Compare a matter wave7levo kcmsz (9q)cs/ * $\Psi$ 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,-elqk0dggw 4* 9qt jg mechanics, particularly the uncertainty0-gw jqt4 , k9gqedlg* principle.

Explain why it is that the ma :pg0 hh2sids1j4e i4 r8cd2fore massive an object is, the easier it becomes to predict its future posishr1 sdfej0 a8dh24:4 iicgp2tion.

In view of the uncertainty principle, a5s6dn2uir5cavhohg / g0ci 97wkn56why does a baseball seem to have a well-defined position and speed whereas an electron dv6 5c7 gcs5/ a0knh6 hruoigandi 59w2oes not?

  Would it ever be possia6 m3mnuc2qqwlf y(1 3ble to balance a very sharp needle precisely on its point? Ew al6 (3q1 32mnuqfycmxplain.

  A cold thermometer is placur;hlsb)wlb m)405eci-4 t) n lp1o xced in a hot bowl of soup. Will the temperature reading of the thermometer be the sabmiln4lh;t-)0x)s4pocr 5 ecl w)bu1 me as the temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principlex:b* cqw6x.vj set a limit to how well you can make any single measurement of positiq:j cb.xw*6 vxon?

If you knew the position of .e)z k0 (yroxc*)t tcjan object precisely, with no uncertainty, how well would you know its momenty*oejc)r c. )k0zt x(tum?

  When you check the pressure in a tire, dq;/.zchx8i u doesn't some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relai.;c/u z xdq8htion to the uncertainty principle?

  It has been said that the ground-state et80c.qn5 0l i aik:pk4:o waumnergy in the hydrogen atom can be precisely known but the excited states have some uncertainty in their values (an "energy width"). Is this consistent with the uncert8m5ka pnt qi4: k wuc.ia:00olainty principle in its energy form? Explain.

Which model of the h:w s:v;jcz0r1mna 5npj z f+i6ydrogen atom, the Bohr model or the quantum-mechanical model, predicts that the electron spends more time n1z60jminfp:z5jcn; a+r:s wv ear the nucleus?

The size of atoms varies by only a factor of three or sdx cs,b bdvibx(2)m3r2f4 m-5gouhc( pd 6 ar3o, from largest to smallest, a mdfmuc h2 )xr6-d 5 ,sgboircd(x(4v2b3bp3yet the number of electrons varies from one to over 100. Explain.

Excited hydrogen and eum otcy,y9mv3 f klsy7n.icz00-p/ +bxcited helium atoms both radiate light as they jump down to 39+zbiytp70n cm so/ckyy,m.flv-0uthe $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron.;2op 5 jaln jnwlvl*o(+vnj* spin but otherwise quantum meaon 2 jjlwv;pjlo5n*. vl+* n(chanics were valid? Consider the first 20 elements or so.

  Which of the following electron configurations are not ajd n)1nguf5*u:7u/ s1j2ugi uj gs x+cllowed:
(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 scrutin5zlyj5ic2q rhh3 3j2qm 3(jb ky across the periodic table on the inside backj2 cjk3 ijq mby3(l z3rh552qh cover will provide useful hints).

In what column of the periodic table would you expect to find the78. gax i82jqe m ona1ftw1g2l atom with each of the following confi17xolmn g 1fig82awje8.qat2 gurations:
(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 properi,,snz7b;wj ev kx;l6ties?

Explain why potassium and sodium exk5h*jl 6 4aqgszkd0ufq 271qthibit similar properties.

The ionization energy for nd*q3sg -u/*km.c u9rt rzy )mjeon $(Z=10)$ is 21.6 eV, and that for sodium $(Z=11)$ is 5.1 eV. Explain the large difference.

Why does the cutoff wavelength6 z*w+ ywv9h:jhnxf7t in (Fig. Below) imply a photon nature for light? +*zjh6w:fwh vn7xt9y

Why do we not expect perfect agri ue gwhe/7m0m(ewj2+ zjk t5:eement between measured values of X-ray line wavelengths and those calculated using Bohr theort 0j(k2i/5mwmez ue7w+:gjh ey?

How would you figure out wtuwuyy e zx174y* d6-ihich lines in an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transi(s wc0o)xz g6htions deep within an atom to produce shorter wavelengths than transitions by outerg)zh0(x6c s ow electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How i6qxamywi uk1k *2*;r red sga-zze+)3s it the same?

Explain how a 0.0005-W laser beam, phoj 7poc(rn i*noe o8, zf/ji;n1tographed at a distance, can seem much strongerocnj ( nioizjfo 87*e;/1 np,r than a 1000-W street lamp at the same distance.

  Does the intensity of light from a laser fall off as) 1lpkgc(fa -s the inverse square of the dipl-1fc ka) sg(stance? Explain. ----待选择----yesno 

  The neutrons in a parallel beam,b+s7hdq:t q)l 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 travelin9ur 4*bw qw5ym0d/ og06jt. 6au 4qi+wjxqsazg 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 q)683v-oda n. jkd azjnwaf/2 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 tyl9gy z;txly 60ouk:1m 8 x4ctp2 egoi,pically $10^{-8} \, \text{s}$. 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 mass of a mu1sy5 xw939 j+edmxkweon $(m=105.7 \, \text{MeV/c}^2)$, 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 contn;lz.v9/d0b t5z, rctbur8rq 8 vxk4yained in a typical nucleus of rv/znr.; ckb58ql 9 bd4r8rx0t ,utvzy adius $1.0 \times 10^{-15} \, \text{m}$. [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 el,rcvby9+k;tcqf2c 4kewn p 18ectron were present in the nucktce cfpqb ,v84wyn;2krc 1+9 leus $(r \approx 10^{-15} \, \text{m})$, 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 pot .s+(d5so l. b gjx(yo4riyj.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 ca4ci0tfzh 83 bcn be in the $n=6, l=3$ subshell?    elections

How many different states are possible for an electron uqr1xhw n+kbnk n+5+ad;pp-) q0ke ( vwhose principal quantum number is q0e+)(qknwpv;x+u 1 5akpnhbdkr -n+ $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for eac2wn:rr w( r(4igu6dvxn/ zf z;h electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electroh2nbn4 v*nb+,yv/m t cn in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen ;x;vbc6 v; bwa* 7d -ovcwjmc9atom 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 ku+5w4 r:1xusmor(fdthe 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 has hfsty:gk 5 s 8-rq 4ns/l7goe4$m_l=-3$, 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 electtpe7ybu(b9 r 2rons in a "g" subshell.    electrons

What is the full electron confbfwgl7cb qsa m8- fij9 8,h2,x8ql od3iguration 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) sel ez -vy7t9f9mbwz /z.yenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the y z/z.yb7 99-zwtvmfeperiodic table inside the back cover.]

  A hydrogen atom is i-m0hncjqz1e r2 k7 ne+n the $6s$ 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 e41d7 9sl37tqhacha v blectron in lithium using the Bohr theory. [Hint: This 1vh9batc4qd3als7 h 7electron 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 filled subshell.7g4h*a9 d fwifc8 fj)v

  For each of the following atomic transitions, sta x ).nyt icmut2,3t+aste whether the transition is allowe acm un+tt,.x2 iy3)tsd or forbidden, 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 a j cajp+k g.7*p ,,brgeuh mdlt7900fg$6d$ 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 striking the fev2pwu hw.2b8ace of a wuw28pbhv.e 2$33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted from an X-wuik4br/d3p u (2 mab vp b049xpkva12ray tube have pd2ku kb143vv/a94a 0wxubrp2mip (b$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavk8m ) c2.(yehm/tvvahelength $\lambda_0$ 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 8e,xs(z3khdl when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelengldlz 2wa p.pq. sn )6x9xu(1ohth for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength fo +rr(usdc u)5-kih ya(r 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 an pzquv9 yhg:;3d an unknown material is bombarded with electrons. The wavelength :qg hz;3v9upy 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 p uzt2+ 5hc.mesuts 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 6/5 jkh 2ywgjrin a 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 beam em xg7fyxe,ip1d+: pk; lerge7fp+i;xpdeg x,k1yl : s 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 of5vuy)y :f/nv7d( sh-q pwed9 a the He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncertaint3a/2lpj* ,h ku o;ke/xo*vupe1lk4n ty 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 anywv ,**oktula h3;epl2 kue k/po4n/1jxhere 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 pozvn5m.)gs4lzx/o vqrod8riwd fj;jw 3. .(- ossible 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 elecmg34(3w+owcvg - ixsftron orbit, estimate the average distance from the nucleus for an electron o4cxv3f i+smww-gg( 3in 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 ,o/te/jt5 q mdoyon(3at $95 \, \text{kV}$ 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 (bindingu g ( v6y9v90rox(goco1z7dzy) 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 um ) + cq3xvbpraw nv:8u+rvv+z y:36p$\sqrt{\frac{1}{\lambda}} = a(Z - b)$, where $b \approx 1$, and evaluate $a$. a =    $\ \text{m}^{-\frac{1}{2}}$

(a) Show that the number of different states for a givxvl ccc0 +3 8z9rvn1uden 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 ele x1ain3*-kj93cl 8zghxmg .f pa(cf: yctron states possible for a given value of (am8c*l9nj gyxa-3ik31f : . hzf gpcx$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narrow slit v or-g62n)uw qxw,w7ks in a barrier. Thxw,)6vgk wu- w7 nq2roe slits 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 hydrogend o nlq*o ;l;)8lpzj,p atom is given both by the Bohr model and by quantum mechanics. Compare the results 8lqjd )*zopo;; pnll ,for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is trave;qbvnv9 rob x-95/ upf(tr.keling 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 gg6tz ;tm0g(bd:k33bpsr s9alw y9.o488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. Esti3tp(m.9r6 y;ssdg 0g:k3 azl otwbg b9mate the lifetime of the excited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerate4 es,.ggjj6hgbo4 c 5id from rest across 550 V. They are then directed at two slits 0.70 mm apart. How far apart 4jghb,s 6eo5g4g ic.jwill the interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, are acceleraqcr3be v+agd/5bwgg6 x j39x+ ted across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the ratio of the+ggjrd bab 3369qwxe5v /x c+g uncertainty in their momentum.

  If the principal quantum number n were limited to the range from 1 to 6, h( e ;r,nc-sxeoow many elements would we fi,enc( e-s ;roxnd in nature?   

  If your de Broglie wavelength were 0.50 m, how fast wouljm k +gn4sd84-vopy7cm33 vk dd you be moving if your mass i3+g7ymp-odvskcjv n4 84 k 3mds 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 ofj6s c5e;mcb.x y )0xtx an unknown element shows a series of lines with one out of every four matching a line from thxc .ey6c0tbx j ;x5s)me 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 emitted5 mnk3::i.kpy h3 wdnqnpou66 from the surface of a certain metal when it is bombarded with high energy radiatiokp3mon u y3n wndp6k:h6 i:q.5n. If this photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive sprz j-s 2oa02hhvpmh8 2eead 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.]