Compare a matter wave (- t(0 sq(i*hqg -gp(pqqfd xc$\Psi$ 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 quahume: 7d c(o)fntum mechanics, particularly the uncert fd7o)u(ch m:eainty principle.

Explain why it is that the more massive an objevs16 vaba0y02qwz 5tjct is, the easier it becomes to predict its future pbt vy0wz2v0asq5j 16 aosition.

In view of the uncertainty principle, why does a baseball see;o+dse;6 eux wm to have a well-defined position and speed whereas+o;xuwee; 6 ds an electron does not?

  Would it ever be possible to balance a very sharp needle precisely on it)vp;7 6 +ljj-qt2h. klg wp :bkiyup4ws point?kpk+ 7) hq-2lbpi:l4.wv6gjy; ujwtp Explain.

  A cold thermometer i u8lus,n2jq2;khxh k:ed3e 2ms placed in a hot bowl of soup. Will the temperature reading of the thermometer be the same as the temperature of thjxdsq,ke22u ;h k8:2n3 u elhme hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well you can make any single6b:g. 9nszkfs measurement of posi:9s6.zbk fs ngtion?

If you knew the position of an object precisely, with no uncertainty, hbvq usfs +hoi4tf ,:;/8/pv zdow well would/s8pfvstv, 4dzhq fo i+bu; :/ you know its momentum?

  When you check the pressure in a tire, doesn't some air inevitably oty e*a(2aqw2escape? Is it possible to avoid this escape of air altogethe wo2ta( ayeq*2r? What is the relation to the uncertainty principle?

  It has been said that the grj lt)r h6z0cs6k0qyv(ound-state energy in the hydrogen atom can be precisely known but the excited states have some uncertainty in their values (an "energy width"). Is this consistent with the uncertainty principle in its energy form? Expslczkr60vyj6 t0() hqlain.

Which model of the hydrogen atom, the Bohr model orq 2or8yzkgaaam4c 49 ) the quantum-mechanical model, predicts that the electron spends more time near the nucleus?ocmayzagr 2q a4)k894

The size of atoms varies by only a factor of three or5+x59 50bpcjnwwrkfv so, from largest to smallest, yet t95n w5kj+r0cvpbf xw5he number of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as they :g sqfy 5.k,fw t+.pgoe i(n5jmdu/ h6jump down to t (peysk:o jut+d.m.gn/wf 6qh g 55i,fhe $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spin bus-0;oqkk+gi4 w m*gw4 mfdl, ht otherwise quantum mechanics were vali ;wmsf44d kgm,h*q0l +koigw-d? Consider the first 20 elements or so.

  Which of the following electron configurations are nb+ng4/fnf v ucvq.wzjx0s2- ug;1wf1ot 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 (careful s-q )w,n3- 7ggkhz- up: m2f srpss;1njdh mi:scrutiny across the periodic table on the inside back cover will provide useful hqu s 2mwz;1ss73:gmsnp)rnk i h--hd-f:p j ,gints).

In what column of the periodic table would y)ad .knco/n+b01, k 7kuvqyrhspq i/8 ou expect to find the atom with each of the 0nkv ).ckp q ,/1 oyis/kdq7+ar 8bhnufollowing 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 :v f.pw5rjwgr pk riqx30d1: +,gakip33;mv uiodine exhibit similar properties?

Explain why potassium and sodium exhibit similar pt*mz;5 l,zg do8s;q anroperties.

The ionization energy fp i56 g68aidxc xyb6+hor 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 (-azm+qd2+ o-vxw 7 aesFig. Below) imply a photon nature for light? vzsx dwa+q+2-o ame -7

Why do we not expect perfect agreement bet:+7tt jydo9 nbween measured values of X-ray line wavelengths and those ty7bd o+nt:j9calculated using Bohr theory?

How would you figure out which lines in an X-ray spectrum correspond to w )2;syy+xexj $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an n,1 oeuj.g.ac0whbg9atom to produce shorter wavelengths than tn g9 egbwhuo0ca. .,j1ransitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary lig3;vqmuv+ n)br2q.oi)gyr9 nnic y/faa m-7 :xht? How is it the same?

Explain how a 0.0005-W laser beam, photographed at aoldm ju r(l46up(hh9 0 distance, can seem much stronger than a 1000-W street lamp at the sapuu(hlm j o96(0rhd 4lme distance.

  Does the intensity of-)q yv2 rkwa(y bs,epvl(b6r ; light from a laser fall off as the inverse square of the distance? Explai pq;y(6y,eb vk(br as r-v2wl)n. ----待选择----yesno 

  The neutrons in a parallel beam, each having k(f;b mxsfp8 j9inetic 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 wite20 o7mv6jy1d-c:ncf0fa)kt 7qxqa jh 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 deoz97w- y2nzto 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 ofuq(lp 0 5difx97 r(tx0h5bggd 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 alohr /t5nblsf48)a,dbu 68 nz 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 enez3cuxtr+ 1+q9s/ le;sx +hl rrt 4zne2rgy of a neutron contained in a typical nucleus t/r el291ne rz rsqh3+cxut4x lz+s;+of 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 :xeaeu6 zw2x m2r-,( mlx9c7bf5 dqb fprinciple to show that if an electron were present in the nuclerc6(wqf:x2,x ublfm e-b2amxdz5 97e us $(r \approx 10^{-15} \, \text{m})$, 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 positnf4na3dor- ,s iy hl:9ion 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 1 9jm ju9)e9 zwqxv1jbs/jy: cthe $n=6, l=3$ subshell?    elections

How many different states are possible fordm)s9d lcj 0o9 an electron whose principal quantum numbej 0d9osl9mc d)r is $n=4$? Write down the quantum numbers for each state.

List the quantum numb ukkc*io b1 yyw8j)9:2mr 2iizers for each electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in tg9f zdr4nr76s9p r d1phe ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen v:+p/z xu;v aq.y4 .jc0kntvzatom 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 of an electron i*f k,nklzhkvo v pl6i;(tldj (6m-0 7gn the $n=4, l=3$ state of hydrogen.
L =    $\times 10^{-34}\ \text{kg} \cdot \text{m}^2/\text{s}$

  If a hydrogen atom h sydu4 nj ue0cbxks)*(-2 k(qeas $m_l=-3$, 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 18icu6)l,36:w;qvo/yiujl3 v fbwk j v( electrons in a "g" subshell.    electrons

What is the full electron configuration uw 8t oudkr6:-zm4y:qin 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) seleniumu )s nmx9q+3.qorz1sg (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see thqgx ) +q19rnum 3szo.se periodic table inside the back cover.]

  A hydrogen atom is in thex .,yibtva 9-q $6s$ 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 Bo8 s.g vp11pmq*(gmcrmfpo d- 7j4b bsxr 7c)v/hr theo m7 p8xjg cp o(74-*p1bms.dsrv) b1q/rgv mfcry. [Hint: 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 filledtk9nnt4/bf;4 tuv7whq :ce7j subshell.

  For each of the following atomic transitions, state whether the-vvw;qhh3q0v(m3 k rc transition is allowed or forbidden, and if forq v3 wm;-qv(3ckhrh0vbidden, 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 2 v50b y-npx55ogizlt 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 electrons striking s 3 b at;8.zzq-)bccijthe face oa bqctbjz;i 38-s) zc.f a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlu,5vq7z*ui f6cn:im,dbf (u jeng X-rays emitted from an X-ray tube have u ucvib6 *:zeif 7jdmq,fn,5( $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelengv;g-a ,fn wy nx4kyx3x-))z agth $\lambda_0$ 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 whe da e3hwhd78j3lw/ao3n a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for af )9l yof,)gve:yyw i,n $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wv3a ohr64 -uhxm,nxs7avelength 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 bombarde2 )nhi7a4 ttugd with electrons. The wavelengu4 2)giahtn t7th 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 retinaso;uwul)qh)dk41i + byrf y .b. 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 lab might hav g h3xzr3qb6nd+w5x7m e 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 angularag;--.gw nom2ch: tt j spread of a laser beam due to diffraction if the beam emerges -tg:ntcwhg2.;m aj o -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 H6l(0p8crff s4mbv r)de-Ne laser?$\lambda $ =    nm

Use the uncertainty ldwtx cmyplcg8j b:y- q(ne+d4e3;.xltq4;, principle to estimate the position uncertainty for the electron in the ground state of the hydrogen atom.4q;+gw( dxd3jc. - l4btpe nxl,;cy8yt qle:m [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 sw; d h);p6 uz /bkc5v+ao0pjvtmallest 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 the radius of an electron orbit, z)w re(g47p hs1n(jhvestimate the average distance from the nucleus for an electron in the innej w4 1(nrze7g (p)hsvhrmost $(n=1)$ 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 arqrn,xm :()+n:*xuey /b jhjq61* iqcb0wkqrt $95 \, \text{kV}$ 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 (bindm2z5q s;mi iqcy ,f7:sing) energy 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 tha;zilp/ sj57 ura(t 6wmd 7zl8os)h.dpt 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 dngrrfxv ,)zohqg2(i w.8;0ga 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 possible for a givc-o p2zz9+ m8a.ry+icttjri2 en value of tr2+9zco-z+.8ic2a prjmyit $n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narrow slits y k7niw-o/ vzoxb s/m 1p-(:svyu:+ho0n vj)oin a barrier. The slits o:xh nvsvy pj1 )osb-ow0nu7z+ k m/:i/-(oyvare 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 pfqv 1(5) dy*oftdh npd+dh .*in the hydrogen atom is given both by the Bohr model and by quantum mechanics. Compare the resul*nvphf1.d *dd+q )y5f(hod t pts for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling with 4h8pg58vltq n5m 6cg ma 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 488 nm. Ca )4tyw 8k1wjhylr l0ku/9z2nde4 )pxsreful measurements show the line is really spread out between 487 and 489 nm. Estimate the lifetime of the excited state that produced this linex sz04dlyuw /ep) 128rn9 kyt4jlk)wh.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated from rest across jpg7ix d ho o/*0/f:z4pb+pu e550 V. They are then directed at two slits 0.70 mm apart. How far apart will the interference peaks be on a scree+ph70dx eo*4bzg uppf /ijo /:n 28 m away? $\Delta y$ =    nm

An electron and a proton, each initi, /yvqqbc f/*jally at rest, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find t*cqyb/qv/f ,j he ratio of the uncertainty in their momentum.

  If the principal quantum number n were limited to thet1kv5 j4 z4ful range from 1 to 6, how manyj41l f 54tvzku elements would we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast would you bf+c y4v+v(z bye moving if your mass is 75.0 kg?cy( 4 bv+fvy+z $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 jp9-1 n ys(ayllines with one out of every four matching a lisl91jyypna- ( ne 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 emitted from the surface of a ce 8zp;ju0jgfvn:k- 7g irtain metal when it is bombarded with high energy radiation. If this photon wavelength corresp:gj zvkf0;7pngu8 i-j onds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread6( (ypxf/x.db/ju sbt*vfkelz *ho28 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.]