ns bcv;po9dz+ix ,oa $3.0$-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 laser?/,c txnq4(- s( hdutun$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncertainty for the el,8xuxz+vb20s c3ycp,/ yvp c jectron 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,y zvc+xp p ccvyjs/bu,x038 2 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 posd7)yggjip. q8tn.t6twz ; hg3sible 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 el+w;amip 3ccoo5mqs.)a.ud (aectron orbit, estimate the average distanc3.i)pcaamoqod (mwac;5.+u s e 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 operates at7s52fs/up ath $95 \, \text{kV}$ 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 outermow219ds2p ep lgq eh*b.st 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 sn96 nozft/e4g )k 0c8 rw8x+ ytmqrz;chow that the Moseley plot(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 different states for asj0jx x8 g,/ s(ayjdz5 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 numberaixf+6gg- kgw -3ezp 6 of different electron states possible for a given value of g- ia 3zpk6gefxw6-g+$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with ener 2 -q)dc2x+ zyyat6xntfct ;.jgy 45 kV is shot through two narrow slits in a barrier. The slits are att+ ; jcqn 2y-txx6 2y.)zdfac 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 Bohr model and b :;3imqz p5nopy quantum mechap;qp zn3:m o5inics. 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 wiuo,a/jv p n5)dth 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 f0xhi qntc3ms9u ;)c dohq7c q76iu,4488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. Estimate the lifetime of the excitm9x)7utu c60i 4sqd;ic3n, ofcq qhh7ed state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated)of dv u44 u/ihemg*y2 from rest across 550 V. They are then directed at two slits 0.70 mm apart. How far apart will the interference peaks be 2ud g oeufv*)h44im/yon a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, are accelerated acm rv j6ns*q8r7juzjf4t:m v;8 ross the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, f68 jr; vnv jmq*zsr mju48tf:7ind the ratio of the uncertainty in their momentum.

  If the principal quantum number n were limited to the range frow)*x-gzy*y*b m cv hr*m 1 to 6, how many elementv*g*c x mw- **)ryhyzbs would we find in nature?   

  If your de Broglie wavelength we 4yp4sj 9fmg u c 3lw;1o;ms+e9ag8ceqre 0.50 m, how fast would you be moving if your m3o 8ccps1ua9;l m44 sge;+yfgmj9eqwass 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 q, hor gr)em)a:/trb3 an unknown element shows a series of lines with one out of every four matching a line from the Lyman series of hydrogen. Assuming thambo3r/)r teh, :gq a)rt 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 cert9dnd ak26r xv;t01cs/td7 csu ain metal wx9u v 2 dstd0a1cn;c td7r/k6shen it 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 sprj+cvmx.act d ,n76v3-qd ) zbgead of a 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.]