Compare a matter wavh: o/s4v,sfouxu 4ta.e $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory 5mlkg .of ccv5hgc.)4of the atom is not compatible with quantum mechanics, p5.o c). mkg5c ghvc4lfarticularly the uncertainty principle.

Explain why it is that the more massive 0qzhz5 f)da e(an object is, the easier it becomes to predict its future position.z e(dq h)f05az

In view of the uncertainty principle, why does a baseball seem to have a welavg 1to+zf fo3osa/u ,yfs)e(02k4 jz l-defined position and speeas g3fka) ( 0jutfeoz42 +s,z1fvoo/yd whereas an electron does not?

  Would it ever be possible to balance a vev)r.-9 sf is3g xupl5iry sharp needle precisely on its point? rl.xf-s3isv 9piu)g5 Explain.

  A cold thermometer is placed 2 q f.)rm8fucml91 dqyin a hot bowl of soup. Will the temperature reading of the thermometer be the same as the temperature of the hot soup l. c1rm2ydqm9uqf)8f before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well you can d 4ai1f1(7xvjfl9l zv make any single measurement of pos71izjxl9dlv (f41f avition?

If you knew the position of an object precisely, with 1 7lpvw,jp 9azdof t)(no uncertainty, how well would youj9 lza w(dt p,)7v1fop know its momentum?

  When you check the pressure in a tk;ky5 o2,lf)da ii(kb g/(d itire, doesn't some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relation tl g/o) dtkk(kd, a;i5bif2i(y o the uncertainty principle?

  It has been said that s(y3, lx w/c.dw;usf s;fi7xuthe ground-state energy in the hydrogen atom can be precisely known but sfx/l;. 3i;7usu, dyx ( fcwwsthe excited states have some uncertainty in their values (an "energy width"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydrogen atzu9zwm(l),q ws9kg s7om, the Bohr model or the quantum-mechanical model, predicts that the electron spends more time near the nucg) q9smksuz7w( 9zwl,leus?

The size of atoms varies by only a factor of three or so, from largest to small)mg cxrgr73 -zest, yet the numcxg z)-r7 gr3mber of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium a*i ck kb9zn(30mr2j5pq.ba cptoms both radiate light as they jump down to th9pp*m(bkr cijc2ak3n0 .5zq be $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if q ld5 f6q4;m p7;firs2 q.izgymt61dc there were no electron spin but otherwise quantum mechanics were valid? Consider the f m mp g frslqd2y67f cidzq;i;.4t156qirst 20 elements or so.

  Which of the following electron configurations are not allowe5w;rka x) z*uu ce60i2copm* td:
(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 (carefu87t 1nkpkdzsvl b254cl scrutiny across the periodic table on the inside back cover will provi14 8ct2slk nk5z 7bvpdde useful hints).

In what column of the periodic table woh)/rn7bj tfp +1lak j(uld you expect to find the atom with each of t+bf1 r ltak7p(nj/hj) he 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 iodine exhibit si kousu;csf)+a1 5(boz u)a 4homilar properties?

Explain why potassium and sodium exhibit similar prohv./ aq pbt 9ceik16(qhw(u4 qperties.

The ionization energy for wo5x z)sn px5 tp:u.f*p k:k4rneon $(Z=10)$ 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 for f cdgs7n6r1 ncan/d72fj w33b light? 3n/ajc6312 7fcgbdf7swnd rn

Why do we not expect perfectia7/s p)zj)y(q id sd f(9 6vxw-vqu;o agreement between measured values of X-ray line wavelengths and those calculated using B(jsd)()xszyqof -d ;vi97u6 wva pi/qohr theory?

How would you figure out which lines in an X-ray spectrum corresz, tkwh-*i;8dcla,o0 7y9,dr gg ic awpond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron tra /v7mmdu6cm 0tnsitions deep within an atom to produce shorter wavelengt0 /6cutvmm dm7hs than transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from opr*cd39o t cn2rdinary light? How is it the same?

Explain how a 0.0005-W laser beam, photographed at a dista n(cp2fat st-2+d1jzp.2o/ tklsjbx -nce, can seem much stronger than a 1000-W st1 pbzxt jfs+plda-ot.2n j s2-k/2ct(reet lamp at the same distance.

  Does the intensity of lighuv;e:v39r z uho u4)kbt from a laser fall off as the inverse square of the dis o)b3euz 9hkvr vu:u4;tance? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each h6xl:v;sk(a:/53 of2mn)cn w dkpqkwcaving 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 a4*+r l2yi95stom wnqlr4an 3jc1b xg, 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 and4(* fvd.wwk m 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+ 03( z d8nls-(yc5a cuj)wmyxxmsh9 u an 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 uncertaitru*g8 n:q8m cnty 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 possible energy of a neutron contained in a typicalta3uua uz)uv *5wg5 8r nucleus of ra )tua3g5w5*vu uzr8uadius $1.0 \times 10^{-15} \, \text{m}$. [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 if an el6tt.mt j s3+dcectron were present in the nuctt.3j6mcs+t d leus $(r \approx 10^{-15} \, \text{m})$, 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 j njdi bwoi88 *, )pvk6xg)og ogh53m;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 be in t q95z- gp.xoa /-ulcpphe $n=6, l=3$ subshell?    elections

How many different stat/ wt1;8/2(fl btfpace5 t v uss-2gmcmes are possible for an electron whose principal quantum number 25;cf1a gp2/ b tw-tuf(8smlc ms vt/eis $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the grouki o4 3p 7qxias;;tvy*nd state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers fofk:s) oajlpy*5l;x/ sll e0 x*r each electron in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen atom ha4*g o.j )rqsnbs $l=4$. 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 momez 1,lhpw)( yrtp; r1p(iyxqr0ntum 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 he)r lh;q s8xlf+5yi 2nas $m_l=-3$, 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 elect/mri 9iyuqh )-gx e 0dh.i9fh.t+6jbxrons in a "g" subshell.    electrons

What is the full electronw,y0 ix)zyn*7yeu 1mj 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 configurate;yfsj b t5i/2ion for (a) selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the periodic table inside the back ei fs2/5btj;ycover.]

  A hydrogen atom is int, l 8le7e fzd.:d1y*a/hexlc 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 lithium w 4+p6ip/v e0rt nz;)ibbsti+ using the Bohr theory. [Hpb+/iw;b) pntr zi6 0+4tvsei 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 angular momentum is zero fvl;9 w/ 2+k: ikvimupior a filled subshell.

  For each of the following atomic transitions, state whether ck7ib75rmb hc cy/ *qy39u7oj the transition is allowed or forbidden, and if forbidden, what rule is being5r hyqcj iyb 7k*/773ub 9occm 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 a* 6xuw h 7gq4sef-.sdo $6d$ 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 eesy :1u:k3k* om8spmelectrons striking the face o:ssueok3*eky 8 1pm m:f a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlubhwlm +)o 7gmtj(l/9 qng X-rays emitted from an X-ray tube have7g)qj9hllm wobt/+m( $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wave3e du(9,ujlgpy5 u8d blength $\lambda_0$ 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( )ge*;sqqonz when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength ft9dwy 4) hhk5g8f6jo vor an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelengthc- n,0+tlvgt56j 1 xdx/ivph e 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 mr:m59 x ql q(z5l9.sugcabm*k aterial is bombarded with electrons. The wavelength ou kx c.gz9al5ms q qr*l(mb9:5f 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 weldoe 8kwug ;hr7i w50p;d detached 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 lm wu+ryt 2+z*uab 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 due to diffraction if the beame c-jv7n 5owhms,ar, l d).k3d emerge,n)7ced w.aos,m l3- hj 5rdkvs 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 wavelengbwljwh fm :aml9p8*10th of the He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncergwchs:eb 3r .u 0 b2 x4*.q7nx9pqcnpbtainty for the electron in the ground state of the hydrogen atom. [Hint: Determine the momentum using the cqgcn0rse27b.px9qp w*.4 :nb3hx ub 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 possibglx go 9s**qx gtzlk8 5cy5z/ .z mi+/w*ja3xfle 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 the g)gzrlc x ))x2average distar)zl)xx gc) 2gnce 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 operats/36 2 pefhb9gawg+ ynes 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) enerbxebv,us pbt)3-o v7 )gy of the outermost 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) can be cziab +n6z.y/ 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 dif4u0nqs+i(y ti* ih.9 pfg2qo(syu8tp ferent 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 possag2hem z k0b:gv0 e3+dible for a given value of 23 +: h00ggadmvzk ebe$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through hz1; 3mpwrq-hem7swt3pc/ + ctwo narrow slits in a barrier. The slits a 3mm -1p+7t /rze;chpwq3hs cwre 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 given both 6rslg5x.:kgy 0z :zp7isf/5igmq k u4by the Bohr model and by quantumy 57.g5l4zq0 ::i /igmkuz6xs sgkfrp mechanics. 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 du fg(cs(ja) 0speed 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 cenen5vm/pp)*x 9l, g 22 xxxsq/5wm riwek5,ylvtered at 488 nm. Careful measurements show the line ie wxqgwse59,iyx ) p5kv2xnlvl/*x m5m,p2/ rs 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 Vgw; f3vwgz qvmo 3ptws2: j:q,l8b (,k. They are then directed at two slits 0.70 mm apart. How far apart will the interference peaks be on a screen 28 m awayvj2t,(wwpv:mk:3zsq , ; fw3 oqblg8g? $\Delta y$ =    nm

An electron and a proton, eazyg)an5;w 20qaj+ v alch initially at rest, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavel;q+0l an z5 2a)gawyjvength, find the ratio of the uncertainty in their momentum.

  If the principal quantumbd. 1s ,uruf7o4g q8r/o;e csm0a qh(a number n were limited to the range from 1 to 6, how many elements would we find in0s qqsor;7/1 u ,umbh8.erdaf ( gao4c nature?   

  If your de Broglie wavelength were lthzr r; 5p:uy(vxyk /d4bn-( 4wrs+c0.50 m, how fast would you be moving if your mass is 75.0 - rxk by(s4wt5pcy lv4/r:hrn( d+z;ukg? $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 s va a0kv( znwcsyj1dv-ehu*yci,./.-hows a series of lines with one out of every four mava-, uvyi hscj.nk -z w1a/(0.* edcyvtching a line from the Lyman series 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 em+gn . eh;tub)witted from the surface of a certain metal when it is bombarded with high energy radiation. If this photon wavelength corresponds b +;)u.gwenth to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive s9u5c) 6kbt)kmy-i *x/d ajduapread 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.]