Compare a matter wave gxty;eb +8;op$\Psi$ 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 mechad :62kpm0xzhi nics, particularly tk0 :2 phidmz6xhe uncertainty principle.

Explain why it is that the more massive an object is, the easier it becw2u+etj ig1ejy kxr.)52 up,domes to predict its future positpyi d+jruejek12.xw5 gu,)t2 ion.

In view of the uncertainty principle, why does a baseball seem ttgax m5shqe ):+d3n*wo have a well-defined positnt3hg:exa) sm wq*+5dion and speed whereas an electron does not?

  Would it ever be possibleqa-b /-.hznpr6b d+5 9gfcfoizm6 (nr to balance a very sharp needle precisely on its point? Expl- z .acmdg zf9phbi+6b-r/ oqnrf(n 56ain.

  A cold thermometer is placed in a hot bowl p ksbleeiy,b89yb9f- (a lzu *:1u + astl5l,aof soup. Will the temperature reading of the thermomete 9z*l8puse:k9(bub se1,ai5l, -l fltybaa y+r be the same as the temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a lim/hq+i gc) tf+vit to how well you can make any single measuremen i+t/vhgq)+fct of position?

If you knew the positib6 fyaq,04hyw,u) o,f duwn+kzw2 i*ion of an object precisely, with no uncertainty, how well would you fk2n wou,w uii y,0z,y6wdfaq)h*b + 4know its momentum?

  When you check the pressure in a ti 5 pru*op(dhm)v(t gsk r;6ds;re, doesn't some air inevitably escape? Is it possible to avoid this escape of air o ()(;rvs ps; mk5 dtr*d6ghupaltogether? What is the relation to the uncertainty principle?

  It has been said that the ground-state energy inmj6 yl8iwk;r) pm;wzq 2c3wml8)sb k / the hydrogen atom can be precisely known but the excited states have some uncertainty in their values (an "energy width"). Is this3 z)q imlk/w ;mlkwp)28s8 ;rjcb myw6 consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydrogen abc-8mzdvj 95yaa+d umjt9 w36tom, the Bohr model or the quantum-mechanical model, predicts that the electron spends more time near the nuc98acz39+mv m5t6day ubd- wjjleus?

The size of atoms varies by only a factor of t0xj i()zmf)oo h).:bak xgbr)hree or so, from largest to smallest, yet the numb :ohb() ) 0rajoib.gzx)m) kfxer of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate l geqxkaa3n.;(ight as they jump down to thge kax;(aq3. ne $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if 5l.i3vbq az tsw,)ja+there were no electron spin but otherwise quantum mechanics were valid? Consider the first 20 ele,l) i jvwab 35+zats.qments or so.

  Which of the following elect6/60g rv e1ajfex bidt304jqw;tzv) cron 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 uranium atom (ca 3*g hw0 jl8id2osc1g 9tf2rdireful scrutiny across the periodic table on the inside back cover will provide us9fddi hjs c 2l*0ow128trg3igeful hints).

In what column of the periodic table would you expect to find the atom with eachbc7hhti 6z ffzv::0 )47oewry of the following configurations: f6047:r h tfevbocwh7zy zi):
(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 exhi: drgv2r8o+r sbit similar properties?

Explain why potassium and sodium exhibit simwpn ,pm fdcpk*-v2j9; ilar properties.

The ionization energy forj f kxf9t)ks7+ ri2t-w 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 ( ctixtzozu+ra7 +z0:*Fig. Below) imply a photon nature for light? ax: *oz zt++ i70crzut

Why do we not expect perfect ls. irc9l ;)bws:6jo 4k:a dozagreement between measured values of X-ray line wavelengths and those calculated u s4k airow) 9:;sojbl.6dzl :csing Bohr theory?

How would you figure out which lines in lq2;aayb3 ,u 5r gmhh)an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitcafsd :76hfg 8.xqb )lions deep within an atom to produce shorter wavelengths than transitions by outer electgb 6)d :.ff q7lhsxc8arons?

Compare spontaneous emission to stimulated emission.

How does laser light differ 7uxszh7mk n r8cv:/u* s,b f0 g/hmz8efrom ordinary light? How is it the same?

Explain how a 0.0005-W laser beam, photographeq sbck/tw3q ,2d at a distance, can seem much stronger than a 1000-W street lamp at the same dqq,s/k2 bwct3 istance.

  Does the intensity of light from a laser fall off as the ia(p wp ,d or (i35pib.+0uyz7cojsza 9nverse square of the distance?z z(p.+ ,39pr sd75ai opyj0w ucao(ib Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each hyx5lnk9o-x(8ck.dv yr z8mu ;aving 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 65bvwr8jfnd 7 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 toz3 s 63qobfa+q 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 angogi 6o+*bwtnqidz9z1 ,mj93 excited 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 x cqcce; :06jk/tzvu7 the 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 energy of a neutron contained 4zhc0opdk1l,;g9 zr rin a typical nucleus of radr,d9gr;z0hl c o4k p1zius $1.0 \times 10^{-15} \, \text{m}$. [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 ifphsq tp-n azp 9e)yl- w4t8-4tdu.ix 7 an electron were present in the nucleus8a p-e4t)i9qtt 7 d s4lhxu.-zp- wnpy $(r \approx 10^{-15} \, \text{m})$, 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 po g3 da0)3gud-c unso7;3hfg ufsition 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 be7g;cnj*nrtp*pu tp)i; j, 8ae in the $n=6, l=3$ subshell?    elections

How many different states are pp2(;ep vum:zmo/ex o2ossible for an electron whose principal quantum number is uoe(zmpom e2xv:p2 ;/ $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the grou72d e4o9f rwlynd state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground state of nitroge1oq:l4qv11ek kf uuu (n $(Z=7)$.

  Suppose a certain hydrogytm;iig7 29 c4ztxny* en 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 ancpy zt8h3l1+v.on .wugular 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 hw 7us56t7d bhbas $m_l=-3$, 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 electr bf n,(ylbl 7z8b;hk;vons in a "g" subshell.    electrons

What is the full electron configuration in the ground sta g t s;e:6td+6wyeyzim e,r;t8te 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 configumkymc95-8 o ufration for (a) selenium (Se), (b) gold (Au), (c) radfu8o- m59cmykium (Ra)? [Hint: see the periodic table inside the back cover.]

  A hydrogen atom is in (5 1ihfo4doia yg t92wthe $6s$ 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 ener5:7hl .b.igvadhpy 5 kgy of the third electron in lithium using the Bohr theory. [Ha5gkpbi 7.v5:.dl hy 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 filledrz1nr56k .(nxq*pv ay subshell.

  For each of the following atomic- i. f(ojpywo: transitions, state whether the transition is allowed or forbidden, and if forbidden, what ruoy(.wif-: poj le 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 ioqa5u59pr-st6 1(k ukhx4 b tkn 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 wd4lpmt wt :7tk7enr+ kwl ; d59s-/koby electrons striking the face o o; k-l+rm7 k/te54:wt9 sktw wldnp7df a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitte x55 kqx5shlehw*2lx5b8*p qhd from an X-ray tube have2eqhx5l55lps *h x8kxw* 5bqh $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelengwp* m2hyeg;*ln)g b )xth $\lambda_0$ 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 etn9y ulo1 82fx-wfl .xmitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength fo ah rqdtt,w;h8t r08z0d*9,hl crc+glr an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength for an:qcmwj. lg1rmg1kf)*)c6cbv 0n(zio $n=3$ 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 vih)vqs1 xht;) cqgry4z 7(tx/rzehe:( -nq+ material is bombarded with electrons. The wavelength of t;) h(1 q+t t-xv)(h/gr:crs7viez yqhn4 eqxzhe $K_\alpha$ 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 detachen/jbpz2v*bztx11o 2 g 5x m+sp ,ious.d 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 xs3m)r;m) r h-zcj(w gpower 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 thfxrj0yz) (yqom.3 fa c os:0r ci:6vq-e beam emerges throc y0s x 0fzcvirm:3(:6.y)fjqqoo-arugh 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 ofq6ye1,to78 sonqp bto2xe)(i the He-Ne laser?$\lambda $ =    nm

Use the uncertainty prinns88gwpu2t 28h 6 ;nsvpz-e vcciple to estimate the position uncertainty for the electron in the ground state of the hydrogen atom. [Hint: Determine the momentum usin p v;eu22 8n8nszh 6tw-8cgsvpg 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 possible valr z-y dm 4sm:rg)5v0cys;a xk,ues 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 r15hn v-2gzxjoq1y*e, estimate the average distance from the nucleus for an electron in the innermost hr1-noxy2e 5gqjv 1* z$(n=1)$ 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 at rs ac 5 xyyvg59 -jb8gz ;)-dz61qhrnm$95 \, \text{kV}$ 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 (bindingdsd6uan 7fd *d ,:1e*cf kwyyz+x/m236 whuso ) 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 that the Moseley plot(Fig. Below) can be written tb ,4am7 h17tr :5qp ud fip8b.wlwn2h$\sqrt{\frac{1}{\lambda}} = a(Z - b)$, where $b \approx 1$, and evaluate $a$. a =    $\ \text{m}^{-\frac{1}{2}}$

(a) Show that the number of different states for a given vah0b4 s*x+jquwk2ev69 hfw2vrlue 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 given v;ka-v2l y43lfx3.b ely co9(bk.mut jalue of ;jbxv(4yeck o u2fb9alky3.t . 3m-ll$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with7ks.iwnm(b/oehtn ( 8,l, fvg energy 45 kV is shot through two narrow slits in a barrier. The slits a( tnf bnli,8( khe wo7gs/,mv.re 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 the hydrogen at jb9uqsbq8rh;m9(y3 3 x8rzivom is given both by the Bohr model and by quantum mechanics. Compare th uqijmzy;x8r 9qb(8b3 hvr93se results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is tr+1 ej7 i5d8k 6:abfu vgvbw7lnaveling with 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 wavelength cemzkzw:pzw:z ;ym21+bntered at 488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. Estimate the w:+z1y;bm2k wm:zzz p 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 dih+ jxq51f xuvl+tvus+bv 950 bx 3g3pirected at two slits 0.70 mm apart. How far apart will the interv+bvvtq31j pb3xfxs + u ui5x09l+h5gference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially4 e *c.i zst q.kgpb,4v49wbfm*rgoe oz.i.p6 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 uncertainty in their momenqb oitbkg *wzcmpgzfsp 496.eirv*4.4eo,.. tum.

  If the principal quantum number n were lim.kjl(5h7rny w3p:fpc /ss+ wbited to the range from 1 to 6, how many elem pl+7b:wfjcpkyr3/h.w5n( ssents would we find in nature?   

  If your de Broglie wavelength were 0.50 m, hoz68vepx s-a k(w fast would you be moving if your mass is 7p s8-(xze vk6a5.0 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 a sel)nl0x/;uwa ur9g 1reries of lines with one out of every four matching a line from the Lyman series of hydrogen. Assuming that the unknown elemenar r/ ;9n)1 gluxleuw0t 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 a6)q(t pl5rh :rzfo 6ffrom the surface of a certain metal when it is bombarded with high ener ltar( :fz oq6pf6)rh5gy radiation. 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 beam, i/x vk dn60i+nqc; rj+$$\theta \approx \lambda/D$$ , 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.]