Compare a matter wave cdxbs6,o:w y+ $\Psi$ 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 quanzraz2v r/ftlo ycl72ap6 (jc,;ey6:ctum mechanics, particularly the uncertaav:c lo ,;y 6zc7t2r6z y(a/p2f cejlrinty principle.

Explain why it is that the more massive an object is, the easiehs o+ tu8gjcn84r-l )or it becomes to predict its futcl8 uoj4ro hg 8)+-tsnure position.

In view of the uncertainty principle, why doeso:sv6+b.6w sa9hhsug* es *pj a baseball seem to have a well-defined position and spesvpa*. *o jsh6g+hbus6:9s weed whereas an electron does not?

  Would it ever be possible sp::f:v;wfm dn +o,s/ gyylt tj83r. wto balance a very sharp needle precisely on its point? Exl;f wyn: v :trg8pys3 .t dsj:w/mf,+oplain.

  A cold thermometer is plac/vfp07wx qdr- ed in a hot bowl of soup. Will the temperature reading of the thermometer be the same as the temperature of the hot soup before the measu-rvfq xdp /w70rement was made? Explain.

  Does the uncertainty principle set a limit to how well k/dpptvt-23o))q aechaiy 1 u0wqk*; you can make any single measurementq) ctkv1pwpy)dak0 eh*3- 2 iqtao/ ;u of position?

If you knew the position of an object precisely, with no unce5r zcr 0(hq3qony aq5s+i4sl;rtainty, how well would you know its ; qas4i 0l3qc +rhrn5(5 qsozymomentum?

  When you check the pressuri h nc8/g6uv gu:f-boht 96w1we in a tire, doesn't some air inevitably escape? Is it possible to avoid this escape of air altogether? What-:6vu hg8fo9wcu/ giw6b 1htn is the relation to the uncertainty principle?

  It has been said that the ground-state energ jb; azd;srf2)z:p8ly(.d kf) x2q8nh rvw-w iy in the hydrogen atom can be precisely known but the excitedj:ip xh;f 2f8swn- razy)k)wdl.;8r b2v (zqd 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 atom, the Bohr model or the quantum-mechapz9g mgf1 p ,u7rn4n:jnical model, predicts that the electron spends morp:4rn97 j1gzungf pm, e time near the nucleus?

The size of atoms varies by only a factor of three or so, from largest b iltve4m( wd19.4ocp4yzu)gto smallest, yet the number of electrons variep44.ctmevg 4 9lz) iowub (d1ys from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as they jump y:k1 t;ea.btv/hs-mp down t:a;s/pbtmht v -y.ek1 o the $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic ta q8g by(s9:scinxey0*ble look if there were no electron spin but otherwise quantum mechanics were valid? Consider the first 20 ele e0cy8sxni*yg :bq (s9ments or so.

  Which of the followingn.6w z2o f1j-e6vg.axcbc/h u electron 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 ura5x xu* geje4bxp 89m+lnium atom (careful scrutiny across themp95bu4 l xexe*g+xj8 periodic table on the inside back cover will provide useful hints).

In what column of the periodic table would you expect tn z 4yejh6 ;k0m h3al67s+bcwjo find the atom with each of the ble h 36 0a h4;z6wjynsjk+mc7following 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 2mvwp-h 6ybb) exhibit similar properties?

Explain why potassium and sodium exhibit simil h6 p6hwog 4w2s)f*balar properties.

The ionization energy for neonhgi ym8/ypv/z:7v ds 0, jtu9m $(Z=10)$ 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 fuxmadd 0+dt24or light? u024mxd a+ddt

Why do we not expect perfect agreement between measured values of X-ray line lr2 ;)hj i9z;m, sii.dzldei* wavelengths and those c9sih. ;ejmdiizr * l2zl),;id alculated using Bohr theory?

How would you figure out which lines in an X-ray spectrum correspond t41 h ow0d4qdbfo $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep with 2x8gdt 3;. -ypdxncb-oe*awwin an atom to produce shorter wavelengt2 -xoy*gn8 e;dd.3bxwacpwt -hs than transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How is it the x*5yqzmgsu2(;evzf19 /r u p8w m6tmpsame?

Explain how a 0.0005-W laser beam, photographed at a 8 8suj6uh,h 8vfi(knm distance, can seem much stronger than a 1000-W street l(jkvs 8h886nf, ih muuamp at the same distance.

  Does the intensity of light from a l8w l(x4i97 jl(fn z1mu6bphflaser fall off as the inverse square of the distance? Explain. m47jl1f6( lx nh ufl9wbz8pi( ----待选择----yesno 

  The neutrons in a parallel beam, each having kineti4;f:e dafw+scg,dbz 1l9cw m8c 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 a 95l;lr;m3dbb6ae 7l ko1bxlr 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 tojmqp rh:g(z 48 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 stat(e;i+ bp r5qkyp4sy+ce 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 mass of a mc*vnu+n jgs3 )uon $(m=105.7 \, \text{MeV/c}^2)$, 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 pt1ew0-hdbzil g 797 ua typical nucleus of i9tw 10hzl7e-bd7up gradius $1.0 \times 10^{-15} \, \text{m}$. [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 electsi/ fa 313reo (bysyd5ron were present in the nucl/a5fedy sryi3 b1s 3(oeus $(r \approx 10^{-15} \, \text{m})$, 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 o3;an5e x 5jvo*g9gtmzf 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 cw1 .1rq8dy82gp/lhfqrpwa.kan be in the $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whose principal gi:x9uiltes 5y*w*b 94b2 xpuquantum number iebl4i9w*:s5*p buu2 gx9 yitxs $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each s2exx0nz)v 8(vi uiqd;5w4mkbqjo26electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each e / 5fb4zwwhox;lectron in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen atom jm;8 phc3qeruu72 h m.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 magnitudliwt4wr )*eflw 3*7fve 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 hd ( wr97pz+cnfas $m_l=-3$, 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" sq9k 7a6r wguv3x:gm+rubshell.    electrons

What is the full electron configuration in the grpuslzxo eg 6eo/h 3- ajt)t)u7l3.fn:, gn z3jound 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) gol/1 wl)hs 6iynzd (Au), (c) radium (Ra)? [Hint: see the periodic table inside the back cover.]6ns1hyiwl/ ) z

  A hydrogen atom is in the*5td9g,zjao t $6s$ 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 the b:5v4hf-kq63 udf ae g5c-wc1y*o jt fBohr theory. [Hint: This electron h uc qdet-a1f5kyjf6 3f-bh*g45 vow:cas $n=2$ and "sees" a net charge of approximately $+1e$.] The measured value is $5.36 \, \text{eV}$.    eV

Show that the total angular momentum il. b.) kormj5:pd ,yhys zero for a filled subshell.

  For each of the following atomic trancq)m do x*f5 0(fmz:2 hhl.boksitions, state whether the transition is allowed or forbidden, ) :l0(.qoho 2hmx5 cdf*mbkzfand 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 a e6hp:r 70dg ca$6d$ 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 electr;ee mr sj kvh-ooq, 4p9,:q*daons striking the face oarj,hq*pd9em 4k:o qse;,- ovf a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted from an X-raydl9bx mu;i,1 /wy/r xt tube have 1//; wxl,urmd xyti9 b$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wampd6rs c8,u 1xvelength $\lambda_0$ 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 when a Ckdv sf cn/;7x0.j.j n9cbtf m4o $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for u 00p*dtlmw 4jan $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength f8hr96 ptncy-k ,e cztbg. +ze/or 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 vpgsht mdq w7.4+4s 3gelectrons. The wavelength of thet+.qwg4h4 g d3sv7s pm $K_\alpha$ 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 retinas puts:j+irrkvgy7a7fwyn8 c--avx/shab 6 wv2+ 2r 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 ) r.mb ewmt)h y)-mr8win 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 due to diffz 0ir ikjhlfh(8-t -h9raction if the beam emerges thro9 - k-fjrh z(0ihlt8hiugh 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-phou+ws-+n: xz,t5 pg Ne laser?$\lambda $ =    nm

Use the uncertainty principle to es i)g0 bsb2eg*w bx y5 :4sbd-m:vqojb1timate the position uncertainty for the electron in th qdb sj :: vybb4gs-bgioe 1x0wb)2m5*e 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 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 poss;q-b5/v cs 2 0habwsxiible 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 formulaxw7,+e vpg2mkwbv exo;e q8ny4/s 11 yih 6ju8 for the radius of an electron orbit, estimate the average d+be xei7emp8/486g1vjkyq n1o ;w x,hw2uy vs istance 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 fgy:tqerw -q3; yu,0 p 2l3etqat $95 \, \text{kV}$ 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 outermost electron in boron 4l;og+o ei+ws-c+-:qqwd kg l 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 written vjvy7 bn90u-b1+bp x n$\sqrt{\frac{1}{\lambda}} = a(Z - b)$, where $b \approx 1$, and evaluate $a$. a =    $\ \text{m}^{-\frac{1}{2}}$

(a) Show that the number of different states for a giv+izoo( in6r2l6qdd1 l en 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 statesks3,8w c8 *a3nzcs a-9skhpbw possible for a given value of c8s9k*s,z-wn b8caks 3aphw 3$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narro/5s:6 ,hrmo cvgk1sin w slits in a barrier. The slits are a distai:hk1/n vrsgc6 5o ms,nce $2.0\times10^{-6}\ \text{m}$ 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 at5(0bjh* dc85old ogqoom is given both by the Bohr model and by quantum mechanics. Compadob *ocj8o5g 0ldqh( 5re 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 +; tix a,ly nihn-ywjv4c3,3x$(22 \pm 0.22)\ \text{m/s}$. 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 a;d y9u-dqua( ld0f .xt bfa 7fc4buc h8v+a:/wt 488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. q8ut9xcw(d.a hfv4-/yu fc +a ufbdl0d7:;ba 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 dire/ d6ld:ow z; .h)tze1jge*sbscted at two slits 0.70 mm apar z: gj6ts ;ozd/shdl1ee)w.*bt. How far apart will the interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton,l 6k6de7 ux9t m;rd. 5qym gl9yk3qw3u each initially at rest, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, fqklr mu6.;69lx3d uk qey 5 t97g3wymdind the ratio of the uncertainty in their momentum.

  If the principal quantum number n were limited ty+0zbu;b wt5eo the range from 1 to 6, how many elements would wez;+e b5 w0buty find in nature?   

  If your de Broglie wavelength were 0.50 m, how falk /fg u g2:mo4p*y7hpst would you be moving if your m:4*ghyf/2g m7 lpupkoass 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 spectrm7 y,w(fkia 7wum of an unknown element shows a series 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 one electron, determine Z and thafiw,w 7k (m7ye element in question. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nmbef(*++ 9mo imiwy, tm nv4f-v are emitted from the surface of a certain metal when it is bombarded with high energy radiation.*+( ,m vwym ift b-4f+moenvi9 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 bea08 nx3 b 69wdptgkv6snm, $$\theta \approx \lambda/D$$ , 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.]