Compare a matter wave 2lb)e8 cv8ilf qrk,6u $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theoryxg(la8)grof+ /:ai sei e+, fj of the atom is not compatible with quantum mechanics, particula:ga ( / olxes+fe+ r,)ig8faijrly the uncertainty principle.

Explain why it is that the more massive an object is, the euf ; vuedjcuyp. 3*-q7 ;atx87h9myehnm0wd 0asier it becomes to predict its future pospd9 yceu u0fm7n8 qv;x3hta7*0w-eu.j ym;hdition.

In view of the uncertainty principle, why does a basb7l2q.z ns x p26 *afnrie9w(.la(tre eball seem to have a well-defined position and speed whers9bqa(n 2nl*7rt 2rw (pixlza6 e.f.eeas an electron does not?

  Would it ever be possible to balance a very sharp needlex4 b(0zd6;1 qafroz 6g)y mytb precisely on its point? Expl1) qm0ygtz;z66 a(o xfb 4rydbain.

  A cold thermometer is 7 dkq;m8t+p l t.-0,b hxrbkihplaced in a hot bowl of soup. Will the temperature reading of the thermometer be the same as the temperature of the hop+tmx bt,7bdkl . i-;8hhkq0rt soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well you can make any single q38cxmtnq ohy9a9:s f q1(2hrmea r9fh9 yh3 x8q(os:act1qm nq2surement of position?

If you knew the posiz ,x +nk4ho(bi(5f4jz hni6nu1fi6gdtion of an object precisely, with no uncertainty, how well would you,6 4n(6hhog i 4dzf5iu1fbijxkn+ zn ( know its momentum?

  When you check the pressure in a tidl1ho*of+s c8(v rc y0re, doesn't some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relation t lfo0rh 8c o*c1dsvy(+o the uncertainty principle?

  It has been said that the ground-state energy in the h(h7f0ksp( ktr ydrogen atom can be precisely known but the excited states have some uncertainty in their valu 70spkf(rk ht(es (an "energy width"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hx0akiig3o,2)n79kh dh ocz (cs s/av. ydrogen atom, the Bohr model or the quantum-mechanical model, predicts that the electron spends more time near the nuclzc v( a .7hag93 hkd,oo0s)icinsxk2/eus?

The size of atoms varies by o5ue upr) 0 +c( w7ei8+r abom95zymaoynly a factor of three or so, from largest to smallest, yet the number of electrons varies from one to over 100. Explaiiuo+pz)e(0e7 uym8wc o rbr+m 559yaan.

Excited hydrogen and excited hep y r7f:;o3sanlium atoms both radiate light as they jump down to ta;:rs7o pf3ny he $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron f1qb* txe2 gjcdigg-t03j(erv 129x fspin but otherwise quantum mechanics were valid? Consider the first 20 elements orrejeb9v *j01fg(cd3x-i1gtxfg 2 t2q so.

  Which of the following electron configurations are not allowedz9:0 dg, wym3ryt(rqv:
(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 (cnd8*ao4 ybhz t1+eittyc 9h:4areful scrutiny across the periodic tb9 otzac*t 1:h 4h4ye8 t+yidnable on the inside back cover will provide useful hints).

In what column of the periodic table would you expect to find the atom w3zr 8*j43zb25x: hiu wkjjhdwith each of the following configu*jhhj4 5j:2i33 dwzk uzx8brwrations:
(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 eqczuyhk 7 s pa://q75exhibit similar properties?

Explain why potassium and31aawpb;:qk 3j +aoi n sodium exhibit similar properties.

The ionization energy for pc g( 5* afo;,prbh6ucneon $(Z=10)$ is 21.6 eV, and that for sodium $(Z=11)$ is 5.1 eV. Explain the large difference.

Why does the cutoff wavelundqjq79z9 u6ength in (Fig. Below) imply a photon nature for light? q96jd7uu 9 znq

Why do we not expect perfect agreement between measured values of X-5o4 kvhv kylt;mg2; (8g k:cllray line wavelengths l ol:2v5kh; y;k klvgc m8g(t4and those calculated using Bohr theory?

How would you figure out which linesn5 ri:lx11ezof83t wv 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 produce( i(jun4tpdj5 shorter wavelengths than transitions by outer e54t dnj( ujp(ilectrons?

Compare spontaneous emission to stimulated emission.

How does laser light diffe ,hxs8t -e qsa.gi 0;w50gnlcsr from ordinary light? How is it the same?

Explain how a 0.0005-W laser beam, photographed at a distanv.w9z pf eg7x/ce, can seem much stronger than a 1000-W street lamp at the same distance..ez vw 9/gxp7f

  Does the intensity of light from a laser fall off as the invers)6 0/z,s)i tkq j1)bnsqtwrkve square of the dis t s6)wqnrs tb/i,vkq1)zk0)j tance? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kineb5 s*vjjs6 v1 vp+0thttic 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 travelingba m+c ag4f*px2k:jh/1c a 5ya with 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 a5 twjl,6 te:4e( wwjicn 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 atom :l3bf-nd a 0 sh5 62w+ubma8 ahj 2splzj*iar/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 uncertainqadgry,r7 2ha jo ),y;ty 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 o sx 9zsmw,/wl4ccq,7possible energy of a neutron contained in a typical nucleus of ,9 sw4c7cos /x,zq lmwradius $1.0 \times 10^{-15} \, \text{m}$. [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 prnh+y* l(5hk ous.ti4;su 6njdinciple to show that if an electron were present in the nucl.th y 5u*u oij 4nhd;l(kns6s+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 of a sd+;8 )ttgsxzc 4al2k$3.00$-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 s qq;nm9oy2yh5fx ; -x$n=6, l=3$ subshell?    elections

How many different states are possible for an electron whose principal quanx o,bf7h0 j* )vx.f(s o(yvrsdtum nyfb 0ov).s,od((f sx vjr7*x humber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the ground state of7y+ 5lfth +a;kf+zpc3 :q ljn3emk,kv
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground state o7nbf 0;wjpckw j(s0 3rf nitrogen $(Z=7)$.

  Suppose a certain hydro mc oufd*g ,:o7oy+.s5 egqp./i7brojgen 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 momentum pm(jvq q nlmkd j.+f2,i 8az46of 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 1yd: ,(.q x6rzuazos/qccy0 u$m_l=-3$, 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 elesf:2gpqxcb r3s:(0 frctrons in a "g" subshell.    electrons

What is the full electron configuration in the ground state for evkb3m b6b,q7bsw: vi1 lements 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) se 4nu54noqw;;ga9uu6qz i b,rolenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see;6w4zu i oqb, 4;nnag9uoqu r5 the periodic table inside the back cover.]

  A hydrogen atom is in t;*ka, -dzfv 8i saqew9he $6s$ 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 lithium using thp7l) p2ichd- )sd85ihl xeea:yg ph9 4e Bohr theory. [H4p h sghd:hc9)ie-ix8ae2p5ll)7p yd int: 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 an jwc89 z3m1gfigular momentum is zero for a filled subshell.

  For each of the following atomic transitions, state whether the transl*bb/ f2sllujvi2 1:dition is allowed or forbidjvu l/1sdifb2b*l l2:den, 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 in nxl 5qccefi3er9 vjvnr/b c07 40n45j 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-wavelengez) mqdl80lcxn+zaay* e ( /6jth X-rays emitted by electrons striking the face of al e d zelxmz(y+ *n8)a60/acqj $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-(qnd p/ hxg zc+2dn2,drays emitted from an X-ray tube havenn2xg2z/d( dhq,c p d+ $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff waveleng rakdueqh;1lo f 4arsm1xc cs:2cdtn.1 o;044th $\lambda_0$ 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 wa 7bf5an.v x+l1 9igpw arpacv1 +;qvx.velength emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for a93;yu41 pvr1li2jdpncquh4xuv )ot + n $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to e.gie17 h/p( a+,zsqvkx (ydzp stimate 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 unknown material is bombarded with electrons. Thejx dyeohpif+3 /b8jy bt+dt+ 0(9xep7 wavelength o be380i(dt 9jdy/7t xe+ ojppxhy+b+ff 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 retinvpsj1/1a;lri ;ro c n:as 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 i7(4 vkwik4g ja0k/2w kwtlg i;n a physics 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 beam 3j:iy:bb 5uluh zpa08due to diffraction if the beam emerges through a ub 5lh:j0abz:3i8 uyp$3.0$-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 u xs/nojn,kfefv1/n,(,5 j rb of the He-Ne laser?$\lambda $ =    nm

Use the uncertainty pri/ - +lvxvfy5ennciple to estimate 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 this result compare to x 5en/vfy+- vlthe 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 anc2g0ho w71 y2)a t ck3tgvj9 t;f z*ww)nc9kufd smallest possible 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 zq6nj hv+ktds +y8e8, the radius of an electron orbit, estimate the average distance t,n6 +vkyehdzq 8+8sjfrom 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 at nrbp 2fhzss 5))i ynqn4h(1i7 $95 \, \text{kV}$ 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 outehl .j*qu v l73ldk((eurmost 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 shhjc0)memuhchut9 .:*x j m+3 how 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 cm)in9mgf0) zdifferent 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 possibl;-xoi)u b3k1 nmg +bhpe for a given value of +kubh)n-po i;3gxm 1b$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy ipjh1 p(7q qtigb3y:)45 kV is shot through two narrow slits in a barrier. The slits are g: )7 q qiyhbp(1i3tjpa 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: vcty0t)*z zfppo96i Bohr model and by quantum mechanics9fip*y vz)t 6otcz:0p . 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 spee o,a6x +6en)yqhbk bni1y5y0jd 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. Carej;mk.zo keai5n,w*.6uc ai2k ful measurements show the line is *mekakuc2 ko ;6,. 5a.wjzn iireally 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. edqh8 9)65ynpaqc c/ bThey are then directed at two slits 0.70 mm apart. How far apart will the interference peaks be on a screen 28 mpy8b hccnde9a q /)56q away? $\Delta y$ =    nm

An electron and a proton, each initially at rest+0 i o:tmg,qet, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the rat og mtq:,i+0teio of the uncertainty in their momentum.

  If the principal quantum number n were limited to the range f+7uy -+:ym5.jd7n eu aslxwlbrom 1 to 6, how many elements would we find in natsual b7nw.+:xyu7m+y j5-el dure?   

  If your de Broglie wavelength were 0.50 m, how fast would you ccug8. 8kfp.abe moving if your masu.8pagk f c8c.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 element shows a series of lie1 gvn(udi5- ones with one out of every four matching a line from the Lyman series of hydrogen. Ass(o5 -vnd1g ieuuming 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 a b3kzhw2.gy d1 o)pbz-re emitted from the surface of a certain metal when it is bomb)31z phgzdb 2w.-koybarded 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 spre-y2h+-mrbhk*p+ qf m saf)+ze ad 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.]