Compare a matter wave ,s -s zx1 ,xchrixkq2bzgt5dt0d5 *s1 $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory of the atom is n (twvey(x2z2mot compatible with quantum mechanics, particularly the uncertainty(e2y xtmw(v2z principle.

Explain why it is that the more ma 8bywh bwuu 9,yw;v.yfku+) i*ssive an object is, the easier it becomes to predict iw*u;ubk)b 8 y+9, hy w.uwvfyits future position.

In view of the uncertainty prinez qjms:z1o8,ciple, why does a baseball seem to have a well-defined position andj,e zqms:z18 o speed whereas an electron does not?

  Would it ever be possible to bmz bqz,r/-nkgv6 qqh*1rj3:f -y2waealance a very sharp needle precisely on its point? Explaizfj2w- rqr *6vkqm,1bhnez3 qa :yg/-n.

  A cold thermometer is placed in a hot bowl of soup. Will the temperatuw;v*) i ayhxnr yp yxk5-4;fi1re reading of the thermoii-y5rxh; 1*)fy4w aknv;pyx meter be the same as the temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to h z9x s)0mk)jvff(c .k8 hxyren5)wqz;hrnl 0,ow well you can make any single measu5 fck0)8hyjr,zvq fx ln ;x)k)e 0.m(s9rzhwnrement of position?

If you knew the position of an object precisely, with)jr t yo3qfb)1/q z l8qjen.9d no uncertainty, how well would /lej 8nb.z1f3yorq)qj9 )dqt you know its momentum?

  When you check the pressure in a tire, doesn't some air inevitably rs ny;;1)wat zescape? Is it possible to avoid this escape of air altogether? What is the relation ;;arw 1 t)ynzsto the uncertainty principle?

  It has been said that the ground-state energy-qkhrs ghklffw vie**v ;jp.9p257+ g in the hydrogen atom can be precisely known but the exc jg*p-2s *k.fifv qg9r;k 5e7v+hlhpwited 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 hydrogen atom, the Bohr model or the quantum-mechanical(: ;ghz*kja0sq9rn et model, predicts thraz09 *; jkq:nst(gheat the electron spends more time near the nucleus?

The size of atoms varies by only a factor of three or so, from largest to s7mzb,puxf ,3zsl p (-bmallest, yet the number of electrons varies from one to over 100. Explaib-p ,,fzm (z3 u7bsplxn.

Excited hydrogen and excited helium atoms both radiate light as they3d*+q slzvwohq 46s8ao(,d(cp p0yau jump down to theals oo6 *( qw+d h0vp zs(uayd,48c3qp $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look i5zuw z ,e8gbtrqifu6q-20qc:f there were no electron spin but otherwise quantum mechanics were valid,g uzczb0tfw6q5 -2i: qr8uq e? Consider the first 20 elements or so.

  Which of the following electron confi4sem -.j p8grhgurations 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 atv7 (kt.y5shw h n,f qroy)2a*lom (careful scrutiny across the periodic table on the inside back cove.,n7y rf h ( htav)oqwksl52*yr will provide useful hints).

In what column of the pqd ,b xwia:xfs)y lp).ord4(.eriodic table would you expect to find the atom with each of the following),asb .)p yxoflx4qiwdr:(. d 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 iodin8mmo *zv q8t6 *4,wb9ex/ez qvxa4pode exhibit similar properties?

Explain why potassium and sodium exhibit sij+hdq zs/h+m z7y) fn6milar properties.

The ionization energy forqlsm7 k:/ 4tbc 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. B0rzrm5 wy3c;jelow) imply a photon nature for light? ;jc5wr03 yzm r

Why do we not expect perfect agreement between measured values of X-ray linb:ni9;;drf d()mn xrl e wavelengths and those calculated using Bli;rd9(n) r ;xf bnmd:ohr theory?

How would you figure out which lines in an X-ray spectr5,ckyw;h 9oaie7s.hl um correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an as;ogt0uv: akeo o44 o/1inxy 0tom to produce shorter wavelengths than transitions bta10ko:4oi ges nuoo;v x40/yy outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary li u ;b*xuh qey,g2uk*0mght? How is it the same?

Explain how a 0.0005-W laser beam, photographed at a distance, can skn* d )8mfkl y3ll5c9teem much stronger than a 1000-W street lamp at thm)t*dc n83f9 l5kllyk e same distance.

  Does the intensity of lkzr vx 6ob1:o y/x/eh-ight from a laser fall off as the inverse square of the distance? Explai /x1 y:rkeb/-xv6zhoon. ----待选择----yesno 

  The neutrons in a pay8yrrp-a6c7 wrallel beam, 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 , - ile3e*iby2upggo: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 hp5qccnp 81d5 n84yna can be measured 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 exciozq(ses7 1: i rd1wnmn )s1k4lted state 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 mass o(p ly 3r8lg0dff 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 aajyho .k-tlvje ju;721b :o-i typical nucleus of ralj1t u:o-j jobhv a2 y.-7;ikedius $1.0 \times 10^{-15} \, \text{m}$. [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 weku sot /n 0a a,*wpb8y(9iiv.mre present in the nucleus 9*y,m .noiu0a(ik 8vwp/s bta$(r \approx 10^{-15} \, \text{m})$, 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 positiony(v61g y pou)d 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 :)s1 :u 3pgk8t qwn vuk6;cbjvin the $n=6, l=3$ subshell?    elections

How many different states are possibleegr 2rrsc-. 4q for an electron whose principal quantum number is gr2 r r.cs4eq-$n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each elecgw2 f l2hf4 zu.vl3gy,tron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for kh,58 :;r ,ffxtgqik leach electron in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogenow a95l w01yxr 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 angular momentum of 3 vjvr h5+e(kban 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 hasywqy+q uyfe.h xhw;-f:q5 0w0/kxh 4 y $m_l=-3$, 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 "w6u i9 u7zz )vih. 0dcucx1z)pha e2(ug" subshell.    electrons

What is the full electron configuration tx2m k (1qj/wu 9vdjv)+huft-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 (ki6wvjtcx)5zkp97eed -bc40, too7 hSe), (b) gold (Au), (c) radium (Ra)? [Hint: see th )cke,6 wjhoxv-pz 94tkbto0e7c 57ide periodic table inside the back cover.]

  A hydrogen atom is in sc edp-h0 +9jne,+ bawthe $6s$ 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 usi)wybhvva6 zf+,:xx1a10yb3d(jre mt ng the Bohr theory. [Hint: This elect dv :1bxjhmytfr0eb )a+( 1y63 w,xazvron has $n=2$ and "sees" a net charge of approximately $+1e$.] The measured value is $5.36 \, \text{eV}$.    eV

Show that the total an g,1r:ztmr+tak8 cm1jgular momentum is zero for a filled subshell.

  For each of the following atomifcmsdx8sxi8wc -/ o(2xk+ j6ic transitions, state whether the transition is all ix2sikfs68 o d-c8(j/xw+cx mowed 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 y 0iogb m.jb(7$6d$ 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-waveli)gjk3;j d g pini3, 2rcy*ir7ength X-rays emitted by electrons striking the face of ad cr;y i33*p ni)7ijjr ,ikg2g $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays wv,vp6 pm rulp zz.4)-emitted from an X-ray tube havew z4urv-,z )6mvl pp.p $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff w ,t,rojyfwk15 avelength $\lambda_0$ 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 wavtk7t yak+lg; dhr, / 01vr8sl0zhjim7elength emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for anii2:c7vim.o o $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength fo o2 dvls,j7zp*g9r( udr 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 bombard hur xxq;ordhq:/p)r b3j9uf7x1 y/x3ed with electrons. The wavelength odqrr/rq ;ou7xhj p3/x)x1uy :3hbf9 xf 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 reti3o3 y- djkl04hk 3uxgrnas 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 9ckh.nb 59 00v ib6fgc01whftq w x)kla 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 o;51pml*nr r0a pmaxf )5qdr4cys7a .zf a laser beam due to diffraction if the beam emerges th )45z.; dq parl*0nxmcrf7pr amsya 51rough 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,rk*4sdhjy k wbd0-/g)rb xf*th of the He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncertainty for the elecn7e ap93tk( w.gv,mu9se/r totron 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 zego 3k,7.seavunm (9r/ tw9 ptero.] 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 possik 8.// hkpwm+qkh 3koable 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 rad 02;n ib.(fgib.hlpf.qa(jbq1 ( zchl ius of an electron orbit, estimate the average distance from the nuclfq.h.a; f q0c(bbg1( ip(hljbln2 iz.eus 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 operatec+a r3 eu)ipf8s 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 thb+:ij6v 7 uzqy0r(v n/7gftxue 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. Bekvg vtd h 1u8odxs482op2: d8dlow) 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 differesl;ysevrc (v; )x)r;vnt 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 di/+93bm0dfsy ipqu9 y8btdek+usi vq9 g9,9osfferent electron states possible for a given value of gyq sqdouy9t/9pi fv b39,8+bdek990muis+s $n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is s4:,, 0lhxggk4xp wyzj hot through two narrow slits in a barrier. The slits are a distancjy x 4, wg,zl:pxk04hge $2.0\times10^{-6}\ \text{m}$ 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 ato3 hb 72kng1x*vxksy4 xm is given both by the Bohr model and by quantum mechanics. Compare the results f bnxk*72vkx1s3 hg4xy or $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling with a spe8klj6+ 9aorx 94bsjfi,l) vwoed 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 4881o bmf6mkvdu y3x7u 9, nm. Careful measurements show the line is really spread out between 487 a ydv,97 of 36kmuum1bxnd 489 nm. Estimate the lifetime of the excited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerat1)2;hqeeg 6yw.xaa+2d 2 ukolnh 6re sed from rest across 550 V. They are then directed at two slits 0.70 mm apart. How far apart will the interference peaks be on a screlu2rx2)e6s. dw2ogha e +;ya6n qk1he en 28 m away? $\Delta y$ =    nm

An electron and a proton,aftb47c mm x-d9uuk40q p ge6, each initially at rest, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the ratio ofbkauq f4mp ug,7d-6tm49e0cx the uncertainty in their momentum.

  If the principal quantum number n were limite-)d .u cu1na x3ae+ww1gkov r6d to the range from 1 to 6, how many elements would we d3aw n k +uc)w6-.e1ouvxagr1find in nature?   

  If your de Broglie wavelength were 0.5bt29ga* d n szmixr9ikt,+/9-s v4qy z0 m, how fast would you be moving if your mass is 75.0 kg? 4rza/m2zt-tdb nq9skiivx* 9s9g ,+y$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 ofcc)i3jn oax i. yqh(-3 lines with one out of every four matching a line fromi h-c3a )o3nji ycq.x( 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 uldhns:rn ::p1/g plxhm )a 8.surface of a certain metal when it is bombah:d1xg:p s.:p8 m/a n)hrlnlurded with high energy radiation. 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 ktln 0g90qb8)o8t ww rui8ln9laser 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.]