Compare a matter wave-cv6q t jqvupfv* 1fc+g*-e b+ $\Psi$ 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 c /s9ivgu bv5-with quantum mechanics, pbv9uc s/i-v5garticularly the uncertainty principle.

Explain why it is that the more0a3juq hrq;5 gs6*bv j massive an object is, the easier it becomes to preb 0r*3;qj56v aughjs qdict its future position.

In view of the uncertain lejk*:i(m*ow0h:pc s ty principle, why does a baseball seem to have a well-defined position and speed whereas asjh o*:iwcm(0k lpe:* n electron does not?

  Would it ever be possible to balance a very sharp needle(d e6( iyb u ,a8l;*lq 5vj+sqwgj;iij precisely on its point? Explain(i5jyli;i+bv j8(e6d;u qqsalj g* ,w.

  A cold thermometer is placed in a hot bowl of soup. Will the temperature readi bv+bxc p z-;fvuw;8s*w3onc3ng of the thermometer be the same as the temperature of thv8 xc-z b; w+p 3*fw;3cosvbune hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well you can dy 6 3ct p. jvh6onhn9mh:jiv55v9z; xmake any single measurement omhh hv;5jvn6pxyn. 6ztvoc3:j99 5i d f position?

If you knew the position of an object precisely, with no uncertainty, pf.fnn+xi- t9how well would you know itpnx+-n9tf fi.s momentum?

  When you check the pressure i *nwcgx/ +v c4akd7 ,+fbr-pckn a tire, doesn't some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relation to the d/xfb nkv-7cap+c,c+ kg4w*r uncertainty principle?

  It has been said that the ground-state energy in th/ub +,v,t,jc)r txlb qw*y5do e hydrogen atom can be precisely known but the excited states have some uncertainty in their values (an "energy wdyt/ ),5 qj ux,+btrcbwo*,lvidth"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydrogen atom, the Bohr model or tx4*2 3m h,c2*tttjvl7nz xrluhe quantum-mechanical model, predicts that the electron spendsxhn,*v2x 7t 2jttrz3l*4 ulcm more time near the nucleus?

The size of atoms varies by only a factm.uw v9r8zt-i8q bje( or of three or so, from largest to smallest, yet tb -8v zqwuj m98i.re(the number of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as they jump down f t 4zo45;b qooot)f:66 5u qmernauf/to the mr:fn5o)qe 4b/ u4f 5auo q;6t z6ooft$n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no ekykm1k(xg34y p ch48z+,g:8lc jc3 oi- qbxqm lectron spin but otherwise quantu +33qg,g :8y4q( km cocm1z-8l pbjhkxi4cxk ym mechanics were valid? Consider the first 20 elements or so.

  Which of the following rb 2zg )xhu63nelectron 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 uru prd(w)imh44 anium atom (careful scrutiny across the periodic table on the inside back cover will h)4 4w (dmpuirprovide useful hints).

In what column of the periodic 5z3s eyp-ut zi,6ozg9n ,w2e(ajdy yu x:3f4ntable would you expect to find the atom with each o2guz, wy,3-y3nuz ta i9ozp6xe fe4 :djy5(sn f the 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 propertiesq bskm825c1md/sas ; b?

Explain why potassium and sodium exhibit sf:2fjax-lo+we9 msq usd 77a7 imilar properties.

The ionization energy fory2psmkc5xa t 2ua.. sa0a *trc ,,ag5j 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) implm 9mbwfwco+v/nhh tp .y8t,+ax:x6 ;gy a photon nature for light? mxbhmv y,ww; xn8c f hg+a./opt9+t6 :

Why do we not expect perfect agreement between measured values of X-rayun pv((9ovu 8 :wjegy7 line wavelev:u( 9j(8ow e7nu ygpvngths and those calculated using Bohr theory?

How would you figure out which lines in an X-radwwb7 w9r7.nfy spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atom to produce sd7mz: 8..fzzbl xyc4 vhorter wavelengths than transitions by out.dc8zv: z mfy xbl4z7.er electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How is it th7eijpjy s e32 4*j mpf dfg:w wo;n-b*8x,gga3e same?

Explain how a 0.0005-W laser beam, photographed at a distanceh(m kjtk,v nse(h;o)3-(awt kck:g m+ , can seem much stronger than a ,cv( - gk;a hht (:mkn(eswot+m3kj)k1000-W street lamp at the same distance.

  Does the intensity of light from a laser fall off as the inverseh0hdt. (j ;/m 71xdhfzc6w2 dkj(qfvb square of the distanc(;bzfjd( w7vj/xhhfmtdq 0 d 2k1h6.ce? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kine gde)1 fqn(l p(zju:;dtic 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 i 6mc8m7t(mdv,bc1k4 pwf-qjeed 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 acuagk afcoi,l83,6(s scuracy 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 typical p1vi4 2ym/p u9its5gu6n8dyro/ zs3uly $10^{-8} \, \text{s}$. 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 o+unz5 efp,8)mar232t5pf p oehtb0h af 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 nuclmpwts5g4fhmsw:md4t2 5i.b bx,5c (d eus of radius xb2 4i.t:pwmcwh dsbt5(d mfm45 s ,g5$1.0 \times 10^{-15} \, \text{m}$. [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 thx19e,vef l rg9e nucle9 ef9x ,grvl1eus $(r \approx 10^{-15} \, \text{m})$, 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.lk9o3n 6c o;tp 2ijrn position 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 thehxhq *m2+tl9kiho50 r $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whose principal quantum nq6j(x8 nlp,2zyzt nf k3bo*v1 unb1fj 8ql6k2zv,(o3 p xz*tyn mber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers fo +k)qag4rvwfn/ung;, fx u:6 dr each electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron iz lq1z.spp) *x bl5a*cn the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen atom has 2mm/ysyc1.)z ju,6jy yy:uij $l=4$. 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 angu*uo9 8-l nhtvular 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 he .dlvldk+3unq +a -/jas $m_l=-3$, 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 yd8z fcgx;gdy o-t8o)*d (,ijin a "g" subshell.    electrons

What is the full electron configuration in the groub-4 bmpa) ;ouyb1on0rnd 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 electrjj.5xboxq3s4 b9o6z xon configuration for (a) selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the periodic table insidx x zo35bjjo46s qb9x.e the back cover.]

  A hydrogen atom is in ,.v+ 8akyp ,e n:mkm/easi4xj 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 electron in lithium using the B62 ctp8bhl fi dy51b3johr theory. [Hint: This electblp13i tb8 h56jfdc2yron 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 j p( 7ysl.kb+zsr s agb462a+ofor a filled subshell.

  For each of the following atomic transitions, state whether the transitio1zw : mn+px.gjmdkqse- j( 0ch)f x1k/n is allowed or forbidden, and if forbidden,1d.n mmx:jkjp wkzc gqs/(0)fe-x +1h 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 rj)1kk f-e a3t$6d$ 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 st37ga:ddr x)i9nth+-a(a tsn iriking the face of t)ia 3tn79adn x+s(h id: -arga $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted from an r (,-g-nj og-w)yisy2ygxz h,X-ray tube have gy2iyg , r),js -hoz-ng-xwy( $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelvkgqjvl9ex.n*0oh ai-5v gg( v0b :0h:zw l7yength $\lambda_0$ 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 emitg4zwz f.4 o:fsted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelengtz*e 8camf +a/th for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelengiy6e t;t n t*mtucw:)4th 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 bomb)ai1lrv+l p8q9yq5cvg 1i .6c1 wrxugarded with electrons. The wavelength of t g 1 cv+ iuq9lr6g8rv x1qilpw)a5y1c.he $K_\alpha$ 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 tz+n:4ml,n gg4v nr(jsxcyc0x,+g / vputs 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 powed1*k -mar1sbar 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 )0s+btot jt. pul /(xsbeam due to diffraction if the beam emerges th(u )l+/0jssxpbt. ot trough 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-Nycp(mg9yr1 btno7 vv48cm2m: e laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the positidsuf 52erb6it ;l t44son uncertainty 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 theutssl4;5t2i r4d b6fe 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 momentum6v:l-b w y4upz $L$ 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, estimao : /maol+vgexk79ie9) av6pxte the average distance from the nuco:/ go +7lev9m6x)9x avpaiekleus 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 operatesl. cyw 8f-/wwz1zss-mixktrh-kfj b 201 ) +os at $95 \, \text{kV}$ 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 boron i, kl89 hijg3y rc rg.(k 2jy5qo2ma+vis $8.26 \, \text{eV}$.
(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 :an3neocu ,2xshow that the 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 db,8jv ww-gno, g.h ;oyifferent 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 possibl06ucj +pzo a1ve for a given value of 0 +c6z o1pujav$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narrow slits in a (nm9vcf d3db4/g 1 qawbarrier. The sl943dqb w( m/facg1nvd its 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 7jd2 *jc1efc.eqi*ar) )ii f)nxc.y(n jfv8xthe hydrogen atom is given both by the Bohr model and by quantum mecicdni12 crjvn(q 7f**e)x.yci.j )aeffx8j )hanics. Compare the results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling with a sb/ djpam)- j:t-/csk lpeed 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 wavy:qs-o ab:*ap elength centered at 488 nm. Careful measurem :-*asb :yqpaoents 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 550 V. 0,,:3ukv 2ogf6 xlqjyrcz0ejThey are then directed at two slits 0.70 mm apart. How 0 30,u :cogfrlv,j2x 6kzjq yefar 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 acceleratyl g ; t8q*(.ukxwa*rnon( mt :+wke6ted across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, fxen ;qm+g8nt*(y ttw(r*w: o. uakk l6ind the ratio of the uncertainty in their momentum.

  If the principal quantum number n were limited to the range from1 awrb6 g/s f(.6gfeck 1 to 6, how many elements would we (s/kec61wff6 .gg abr find in nature?   

  If your de Broglie wavelefu w41 wmg;z;o acy+f:ngth were 0.50 m, how fast would you be moving if your mass is 75.0 kg? c:+a u4m;ofwgyz1f ; w$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 stzj /wqc0 9/ioeries of lines with one out of 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 elemz0oc t/iq9wj/ent in question. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm are emitted from the surface of a certain ax; z*v 6f;liw2(vfss metal when it is bombarded with high energy radiation. If this photon wavelen62v;xwazil;v fss *(fgth corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread of v8oe1ao4 jvf * k.eey(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.]