Compare a matter waveu 1a7x4;a )ewxxez2ob $\Psi$ 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 compat6lie r u:zk+8vible with quantum mechanics, particularly the uru:zk+ev6li 8ncertainty principle.

Explain why it is that the more massive an object is, the easier it becomes y :q;shhk: hc/to predict its future pos:: hhsy/kq hc;ition.

In view of the uncertainty principle, why does a basebage0 fp4y/nmg(z:qo9 i *ls eo,ll seem to have a well-defined positien0,*g ylig: 9smz(qo f4p e/oon and speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle prem3k 8ri4(y ahycisely on its point? Ehka3 yy8i4 (rmxplain.

  A cold thermometer is placed in a hot bowl oc*qw-y9ajweq:* gfpap -/j3mm5ex d , f soup. Will the temperature reading of the thermometer be the same as the temperature of the *ap ayq, -mmfcgj :-9w53e q* dxjpew/hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well you can make any single gix :x9vly/3f measurement of posifi9/x3gv :ylxtion?

If you knew the position of an object prbcen (5k1;9a lrp q2niecisely, with no uncertainty, how well would you know its momentum?k bnln(95 ;repqaic1 2

  When you check the pressure in a tire, doesn't some air inev(ih h.ld+n7w9 2lbrjj-uhhn 9itably escape? Is it possible to avoid this escape of air altogether? What is the relation to the uncednhhh92lb hl +iw9 r7u -j.nj(rtainty principle?

  It has been said that the ground-state 50wbos i8 lv nnvgbmr)ve7/zy,-8xe+energy in the hydrogen atom can be precisely known but the excited states have some un v 8mle,g-x)obn7 z5 v8rs+b/v0w iyencertainty in their values (an "energy width"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydrogen atom, tdna aoh 92h-6the Bohr model or the quantum-mechanical model, predicts that the electron spends more time near th aotdn hh9-6a2e nucleus?

The size of atoms varies by only a factor of three or so, from largest to smaf4(di3s1twvr eb/8m zllest, yet the number of electrons varies from one to over 100. Expla31 dm8btz/ isrv(fw4 ein.

Excited hydrogen and excited helium atoms both radia+1ag0;hh fflicflkb2b x 2ij4.+ll0p te light as they jump down to the1b lph+2204 ligfjfafib0k ;.+llxch $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table slifk 2 jnljp ma0gybz0 *118/qpko: 3look if there were no electron spin but otherwise quantum mechanics were valid? Consider the fir* qpnp3/ :1jbl 2zoa 0k1sg8jymkf0 ilst 20 elements or so.

  Which of the following electron configur1/c4ylaa dt /e+ dxhn6u+*ps osy4jdt pay(, 2ations 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 uranium5 9 1+dbsyvavt atom (careful scrutiny across the per5y v91btv+dsaiodic table on the inside back cover will provide useful hints).

In what column of the periodic table would you expect to findpvh(k4x 1h5s:9l+h ,f mrjm 0b1rrouw the atom with each of the followingb5:, hrm+j9ok0hxf u r(wprm14l1 vhs 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 exhibxic8fo9*c ,1qnsobxi29og / b rrq*:xit similar properties?

Explain why potassium artd/vas6zjbx,(8 /ptj7g 0zu nd sodium exhibit similar properties.

The ionization energy for neon 9k;)lgj rwfg* $(Z=10)$ is 21.6 eV, and that for sodium $(Z=11)$ is 5.1 eV. Explain the large difference.

Why does the cutoff wavelength in (hct0;h09*8dp ncqvzgc dmg 8: Fig. Below) imply a photon nature for light? phg*mthc0c;q 8:9 g 0dzdvnc8

Why do we not expect perfect agreement between measured values of X-raye f+ihd(ph):e line wavelengths and those calculated using Bohr th i)ep: edhfh(+eory?

How would you figure out which4wc ejgernacp ( ,3b 8p99qm-s lines in an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an5)eus dfg 8s y qcd*mr0f1vuign v/3on1/y -z5 atom to produce shorter wavelengths than trany0i/f8*5ne goudq 3cuss- nvv1rfy g)/d15zmsitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light diim8* dcff9, ,etjmb-effer from ordinary light? How is it the same?

Explain how a 0.0005-W laser beam, photographed at a he y..y-geqz9 iwsr8ks 1)u f/mp,e +xdistance, can seem much stronger than a 1000-W street lamp at the same distsi) ryxk,qe.fhu1 egy /+psm-e. 8z9wance.

  Does the intensity of light from a v2ahnu28xl:4x 5k9twpiwl8b laser fall off as the inverse square of the distance? Expl uw5lxb8:tw4x22l kan vp8h9iain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic energy:k iiuhh itu2r u)+7.yht*9op $0.40 \, \text{eV}$ 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 spnrb5f fvy6h +f1 mfiv.v4g ;:need 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 measu 6y8dqxbex 2*np7 z4oyred 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 typ: ns6/b6pi;aday f6blically $10^{-8} \, \text{s}$. 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 uncertaint*toguvjn/ 7yitg yy) 0gx69;a7 ;sq wty in 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 nlxa2lizw d)4 v521+ lxf 3wvyenergy of a neutron contained in a typical nucleus of radiu1v 5 nz2wxl24y fl+adi )3wvxls $1.0 \times 10^{-15} \, \text{m}$. [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 sleb(hz p5bx 3*):f v;ic3ndla how that if an electron were present in the nuc5e;3 x dvpn :)b 3i*llbfch(azleus $(r \approx 10^{-15} \, \text{m})$, 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 j/dhw bp/8cg0sition 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 the p d xejwdb8- rg. x3,+/(mu*mgndhj4b$n=6, l=3$ subshell?    elections

How many different states are possible for 00merw rfek* )3wkaz( an electron whose principal quantum number ism * )wr3ekfke0zra(w0 $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the ground state of ctoh l :atq9 p)yg )*f9t+)ubs k.owl;
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron.q)(p3bpic ef: 2gnov in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydfl bhn+ij3t-aof8f;i0 6lox ,8jmf)e rogen 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 anu soxmls20c1:qxe x,( yc.v lqm5 0rw;gular 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 hasts la355m4gox9 7voga zv9.e c $m_l=-3$, 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 "g" subshellxt395 )wa zbga.    electrons

What is the full electron configuration in the ground statefja23ynp.+vxmn qpg4o*44 rc 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) selenium (Se), (b) gold (Au), (ckdzu ) 8i: d3:dvsid .zrz+i2qpkz 2b8) radium (Ra)? [Hint: see the periodic tabldkisib+ur3v2z. pd 2)q :zk: d8zidz8e inside the back cover.]

  A hydrogen atom is in o7 0 99x ; af3vho:*o6a8zbvynffnmhvthe $6s$ 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 27bxk/keq u(vBohr theory. [Hint: This electron hasque xb/k(2v k7 $n=2$ 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 subs6urbodu7f*c fyno p4 -/+)cjjhell.

  For each of the following atomic transitions, state whether the transition gt dtj*n7 p h*15g1w:h:sy3 xgj/anglis allowed or forbidden, and if y/j :1*xangs3dln 7 1h:*5gtggpwtjh 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 i2 xol2ns *: j7nycs/unr2 kbp(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-wavelength X-rays emitt+uii0g5 kutl nrj4 *p+ed by electrons striking the face of t0 uk5+ 4jr*+liiun pga $33.5$-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 c/.aj.nmnb 0e w3z5tr ldh*5yhave j5 ywb /n3.nl*0d.5 hemtzcar$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelength0tsznnc q+d0, $\lambda_0$ 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 0a4*sfkpr( 9 u f8c iisp,,bndwhen a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelen):te)r hxvq9v.xo- v r.9tx8txy04c6 gie vnl gth for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to hjn k5b9rvr 64c8aacv v2,pa9 estimate the 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 unknown material is bombarded with elp zu: tq+t0aa/vmfn 2 v16x t g0d:kt6qxdw+m,ectrons. The wavelen0 tq,nvfp0ddma1 +vx z 6qt2/mk+ttwua6g : x:gth 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 detachedtx2 (p; pybh1w 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 poo m2z:wn)xdj5dd5l7 d g3d2ex wer 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 lu zud o3o-27 tneki7db(17p +k)inic daser beam due to diffraction if the beam emerge7i d7i )o + 1u 3ndcpto2unbi(kekz-7ds 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-Nwb q5d- ic j-*fxz:,lje laser?$\lambda $ =    nm

Use the uncertainty princi*1g7(6 nx usbs)b,unb6p qwi3u f dpa0ple to estimate the position uncertainty for the electron in the ground state of the hydrogen atom. [Hint: Determinu wu3(bs66n) ni dbqsp*,fa 107pgxbue 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 smallest possible values for the angular m 5g0-4ow9j *;f moygnqgkc uo.omentum $L$ 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 av,:)p: wa2h rka+rc i, jgqkcs6erage d)chs:g,ar j,qac+kp 26 ik:rwistance from 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 operates at id(k)z27kfd h $95 \, \text{kV}$ 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 i28;2dz 0 wjb:b hfj usynzo2rtk(;k4 vn 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 thex.fbis 4 q8(0wf:nnkf w1ay9m 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 a k mi4ib, (dsj,ya j)j5given 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*u1zyn juj7z5dq* 8ae fferent electron states possible for a given value of 5 8 aznjzu*7yqe1*d uj$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two nartn q+8z( u 28geypb u3)esedd,row slits in a barrier. The slits ar)uun8 sd d2ypetb+qg( ,3z8 eee 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 hydrof mfxkk3izo1l+ -(kq/mfjd)i 7 4rj0yfe/,qggen atom is given both by the Bohr model and by quantum mechanics. Compare lr7/if m-ykof1qjff+)e(gjid /3kkz q,0mx 4the results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling with ai lv*nigp*z, -s5ps5k 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 ll ros3xmb) qx/x u-1 fig2,gp+ine with a wavelength centered at 488 nm. Careful measurebg ux-g2xofqxr pl/ 3m, )+i1sments show the line is really spread 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 accelerated from rest across 55;y 4bjec+46jny(e98 jdshcr ;uwn8 ps0 V. They are then directed at two slits 0.70 mm apart. How far apart will the interference peaks be on a screen n; r(d e +he4 b9u4cnyjpsjwc8y8s;6 j28 m away? $\Delta y$ =    nm

An electron and a proton, each initi vvmxxw+ fs1i-/; /botally at rest, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie waveleixb f xos 1/-wv/m+;vtngth, find the ratio of the uncertainty in their momentum.

  If the principal quantum number n were limited to the qvtutza 4,r :(range from 1 to 6, how many elemen, qrt a(vzt4u:ts would we find in nature?   

  If your de Broglie wavelength were 0.o-hbsaw74 varz; h c4250 m, how fast would you be moving if your mass is 75za 4h;4s7- 2w hroabcv.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 series of lin8hseuc2 zc)y:m: uc+ oes with one out )cs:o uucyce2:+z hm8of 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. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm are emitted from the sp y lv u7.lx3(6wv7wlgurface of a certain metal when it is bombarded with high energy radiation. If this photon wavelength corresponl p l7w6xy.vwugl(37v ds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread of a laser beam,fibl*1a-+wmpf07cms c ecrthq n 7 93, $$\theta \approx \lambda/D$$ , 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.]