Compare a matter waveezj7zm,qk t+ , $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory of w2 vu89jhch7p( b:bhu; vrdcl.o0r+tthe atom is not compatible with quantum mechanics, particularly the uncertainty p j.durhu 9tp8;hvrvcl7ocwhb: 2b+0( rinciple.

Explain why it is that the more massive an object is, the easier it becomes tgex(c74f5 j.5/pr:lguka oyio predict its fut5iolju/ycf k4ar g.: g (pex57ure position.

In view of the uncertainty pr )e)a gtr m8tj3d6*rc7 ldy:rrinciple, why does a baseball seem to have a well-defined p)6 t*8rtdjr3 m)ryerlg a:cd7osition and speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle precisely on itb si4a91nd:f +s(6:w y tuiates point? Explai+ai(:iusn fd:1 sbe9 w4ya6tt n.

  A cold thermometer is placed in a hot bowl of soup. Will the temperature ra/ ku7h*bbv6ry 3z ,bmghyc: 9eading of the thermometer be the same as the temperature of the hot soup before the meak buyh/ 7r63mbzv,9a *hb:gycsurement was made? Explain.

  Does the uncertainty principle set -zs 8n6ciyz aq8,/loia limit to how well you can make any single measure/l8zsc6ziin- y, qo8a ment of position?

If you knew the position of an object precisely, with nanpp , jm67vf1wxjo+/o uncertainty, how well wa176v j/xjn,o pwm+fp ould you know its momentum?

  When you check the pressuresq n 3 lndl3b2;gzpa(./xdz- v in a tire, doesn't some air inevitably escape? Is it possible to avoid this escape of air alto dn(bn;la-/ 2z l s.g3z3qdvpxgether? What is the relation to the uncertainty principle?

  It has been said that the ground-s2a *opwdap 3p8tate energy in the hydrogen atom can be precisely known 3ppoa* adw2p 8but 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 hydr*vyqh14 t5apgogen atom, the Bohr model or the quantum-mechanical model, predicts that the electron spends more timt5p*qv 1y4g ahe near the nucleus?

The size of atoms varies by on1/ )e uj)llcyajuz2 f1ly a factor of three or so, from largest to smallest, yet the number of electrons varies from j1) jzfy/ )luule2ca1 one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as they jump down tytxxrz(p 2xy2dq0wvt:g89 6ao the txz (2yy 0p: advrxx2w8tq6 9g$n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spin but otherwisej2gxmn4r 3.hc g/z0x f: .pvid qslj0ynt7t;5 quantum mechanics were valid? Consider the first 20 ele0sn2q;7:./j.rmhx3 l4v 0g d5ttpcjiyzng xfments or so.

  Which of the following electron configurations are not allowed: vu.,p upoef51e fz6,t
(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 z+ ttprq0s gl(sbig:6m2a4 *efor a uranium atom (careful scrutiny across the periodic tab*ae6 qb rtzt2:ismg +pg(l04sle on the inside back cover will provide useful hints).

In what column of the periodic tabz iouu,tl .*f 24xr8tvle would you expect to find the atom with each of th2l*v.tu , zort fi8ux4e 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 similar prosa*-fmkyvc4k r 20o yys 6pp(.perties?

Explain why potassium and sodium exhibztdo 1yn g)g g 2+pu* (oo/fn; :cs1rsa(hwc/wit similar properties.

The ionization energy ixucwkf6lze2toz,a+0(eu z i8fkz-q8 :q;x2 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 p1xafbug q9.7 zxf65lh,w1 dm;tb gy2zhyru- 9hoton nature for light? rf 1.yz gf;h99bud6yzagqt,m2 -51 wlxh7u xb

Why do we not expect perfect agreement between measured values of Xe 9n u3ccsyhy)3dz7*4* oithw08legb -ray line wavelengths and those calculated us09dh3w8us7 *h cb*lgyoc4 ne 3yt ize)ing Bohr theory?

How would you figure out which lines in an X-ray spectrum correspond to 6rhp-j q5j.ma$K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an at01rgw25 7qbrm: zttvlj/x) gkom to produce shorter wavelew0l1gmq) : tx5j grvt7b2r/kzngths than transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How is it the *h 1zo3r nx-kjsame?

Explain how a 0.0005-W lasz.qqna0n+-u 3zlc )h ter beam, photographed at a distance, can seem much stronger than a 1000-+)u3cl. zh-qnz nqat0W street lamp at the same distance.

  Does the intensity of light fro c, rg8j7svd j+07g;y emr,lfym a laser fall off as the inverse square of the dista y jyvr0cgsedl7 rj8+;, 7,fgmnce? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each havink+ a9b3hjg +*b o48q5 hftxocqg 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 sp.cqhk* qk ./nxfam)r 3eed 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 an acwr9p61 / z,c 9 m5gsavehqtj8scuracy 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 stdmb). py+h82ey6vlp )nib t f5ate 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 uncertaintix0f dbrht ;63y 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 energy of a neutron contained in a typ aqpnlh85 3xq4: uai*wical nucleus of raanp:xl*a8 h45 qw qu3idius $1.0 \times 10^{-15} \, \text{m}$. [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 if an electron were present in e y a)4ig ch2*cir6j;4g w9xixthe nuccj4hyiii ;6g9 x)4a wgc2 *erxleus $(r \approx 10^{-15} \, \text{m})$, 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 polje baq;zub7b5+n b 3.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 the6)ik f qncnx2*sd-;sf $n=6, l=3$ subshell?    elections

How many different states are possible for an elecenevupl c+ .-gs ght83so4 ijwr3 mu5g+i-5.a tron whose principal quantum number is- ohupivgc++sas54r8elg ti e.u- 3w 3mnj5g. $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the ground state of tbr.205z0uiidi/ukn yv m-8m
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground 3ku2ir*o h7e c jlkj-w gqc3e-sy/. -astate of nitrogen $(Z=7)$.

  Suppose a certain hyd:9yv 7gacp5;z. eg ptvrogen 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 vyymhf-waw 7b3/wlr;,fh j(9 of the 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 hz vax +e;c5*cqas $m_l=-3$, 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 benpgwwvz6 *v t4tt8ak jl6 +7n; 18 electrons in a "g" subshell.    electrons

What is the full electron confi hx:-w5m)f*w9vyjezbxm j4 w-guration 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 for (a) selenium (Se), (b)8qevj xdtv. v:(c+w7 h gold (Au), (c)qv+v.d8he x :cw(7vtj radium (Ra)? [Hint: see the periodic table inside the back cover.]

  A hydrogen atom is in th:s1 k 4c;uiycie $6s$ 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 uss+ri6zn e3x 9+/fyko 8 oftdp,)mzp+4 eki)huing the Bohr theory. [Hint: This e+tefxekiu/hz s8pnf63 iyr o,)+ okz+4) 9pmdlectron 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 fi:f 4v zyn-*w yfycu(9hlled subshell.

  For each of the following atomic transitions, state whether the transition +sr8kx3w +tmqis allowed or for8ws3+tq + rxkmbidden, 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 il;tts8n 5-iskg 8ft6pl rh0+b 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 emitted by electru q79f9 e8fj y ;p0,onrn,iknqons striking the face oq9;q ,ofn n097rnpfe8,ij y kuf a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength brcshu(++tk z1demsstrahlung X-rays emitted from an X-ray tube have1zk+ t+c(dh us $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff w/ygb4* inw(8 jv3fbmqhs:3r ovuga (5avelength $\lambda_0$ 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 eiuh lashmqpxv )9u-pd s,/562mitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength / rtr; j8d,uh1z rh9rz7wwk,p for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to e6 0 pzlv)ksvsfv 3v/;vstimate 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 electrons. The wav z/;/;hg y+(thjwrbz5siyd lhho- 0 c8elengy5d o0(-z/h 8z;shy+ r;ctl/i jhhb wgth 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 outk-9qw nvqx.75 che5rl $28$-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 ic0dwd8rp ;8 m7 o4miia physics 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 diffraction if the be f,+sk3sfr 1a8dtmtf cd g9txr1 ft60.am emerges ths+kfr 1xct tf 1.t 80gd9f3ftr6,sadm rough 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 laserek8;9flm v66 fonna9a ?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncert/fz5z. h6du,f -iqug kainty 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 momentum can be anywhere between this value and zero.] How6fqg zk5/ d -z.u,fhui 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 momentum c.l0lbcg-z )p 4ne,cb$L$ 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 electrqmqmd6:lkez6m 9/j7 con orbit, estimate the average di:z dmmcq 7mq69 k6lje/stance 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 m4 mvl(*yq( ah$95 \, \text{kV}$ 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 bori h ftnt*4lxpjn4w0 21on 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. Btl-6 b4 eq/-xwit xm,uu56 xvaelow) 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 number9t 1/k59/ nr4dlqboti 7ln(/bw baqby of different 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 different electron states possib:*0mdp hpb 7jile for a given value of 7jp p0bdh:mi*$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with eneha a 88vpx/ f*vj8m9irrgy 45 kV is shot through two narrow slits in a barrier. The sph9v8x8*a /mi8rjfvalits 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 theu o:zb q /hsi*f0 (uga/q2sbp, hydrogen atom is given both by the Bohr model and by quantum mecbif/*(,q 2pohb /:sgszq a u0uhanics. Compare the results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is trave-nb.e qab3* kiling 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 centered at 488 nm.t5ln/( uzum v +rlixb1+v-5bc Careful measurements show the line is really spread out bz(l1m5-n+5lv/t b v + ubuixrcetween 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 v-drporg z9uc/j 8v(*7n s/3nsdi0ra550 V. They are then directed at two slits 0.70 mm apart. How far apart will the interference peak/g(*rcvr8v0-rn z j3d/sipadu9o7 ns s be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, are accelerated across the samwyo-r03kzc9 kdel/pz; xv/ 8ze voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the ratio of theczzdl;vozk3 e 9 8w0yk//x-rp uncertainty in their momentum.

  If the principal quantum numbe fbk4g -f4 )zryx1goh:r n were limited to the range from 1 to 6, how many elements would we findy44fx-rbog ) gfhz: k1 in nature?   

  If your de Broglie waveld/dna .0wjrg;9 uz,szength were 0.50 m, how fast would you be moving if your mass is 75.0 kg0 ua z z.;/nwgr9s,ddj? $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 wsc i5rk*,9.g.z:mg0 zn uacolines with one out of every four matching a line from the Lyman series of hydrogen. Assuming that the unknown ewc,.zn g* 0 u.rmgcko:i59z aslement 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 surfapu7etfu 17brct)21:p lz ykp 3 xo-rh+ce of a certain metal when it is bombarded with high energy radiaticr- pptx y1zulu2 e7bh 7f+t 3k)r1:poon. 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 beame2fmf5s.r *sid4 z x9j, $$\theta \approx \lambda/D$$ , 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.]