Compare a matter wav6sryt 2wsy28e dq 9)fbe $\Psi$ 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 with5h37b ncg;zm2 d3ovb b quantum mechanics, particularly b 3hcd7b3o5v 2nmgb;zthe uncertainty principle.

Explain why it is that / pg;jckbcha c*+,c.g5ctjv0the more massive an object is, the easier it becomes to predict itacv.5h cjc0;g*kb,jg pc/+c ts future position.

In view of the uncertainty principle, why does a baseball seem to have a welj:qrwvy.4 ov6-du4rp l-defined position and sp-4orp y64.rj:wuvqdv eed whereas an electron does not?

  Would it ever be possible to balance a very sharp ne6*,b kztm d0q *ap,iasedle precisely on its point? Explqts,a*z*ib60a k,mdpain.

  A cold thermometer is placeiaj03):6ke8x,m+ 6ovp9 /juk t lfwaz vq wt(ld 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 measurement was made? Exp tlv,6jwmkxvk)3 8 lp 0 a(/jua+fqw:zei9o6 tlain.

  Does the uncertainty principle set a limit yu d 7 x0rwguqd.6tfwsi22y(u 5n8 xl-to how well you can make any single measgl7 6x8wnwru52u.id-0yys (ud x2qt furement of position?

If you knew the position of an object preci m0jrr hl3lc9uaf+8 y+sely, with no uncertainty, how well wour+r+h8l afj c y30l9muld you know its momentum?

  When you check the pressure in a tire, doesn't some air inevitably escape* g( ekz70gbfk? Is it possible to avoid this escape of air agfg k ek0z(b*7ltogether? What is the relation to the uncertainty principle?

  It has been said that the ground-state energy in the hydrogen atom can baq2bjwik+*ay 9wb m/ *qu9ij)dqk -1v e precisely known but the eva9 jyiq 2iu-1 bw *bqkj/k+a q)mw9d*xcited 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,6/0y c)jmy cya the Bohr model or the quantum-mechanical model, predicts that the electron spends more time y0ymc)c6yj a /near the nucleus?

The size of atoms varies by only a factor of three or so, f4 df r lg4ylyv4e6p*+un bqq(x) vq).erom largest to smallest, yet the number of electrons varies from one to over gdq4yr yqv 4u4+e)bvl.e) *ln fp6(qx100. Explain.

Excited hydrogen and excited helium atoms both0ho bgyy u37p5 radiate light as they jump down to they o7g3pb huy50 $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no e38qjt7s wlupj7me3 ;qjrxl;7 lectron spin but otherwise qu qj;l7 rx7u q;jptsjem378wl3antum mechanics were valid? Consider the first 20 elements or so.

  Which of the following electron configuratir:15w . kobjcwons 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 f5,n1-acg 3xlj cnby5 uranium atom (careful scrutiny across the periodic tablfx1cj,-g5 c5n3ly bn ae on the inside back cover will provide useful hints).

In what column of the 9;;tgfgl/ib1w ;9zefqb sb5kperiodic table would you expect to find the atom with each of ;9;/ zgsg qf i;wke95b1ftbblthe 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 iodinw:duy5 abm/ y,e exhibit similar properties?

Explain why potassium and sodium exhibit similar propertie5;luwdn 4f-4 h lo hfd.wr8:oes.

The ionization energy f f5)r -y.l1;bmdscerkor 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 wu8sj vrx;t i/4avelength in (Fig. Below) imply a photon nature for light? tv 4 irjuxs/;8

Why do we not expect perfect agreement between measured values of Xua ge0dg m*4 0sr)mz2w-ray line wavelengths and those calculated using Bohr therdea4)z2g w0*sm0g um ory?

How would you figure out which lines in an X-ray spectrum correspond fk)w80mw1 ( ycx ;2k ).fdspfl oi;gddto $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep wqp5vmc ro6x 0l ad.2f+ithin an atom to produce shorter wavelen lqc0fp 5vam .2r+oxd6gths than transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from yc chu;5. *aoq kxq1+mordinary light? How is it the same?

Explain how a 0.0005-W la0 d b3fggp.y;a;(f suvser beam, photographed at a distance, can seem much stronger than a 1000-W street lamp at ag3v sudp(;0;yfb.g f the same distance.

  Does the intensity of lo0 p(sw.xlr-o lx3k r)ye mq6jg j5by7pwy27 (ight from a laser fall off as the inverse square of the distance? Ex eowyjy s)jkmb. 67rqxr53lo02(pl-(gpyw 7 xplain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kin c j3mpkf(tvc9.t23v9uynrv4j v .+uxetic 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 spe)8ja4n 0guni qed 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 measu6jjue1s ,oba- red 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 +u+x ;zwdo6 ;pxw h:nzon+ 6mcexcited 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 mass2+xg*amt;4j hjt,o er 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 neutroq+,s o5rwrdpd;/ pa0w;jmm1g n contained in a typical nucleus of radiuqwdgm;j5orpm+,a d /rw;1 0pss $1.0 \times 10^{-15} \, \text{m}$. [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 t2s5jb,,h6ik)u.ojp7fd : 7 ewjwxr pihat if an electron were present in the nucleusukp.iwiwjrfo7),27pxh,d b6 :5e j sj $(r \approx 10^{-15} \, \text{m})$, 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 thexfz,rhx2,m3;agw 8mfoc j. j0 position 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 wot ascl hx-*v9, 83wc z( czm;z-+lnwbe in the $n=6, l=3$ subshell?    elections

How many different states are possible for an eleq+i n8ye pyb(0ctron whose principal quantum numeqi8b( +y 0ypnber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the ground state qu;:e , a+ ab6o-aurgeof
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electr/tlbq x k2js27on in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hy.0rad,e ) z;wvkrh, ycdrogen 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 of an csk(fe2 v*u w9electron 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 hasa yir i tam8:7wm*3vz, $m_l=-3$, 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 "gou- izdz h815f" subshell.    electrons

What is the full electron co .kru;.sjzr5q ls 0atax2:/ tpnfiguration 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 f i(twgk y76m4aor (a) selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the periodic t76(gkatmwi y4able inside the back cover.]

  A hydrogen atom is in the qd e0d4/3 eshe$6s$ 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 usigd+l dqeg 5quwv(1 fu)n j7,7sng the Bohr theor+7 7u1f5uns(qgq)g ,j wl ddevy. [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 filled subshellf1bf(/k o 9caksz) i1s.

  For each of the following atomic cwtdkc +2 w12nqk)1xgtransitions, state whether the transition is allowed or forbidden, and if forbidden, what rule is bqw+w)kdcn ctx12g 21k eing 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 wadsj 9al3h k- 1 ncx5cz--kk6(uw/ spa $6d$ 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-wavelen penwa9gp hur xwit/r3 (t*--1gth X-rays emitted by electrons striking the face of a u- 1(r i wawe9- hnttrp*px/g3$33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted from an X-ray tube 3tbkep3)3iu d.-q9wphvb v,d have ib 3wp)hb.,qpevt93 d dk3-uv $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoffqest h46/yovf* iqt)+jv (l. l wavelength $\lambda_0$ 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 Co/a(so )k,vu2y/ vkkutlfm),a $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for an xw4 z:b7qe)8(e hvnk: ep:bry $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wave ) 1)qrmlwy35xnoab .qlength 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 bombardedtfnzfvz j0+p(vtm:ln rhlg;xu6. p+7/7 wv+ c with electrons. The wavelegnxr7.(jpzv;lluf c hf t +: +tp 7v06wn/zvm+ngth 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 retm/.q8 jr5gtjj p0nhu9-b n mk/inas 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 7ntbag, ;1j(+paguchmight 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 t.p6k/bqzfzzocl5 0+4ql- vp6r ,qu cthe beam emerg ,4f50.lc zpbtzq +cqu6kqpl6-orzv/es 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 He-Ne lase 18mqonv3yb0;b oa0wur?$\lambda $ =    nm

Use the uncertainty principle to estima f2slnqf6tpw 072(sodte 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 momentum2o ts62sp7nfd flw0 (q 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 a:b*33diyu9qq gqr p,lg ic:c+sl/j/t nd 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 the radius of an electron orbit, estimate the averag,6cin6p:d dqitw. cyc 0kmfhk.1 27xue distance km72q. i 6xfyi.dnc:6c1whu0 pc ,ktdfrom 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 operatesdt)krdbf 5; bvs qw6cas*/ )+c 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) energy of ,1 q/ el;jorhpr4 xfj3the 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 Mosel6qtm9fkz.s22tb d 7pzg91ie jey 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 s a9pd8c)l9 3inh/uzyt ae:d, qtates 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 di/k5gw8 gyvyw;/b v *;o2cgnmifferent electron states possible for a given value of ;kv5 nv8/gwwog y/bmc;2gy *i$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two n f; k jv,opdw50wsx3 safkzpp9.*:0 eharrow slits in a barrier. Te 0s kvzwj .kp95ah;pf 0:*xspod,3wfhe slits are 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 thmj-vwpsaza fx8 3n/1dt5 8j: ti+mcx*e hydrogen atom is given both by the Bohr model and by quantum j m8tp+cid*/xa1nfx853sm w jt:v- azmechanics. 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 wysm0 h8t p,h,lith 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 wfqkthyu nw 4n78c *1d-avelength centered at 488 nm. Careful measurements show the line is really spread out bet 4n* 8wnkh-uc 71fdtqyween 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 restu 8t ,wk:a,hjna6n8te across 550 V. They are then directed at two slitaan,6 ,8e8tkwj unht :s 0.70 mm apart. How far apart will the interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, are accelerated across thry. q*(pldcklh*e a 8+e same voltage. Assuming that the uncertainty in their position is g.8eqh y*lr lp+k*(c daiven by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum number n were limited to tfa))v un. jm3v0z;l/ rxruok-v5/owdwd39wf he range from 1 to 6, how many ele/uo3fdr- o 9w.0r;dvjww xm)nu z/)v3vklaf5ments would we find in nature?   

  If your de Broglie wavelength were 0.50 m,y* hgq7z1hnqb1d ;*ig how fast would you be moving if your mass ii*;dz7 1g*1g hqynbh qs 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 unkn- , dz op o*v*iare-i+bk9qc5pown 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 the element in question *9boakqdo-vr cpz +-i*p,5ie. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm are emitted from ro5 xx99+2 nmf dyap 7xmy mml1:s0b*nthe surface of a certain metal when it is bombarded with high energy radiation. Iy9nm: rp 0bxlm7n5y9 x fdomamx12 s+*f this photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread f26sgz dpn3t ;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.]