Compare a matter wave : y5vdu7 2dzgqiw6f0s $\Psi$ 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 qz zd02t ,7)2vfjb l*5kvmghofuantum mechanics, particularly the unc d f7fbozvl2tzh), *k20gvjm5ertainty principle.

Explain why it is that the more massive an object is, the easierreg9h)) sxmc(6kc -s s it becomes to predict i)c-(s s )hrceg6m k9sxts future position.

In view of the uncertainty principle, why does a baseball seem to havg+p;b.i r bk;7:w o;u4bth lt322my( txujgfqe a well-defined position and .utbpb ; ri; hy b2; g4t+uwqlxj:ok3tgf 7m(2speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle precisely on its poinca6hs t :t) a f1;d/zykyr+vi5t?f z6y1/;hr s:iy+dta) vtac 5k Explain.

  A cold thermometer is placed in a hot bowl of soup. Will the tem51if 8 8fbzr9b fspu+mperature reading of the thermometer be the8pb89mf u 5zf1br+fs i same as the temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how wel,lhr7/ocj0 z v3 i8ofvl you can make any single measurement o v7o/ 8clrv 0zo3hf,ijf position?

If you knew the posit( ad +wd4*exls+ (siqru l04zw6m1btj1g 5m aiion of an object precisely, with no uncertainty, how well would you know its momemsiat+u bwimls11+ z*5e(xd 46rg 4a wj0qld (ntum?

  When you check the pressure in a tire, doesn't some-qa9 69c xmkjkvvb db5s6h2x/ i sn*-r air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relationbk *m-x6 v6 9cxk59h nrsd iv2sja/qb- to the uncertainty principle?

  It has been said that the ground-statetaxcd*; fi5 a9 energy in the hydrogen atom can be precisely known but the excited states have some uncertax a95*;df iactinty in their values (an "energy width"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydrogen atom,a) x bpnhbci 5o44ycji.:k55s the Bohr model or the quantum-mechanical model, predicts that the electron spends more t:b55kcpoisanx)hc4 5ib.y j4 ime near the nucleus?

The size of atoms varies by only a factor of three or so, frow)gb5(*q;xf0j pva h b8ex:bwm largest to smallest, yetgb)avw;p8(b hx*j e w: qfb50x the number of electrons varies from one to over 100. Explain.

Excited hydrogen and-awvbd qpl. vkh;/i:sv6 jw 6) excited helium atoms both radiate light as they jump down to the 66 /va-b.w:wsvkqhdlp )jv;i $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if thbwxi(9ds1l-rw tsj5 :ere were no electron spin but otherwise quantum mech5jw:r1( l - st9xiwdsbanics were valid? Consider the first 20 elements or so.

  Which of the following electron configurationsrd11s*h 1dc yy 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 (careful scrutiny avzqy2aq6rdws s5c . -9cross the periodic table on the inside back cover will provicav.-9 q rd6ys2q5zs wde useful hints).

In what column of the p(rr n7gt v7)dueriodic table would you expect to find the atom with each of the fo7rn () v7trugdllowing 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 propertilopy 9ed7:b3 8ll nfnv7 zs/j mf+ap99wt4 u;pes?

Explain why potassium and*:tpuf*5w *f 0qw asnf sodium exhibit similar properties.

The ionization energyjn l kl t); npb7obn-ch,45m)a 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 photon nature f9rnn+-i 1teqgla9 th 2or light? r29+tnnig91a heql-t

Why do we not expect perfect agreement between measured van )+xp4 /y0za xsmps/wlues of X-ray line wavelengths and those calculn mpyx/+ sspz4)x/a w0ated using Bohr theory?

How would you figure out which lines in an X-ray spectr r+ikaq2 hjc)0um correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atom bqp3 t jrm1mc o-e,l+ie8 hf2*to produce shorter wavelengths than transitions by outer electrons?ict+lbf 8,ojh1p3m-er *2qem

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How is q mfl4 g:)6:mdf)f6tqmv g9 mth qsr(2it the same?

Explain how a 0.0005-W laser beam, photographed at a distance, can seemy+s+)4wga c- 6q;j hwkijaa p4 much stronger t44aa jiww a+s+k q 6cgh)j;py-han a 1000-W street lamp at the same distance.

  Does the intensity of light from a laser fallbny h*knv1i.mq74y h o/*7sfy*)zqd h off as the inverse square of the distance? Explain.i/1 dy 7hyz7** sf )nbnqh*k.ov y4hqm ----待选择----yesno 

  The neutrons in a parallel beamhiu4 ;uc )1coh, 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 traveling with a speeq j z.rb.vqm4k . )/:lamtq/yed 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 meapz+d 84h:n 2u2f*qbqgq wnem.sured 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 statet y zhfbddta- ni(c66;(gx 4:n 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 the masshts)zj2wct5u9,g1 p t 4 2kcjgiq c09b 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 typical nucleusuy.iv:hhg;tj 0, qjg+ of radiuq g ;:jhv.ju0t,y+gh is $1.0 \times 10^{-15} \, \text{m}$. [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 weren* ) :a -2rxoe)bvv1 vk t/fcqhcen9d- present in the nucln d2*v)a -or t/becvqn)1h9x -ekc: fveus $(r \approx 10^{-15} \, \text{m})$, 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 positic ri5ol9w4caks qbu e* o/))93 xm7xruon 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 q p b;2o7hu1gy/3bbzc:gwg0 q$n=6, l=3$ subshell?    elections

How many different states are possible for an electpmfx w 6t:7: t99gsverron whose principal quantum number istm:tx97p g rsf9wv :e6 $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron innu/qrimk im:h 5 ok836 the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground state otog9s5ox3 5 wrzxj 8u3ho fmla y2p:0:f nitrogen $(Z=7)$.

  Suppose a certain hydrogen atom has l l0bcotl nvhn9 6f*/(cua;m7$l=4$. 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 an elecov83e2 /t.os oi+vvi qtron 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 h 6;4l+fnlm 5mjsrl-uras $m_l=-3$, 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" subshell. 6z ;hni(2 omi0tg jb;zpa+fv(a o3 hw:   electrons

What is the full electron configuration in1 jl)yc1f/0ii 0lh4 jus)xxq f 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 configuratio)eqlelvc,esp 8 o r6/w0ebtc6u382egn for (a) selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the per60pc l)6tue8re2beq ve3ow,sc l8g/e iodic table inside the back cover.]

  A hydrogen atom is in thevs go;k fkq/1e:r:q5 -hcam;w $6s$ 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 Bohr th -fivi5ztmu)f9 xim1(eory. [Hintffvtm5im ixzu 1-9(i) : 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 mom 6-,me;wectjb0s as6v entum is zero for a filled subshell.

  For each of the follh01r+*kpkm osowing atomic transitions, state whether the transition is allowed or forbidden0*p1ks omrk+h , 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 in o;gki4w y m5q2o*(uwz l(k-lma $6d$ 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 en0 6uc vbz/ brj8s5g:ulectrons striking the face of8cr0 :/g5njs6 zuvub b a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted from an X-ray tub m. +va x;-cl;z*isouf gzp+e2e have .a cg p i-+zfo;e luzxm+v2;*s$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wave+qok-9zt q1 ctlength $\lambda_0$ 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 whf nm7h5o8yo+zgv4z6 - d0r g6mj / l6sllrrrh-en a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelen(k qzg1rpt ,eafuvzr8;3.)kwgth for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate 0-m xdfg nqd0r.nm8, rpnb zqq/mx.36 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 matpm pas9+n9s9s yy m,9i 1,lklqerial is bombarded with electrons. The wavelength ofla9q,yk99m1ilsy m s,npp9 +s 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 detachedsz(;- 8 ,feq sz;zivaf 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 akvr x7,p45qyidv z1e9 m ph5a, 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 bwyux.nwht6p15 o74 hn sig/n x+n s+y8eam due to diffraction if the beam emerges throug+x wsn5 n8s7w+pin4 o6 gxu/thn1.hyyh 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 waveleng+ 2endukhs/blrk5; 1r th of the He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncertainty for d2; tdk,smwa 7the electron in the ground state of the hydrogen atom. [Hint: Detedsk,d; wa 27mtrmine 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 an4cg )smhuts (1d 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 radius of an electron orbit, estioi2 9*rete h--eghgie16tyf0tw i:k;* t 1n pomate the average distance from the ;:6 ooe21e-t*hgn f0t iw 1i-rekh*9gpyi tte 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 k). 2yxsjoz9m mdc92v$95 \, \text{kV}$ 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 (bindiiq +k(hbz5cdnf64 qh*ng) 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 Mo + ta-k*vducw:seley 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 give f7uo 7(0fw if(e xdqub8w5ux7n 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 numberb-ud;isea 6y jwi.f8/ of different electron states possible for a given value of ie;y sbj/ adw-ui6f8.$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narrow slbbj9vatn: xrnu:9s 297enlw * its in a barrier. The s :atj:b 99 nlxns web7run2*9vlits 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 the hydrogen atom is given both by the Bohr modep*w8 byr-x1dgo2 f p;vl and by quantum mec;rxw2vbp -p *go8dy1fhanics. Compare the results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is trfdob, z-0 oqv 2c9lgj;.h2el fe)dat. aveling 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 linppn me(.xm je9;f in-,b8 8maxe with a wavelength centered at 488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. Estimate the lifep8meip;nm-feab ,xn xm8.(9jtime of the excited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated from rest across :lsw,zfo1 yqk70vd.k550 V. They are then directed at two slitqf7k:,owy. sl10 d zvks 0.70 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 initially at rest, are accelerated across thfj3v)j0u3 rf*wv;kocs u3jg 5e same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the ratio of the uncertainty in th v0su cogu vkw)*3 j;fjrj53f3eir momentum.

  If the principal quant) 47t uk/n/glm ss2hdhum number n were limited to the range from 1 to 6, how many elements would we find in nature? d7hsgn/ t4u2hk) /l sm  

  If your de Broglie wavelength were 0.50 m, how fast would you be moving if your he--x.hws jb2 m-exh 2hj .sw-bass 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 eleme3zic -dm5;ei.aul3,sc w d:w)sooe ;f) mgr5ent shows a series of lines with one out of every four matching a line from the Lyman series of hydrogen. Assuming that the unknown element isedz;c ss wd aru,3c.i)e3l 5:-i5o;g wme) fom 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 surface of a cert qbt5m 9 xgv*7;3wb(ig;aeiuuain metal when it is bombarded with high energy radiation g7w;3 xu;mubgv5i*t ie9q(ba. 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 bl6h4:/qvd)h4 uzqb5 qffn6 bheam, $$\theta \approx \lambda/D$$ , 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.]