Compare a matter wavf09vmats og4+ ps y.l8e $\Psi$ 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 q.p900tffctjec* :fk1zc k +r vuantum mechanics, particularly the uncerttffzc9f0 p v:0tk*1.k c jcr+eainty principle.

Explain why it is that the more mass :3h1zpohw7 2xo es8zxive an object is, the easier it becomes to predict itsh :x2h poz sxzeo8731w future position.

In view of the uncertainty principle, why du9 3obp7vmqqvuk+1if49 nx0 hoes a baseball seem to have a well-defi0ukxuq qv+p1mvnf79o9 4bi3h ned position and speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle p-glkb tg b6)v:,-hrtv recisely on its point? Expla6bkhtl-r -bvgg v):t ,in.

  A cold thermometer is placed in a hot bowl of 6b jgc5djn+ ,5v59qudki a1wpsoup. Will the temperature reading of the thermometer be thedac v9i5qpjdgb1+ jk5u 6,5wn same as the temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well you can ma,v e/m7b w0qbicwko .9dpefe0kr 9c :rsu2:6jke any single measwe60.2u/9vpc kib0e ,c bsr:o jw rf kqe9d7m:urement of position?

If you knew the position of an object precisely, with no uncfsz062, ep tlso86rp f5b8oexertainty, how well would you tb8 oeez5,ffrlpx8s s62 60 poknow its momentum?

  When you check the pre hx;x2nz td6mc+v-fjo/hu.) qssure in a tire, doesn't some air inevitably escape? Is it possible to avoid this escape of airfd/thn6q hv;. +-m2)cuxxjoz altogether? What is the relation to the uncertainty principle?

  It has been said that the ground-stj1(irq2w n go-- fckcwjrf.6t5 l9n 0sate energy in the hydrogen atom can be precisely known but the excited states have some uncertainty in 6 r qn i(l-fcs. fwrwcjg152-tjn 09oktheir values (an "energy width"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydrogen )pia1(olqp-1hcrtb ) atom, the Bohr model or the quantum-mechanical model, predicts that the electron spends more time near t1ob a lt)1-hqcp (ir)phe nucleus?

The size of atoms varies by only a factor of three og6);b cbck)l.,cuca8q6i vnnr so, from largest to smallest, yet the number of e)c6 8ql ;b) bvikc,agncnc6 u.lectrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate lighjg p-wxd,f2 /on2 xv5l)r5wfht as they jump down tdjx5 wo,2f -g vxfr)2w5 pnlh/o the $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spin * foqc9a98ox 7g:uqwybut otherwise quantum mechanics were valid? Consider the9 :qq o7cua *oy89xfgw first 20 elements or so.

  Which of the following electron gc e s 2unr)x 2qrmdq.z1f00k )8icdm2configurations 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 cw64p( gf sg z(mjfewvv zw/)vy.t,/a0onfiguration for a uranium atom (careful scrutiny across the periodic table on the inside back cover will ,6/v t/v(zzm.wsfw wyg4eaf )0j g(vp provide useful hints).

In what column of the periodic table would you expect*s)ihfa + ay*8z 8ptob to find the atom with each of the following configuration)af* sph* io8zaty +b8s:
(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 simi 86tc9-a spcwilar properties?

Explain why potassium and sodium exhibit similar prop8pe2+ 4mnjsw -fjd1fk e6uzd /erties.

The ionization energy for neh(cyf93lgde, /1o ygmon $(Z=10)$ 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) i:udxr0+b5oh 4apoq. kw*8 nwumply a photon nature for light? o*x p .4h:o8b+nud urwwa05qk

Why do we not expect perfect agreement between measured values of X-ray line wm+ 7oyx jry,ex6j-sbkn5, x9savelengths and those calculated using Bo, s mj7ns,6yy9b +xr5j-ex kxohr theory?

How would you figure out whht5 ivxtqz;j t(r:/x3mljgq23qu12 cich lines in an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electro ncdg.julp gg.-s gj)*a0u, 6un transitions deep within an atom to produce shorter wavelen-gdugau gj) c.n,u0.sjlpg*6gths than transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How is it the same?--,nnuhyl 0 gs

Explain how a 0.0005-W laser beam, photographed at a distance, can seem much 67ov jlin+5 gwstronger thanlw7o6v5ngj +i a 1000-W street lamp at the same distance.

  Does the intensity of light from a laser fall off q dcjjzd n80u)mmn8 sbe x-u/cfj.)1-as the inverse square of the distance? Exp f/n mmjxcd8jebsn)z1-c u. -80d juq)lain. ----待选择----yesno 

  The neutrons in a parallel beam, each havinb-bnx e,;. jmni75gvj rtp06og 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 a speed o2t2ll13-b (i pu,agtoi, jiqj r;rwu2 f $(6.560 \pm 0.012) \times 10^3 \, \text{m/s}$. 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 w :zuu2khu,/ ncan be measured 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 excited state of an atom for m+zouqtyy63 j4v8; p y+yqzu)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 ofplpyqxz s1 v1hu v,,3: 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 typical nu b/wfgw-3kv 9wcleus w3wfgk- vw9b /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 principzdu-) ch -l4u1( dxqtm 1v(( ewkc)mcxle to show that if an electron were present in the nucleus(ldm1wzv1)hd x(uux m ec -(qt-c4)kc $(r \approx 10^{-15} \, \text{m})$, 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 pox5z-a 5,g 7 qsv0w4mvn0jkcnh sition 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 j0 wiji u7/9isthe $n=6, l=3$ subshell?    elections

How many different states are possible for an ele(slv*og /f; llctron whose principal quantum number is *fl;ll( s/ov g$n=4$? Write down the quantum numbers for each state.

List the quantum numbe8g6ye9 *jilp/tvtp8/t) ,f zh9w dvgprs for each electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each w5 cl1m g g6p dwzeaa(:dp+z)-electron in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen atom has2 +jaq5jce1yoeeb4q;0vmi:, q ot :yttj)+ws $l=4$. 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 t,ly7 mvw2ssu ,0 7yxrh+repg 6he 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 has g5yk7e*hnh - h$m_l=-3$, 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 b p(+5eqhmngw +e 18 electrons in a "g" subshell.    electrons

What is the full electron configuration in the ground state for elemehrspj/cf31p-8t2nqt , tt gy,ezr)0mnts 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) goldq r0k(t6n wdx9 (Au), (c) radium (Ra)? [Hinn0d(x wq k9rt6t: see the periodic table inside the back cover.]

  A hydrogen atom is in the zhtk-maudw 5 ar.552x $6s$ 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 thp dv e0c2+n- qy-aou9oe third electron in lithium using the Bohr theory. [Hint9o-douqn 2c0py +e -va: 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 es,gd,x8 pdjh9v+ ajx(0ev7*u dj k( jangular momentum is zero for a filled subshell.

  For each of the following atomic transitions, state whether the transition is 6lxka+ z zt3ng.f3ls:p-*hyrot0k 6ualf 6x.yo*l k3h:tt3 rlu+nps6z a-0gzk lowed or forbidden, 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 ihe6z845 fx9dn m* 9mu,ulx5oykvq bz- n 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-wave mcbhf4wx55 6elength X-rays emitted by electrons striking the face oxe6 5b45 mfwhcf a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-r jb(3k: o.y . o:yvbj3ifmhfc2ays emitted from an X-ray tube have 3oof3h: yk:(2.iyfbj .v mbcj $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelengthqbd.3j g)kl -s $\lambda_0$ 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 wavelengtiji8x.on++imt2 jmwha -h, 1a h emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for an y svs 5d+h5nv7$n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength forzrx f j(v;5dq;u-sp)x 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 matp;:p*bi+cww y4vfm3 perial is bombarded with electrons. The wavelength of pwp:b yv4fc+ i; wp*m3the $K_\alpha$ 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 detach h; wm.vgw8yub wl*dv zm7(;5ted 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 lab might have a power z54z6 i)akkmp. v opq7of $0.50 \, \text{mW}$ 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 op 0((spn2 ysurd-l; zwf a laser beam due to diffraction if the beam emerges through s(p2w (r0yn ;dup-l sza $3.0$-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 zb: gwp x;ao paj .ag5d q9+h9c;zr(;xlaser?$\lambda $ =    nm

Use the uncertainty prin h3 6e(qmxfe:tciple to estimate the position uncertainty for the electron in the ground state of the h63he:(mxq fteydrogen 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 s qr+ n +znak9*9u9lowrmallest 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 radius8 7;gmw*(gm b:qok9ws bpp0ml of an electron orbit, estimate the average distance from the numk0 b8 (pgpol;wb gmsq:mw*79 cleus 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 azy9z(c t fk4k2ws,g n4k k,ry/t $95 \, \text{kV}$ 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 ih; 8y8dy3f tm,;:o0faroob ljs $8.26 \, \text{eV}$.
(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(Figtq5 jg3xrm7d;lunx-lg9; z( o. 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 diffe)s vj k bh)ujtq,)p7s:rent 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 dis jv-eeny l.4v0,uz (lfferent electron states possible for a given value of ( v v,ez l0l-.uys4jne$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narrow slits in a ba5 kyx3g-* r 8f45zu1jps svhvv :k/srkrrier.zku*1psj3v h/8k4 gs- sr 55kvvxy r:f The 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 thkd(g t+5okk.l qzh7n3 e hydrogen atom is given both by the Bohr model and by quantum mechanics. Compare the resultlt3(q kkdz+.g7 k5h ons 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 o 9hh,1lgruhh)x3zq 3 0z20rsqvydt q/f $(22 \pm 0.22)\ \text{m/s}$. 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 xpq)gxf+wm/ x4in h*0m fobfwl5g71+488 nm. Careful measurements show the line is really spread)iw l gf*wx /bopm+f4gfx+1qm 507x nh 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 acceleratedc)fw3y:v ljxkpr68 b. from rest across 550 V. They are then directed at two slits 0pwy 6)k:rf.v3j8cbl x.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 i jghc y.yv,8ls, k,5gqnitially at rest, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the ratio of the uncertai8ycvqlg y.s,k jh 5,,gnty in their momentum.

  If the principal quantum number n were limited to the range from 1 to 6,irbfoixtu8l 52/s.*x9grjc efp, *5l how many elements would we find in nature?/l.2** fjsoe5l8 pft ,bcri x9xu 5irg   

  If your de Broglie wavelength were 0.50 m, how+cs4 o:w/7msod. s (;ajy0ioflm2rn j fast would you be moving if your mas (/ysnmjs odfa:.7clms+jooi 2;r 4w0s 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 gqb0(eao ;wf9a 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 oeb;wq(fg a9 0electron, determine Z and the element in question. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm arp;axiwwhx-nk d )1q(rz qyz17*(zvh ,e emitted from the surface of a certain metal when it is bombarded with high energy radiation. If this photon wavelength corresponds to the pxh-,zr ( qkhy7dx z;qa1(w1i)nwv *z $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread oftoe).l,jfo+xj o( 2h( v ibdr1 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.]