Compare a matter wave bl6 kvp.:h1vumd y)q/dd2d , v$\Psi$ 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 quantum mpm3 edisd.15c echanics, particularly the uncertainty princicpis 51.dd3emple.

Explain why it is that the more massive an object is,n8dy2xr d;m+7 pp8ibm the easier it becomes to predict its futurx dbi2mpd8 +r;np7ym8e position.

In view of the uncertainty prince3a2-:nz qp8 eoj 7/e;tcfdhxiple, why does a baseball seem to have a well-deffxzhee ao:-2;3 ptq8e cjn/7dined position and speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle precic u2shqf zfe(8i7;zc 9x9n hzbo*a(c,sely on its point? Explo92nqhi;(x z c f,98fzhec7s(aub*zcain.

  A cold thermometer is placed in a hot bowl of soup. Will the tempe u:mfn+w/y x-urature reading of the thermometer be the same as the temperature of the hot soup bewyu/-+fx m:unfore the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well you can make any isa)o 2-lmg0dzjcjn 43)u1yd single m4 3aj c 2l0m)ji1odd)yus-nzgeasurement of position?

If you knew the position of an obe -lv 1idv86buject precisely, with no uncertainty, how well would you know its momentum? vb8-dlv6 e1ui

  When you check the pressure in a tire, s049yjovr35 d.hxf 9 hc;m uxtdoesn't some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relation to the uncertainty pr vfdu 9 .mrh3txxoh9;4jys0 5cinciple?

  It has been said that the ground-state energy in the hydrog+ uw eer/ocy8qkp :87aen atom can be precisely known y8pko ua ewceq8/+:7rbut the 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 atom, the Bohr model or the quantum-mec8wdc* mm(n84ngeon9 v 7c to+nhanical model, p ce8 m4ng*89tno+ncd wmn7v(oredicts that the electron spends more time near the nucleus?

The size of atoms varies by only a factor of three or so, from lar 9 ;;ngwiwi(wuc4t 80pfpxyp;gest to smallest, yet the number of elew;(p9 ;yxi 8 c0pwfti4w;npugctrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as they jump dmrgj6c6j2g5oa . /ogpown to themga j6rocj/ pg.2o6 5g $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table lld92,fr g u:cag9xb)look if there were no electron spin but otherwise quantum mechanics were valid? Consider the first 20calux2,:rg )9gb dfl9 elements or so.

  Which of the following electron conf*qmv-up oo:7digurations 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 uran nq.rlb pvi/9ow9- 74b;q4lpj7nh y rnium atom (careful scrutiny across the periodic table on the inside bac jrl h9y-ovpiw;b7.nqb nl/79 nrp4q4k cover will provide useful hints).

In what column of the periodic table wiz vt ,0t;z3qpould you expect to find the atom with each qvt,;zztp0 i3of the 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 simi( / bye,oiylo7lar properties?

Explain why potassium and sodibuce b0ogou0xeu.p8 3s)4 jd*um exhibit similar properties.

The ionization energy d2n 9bgtnob6kka 8)*gl + v.xw7vtxj,for 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 (Fig. Below) imply a pf++zi8n ow.( tehi(b pwt) e-hhoton nature for light? w (heef h8tibnwo+tz+i() p-.

Why do we not expect perfect agreement between measu mmzox ts 7.wu6z626dzred values of X-ray line wavelengths and 6 zmod. w66tzz sm2x7uthose calculated using Bohr theory?

How would you figure out which y6 0wwbo ys/zb(r -8m5exf3 jeqm3rap 0kkf)/ lines in an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atom to produ re*x0 z03ksi:yifzl.ce shorter wavelengths than transitzel0i3:fr ys*0. ki xzions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How is it 8e+ g7y- ymfbmthe same?

Explain how a 0.0005-W laser beam, photographed at a distance,m f;( 36p)-4s kuxcoaqfy3zq n can seem much stronger than a 1000-W street lamp at the same d(3noys4z 3 p-q )af qmx;ukc6fistance.

  Does the intensity of light from a laser fall off as the inverse square ofm)/kt-/yiz6*poi ; x c;po3wzi +snpq the distt)wpkc s-x6; oi3no+ zpq*myzii/; p/ance? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, bkj) :eb3 7v)whbmhf5 each having 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 travelin;zk/ ouf8ns7 (5xhdhug with 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 to :ppj2z3 )k layc)znm*w4szh 9an 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 t-n i*8rp*i 6ufyfhk k 6f:(bivypically $10^{-8} \, \text{s}$. 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 th0zgz6qi6: u+v-jl+5cp m o amne 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 enqrr se y.*ugf9z0+;myergy of a neutron contained in a typical nucleus of radiusyzus.r ;gm fy*e9+q0 r $1.0 \times 10^{-15} \, \text{m}$. [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 principlet4 / h5rb)s 2z-ohxtoirg)lahq02x9r4f b v*j to show that if an electron were present in the nufl-rso tzhh9*j a x) gb4 24t)o5/xi0h2rbqvrcleus $(r \approx 10^{-15} \, \text{m})$, 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 thes, :t hv1nf0ikz+35 auu*v8u h,b iswy 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 be9nln8b7oaifm*l ( g9)az7de z in the $n=6, l=3$ subshell?    elections

How many different states are possible for an electron way8afx:dz+4 p n 1u vm4q nk32j2rp0xmhose principal quantum nuf8 av20u aknzym4+r3x d1 jp4pnx2 :qmmber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the x+lr ki( honc9a+r(,w ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in th w-yz ) r2ifobze2rd(2e ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen h;u;yy0.y.um7zm xjratom 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 at y(w au c-)03wq*yvtbgvuk69 n 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 hamf ojp2l,r, ,es $m_l=-3$, 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 :m31e ohiljv .a "g" subshell.    electrons

What is the full electron configuration in the ground state for elements withrcss bb+v,on -0.o, zd,t*lbj $Z$ equal to (a) 27, (b) 36, (c) 38? [Hint: see the periodic table inside the back cover.]

What is the full elerw-:o g99y1n)vclpmt z ydt-,ctron configuration for (a) selenium (Se), (b) gold (Au), (c) rdmzy tl)c 9ton rw,p1gyv9- :-adium (Ra)? [Hint: see the periodic table inside the back cover.]

  A hydrogen atom is in 6(ogmfkqzfs q:y7t2lz yk1vq23p94qthe $6s$ 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 e s/ws m0qi5u )9sfmjmcgv. a1b9iiyd*:b3h x3lectron in lithium using the Bohr theory. [Hint: 9 s /chiubmd5f :0 3a)js*xiqmiymv93s g1w.bThis 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 jw751fhf.u)q0iyz ydre*hwfl)h t 8 tifj5 )9 a filled subshell.

  For each of the following atomic transitions, state whetheu:9i6b7g def 1mzqncv)lj 6t8r the transition is allowed or forbf 9lzv6 ngc:)ji8e 6d1umt7 bqidden, 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 i qchxi) g4dpt3 2u2-1w nrlm9jn 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 strtd1x 2))fuu8)uk0cze f ehx2)9o ybuxiking the face of ax9zbey tf8)h )o e)c2xk 2u)uux df1u0 $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted from an v b/u dd).,p xn3:/ pzwsnr)x yx;div1X-ray tube have ,/dnvd:nx dzi31py usxb.)vp) w/;xr $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wae w;m5i2m iwq:velength $\lambda_0$ 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 wh k sw19 6jo-0nsd8:*qjxs pnwnen a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelengi 9gkmdniixzu3v3l:qc ,7 q5r 6l)zm* th for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate thgksm1) v4e nzgs(a n/1e wavelength 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 unknoe-ea68lk/br o.) qdrk pm3a7hwn material is bombarded with electrons. The wavelenh3mpb/k-6 kod 8rq r.eel 7a)agth 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 retinas puts ks1tpvryu* 85 ja6am;jx-ux 4out $28$-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 2g bl .:tn05aicjp/zcphysics 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 diffrac3 jnx,qk m1vvu.l 27m-ypnhb9tion if the beam emerges thron7u 92nmvx mhq 3l-y,1.pjvbkugh 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 lasei-j;i.p:z .kgt, . fhidh3 ggtr?$\lambda $ =    nm

Use the uncertainty principle tozl/bz5 r,qdmn7 u;he2 estimate the position uncertainty for the electron in the ground state of the hydrogen atom. [Hint: Determine them,hunz7 5eb l/zq 2rd; 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 a(90kwbhdqy 4cb4o 9p l+t vvb1nd 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 radiu ybpo4.nna:-hs of an electron orbit, estimate the average distance from the nucleus for an en.ayo4 pn-b:h lectron 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 operaten9ixuh2tsl4 ;4h) ines 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 the outermost electron in boron iq m))tj4(y nrbs $8.26 \, \text{eV}$.
(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) cx9gdv6g bv 7gtkyi t)h9- 1v+jan 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 a given vg . nhkw(mse4cic;d c72k h;i(alue 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 stfslm /vlih8 .ep1k7+w ates possible for a given value of ps87w fl1 +e.mk/vhli$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narrow slits in + ugw3 7amw3lx357kevs t ix:sa barrier. The slits are a di ae3 x7wmgvwt7ki5 uslxs:33+stance $2.0\times10^{-6}\ \text{m}$ 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 at hlsdljgngxk)s1l6o-rvb4z p151 9d0om is given both by the Bohr model and by quantum mechanics. Compare the ) lhd1jgdl4l k90pvz6sxo-gn 151sb r 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 speipzh) : yrdk7f(w,ah6ed 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 centh7a23c uy1mngered at 488 nm. Careful measurements show the line is really spread out betmn2c 31 gyah7uween 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 V. They ar/y6 +u37;kav-j0g/tjmr mtpb 5c sfxke then directed at two slits 0.70 mm apart. How far apart will the interference peakk+ a0bv/sk6xm 7cgjp/f-t5yr ;m uj3 ts be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, are accelerated across the saz ;p(y+5ftme :syfuc. qn-u5zme voltage. Assuming that the uncertainty in tz55sm(t . cu+:fqnu -p ;yefzyheir position is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum number n wvhrldc:ceq0.: ; (((f(mmpq 5tdp. i nfsek s4ere limited to the range from 1 to 6, how many elements woq e(nm(p5p hl (:iv sd4cqcf. re 0mf.;st:d(kuld we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast wourl8whmi 446 p6lxdg,qfy 91omld you be moving if your mass is 75.0 kg?m8ywhif1qm,or64l p964g dxl $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 lines wit 5ggomtx7 0diu(8kc3 lh 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 olmid(o07ug x 5k8c g3tne 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 unk)g/ qa+f,ia certain metal when it is un+/q ia,)fk gbombarded with high energy radiation. If this photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffracthax j9.c ,tb(p 27kvvnb5qp.xive spread 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.]