Compare a matter wave ec1ig)m--;q -v+bfwl; rhg hn$\Psi$ 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 quantlqnbh+.fd :8t/lvgm )um mechanics, particularly the u+d l:8hb)qmlvf.t/ gn ncertainty principle.

Explain why it is that the more massivha(83v i17x5mfd vm: td yhldx2;fr w6e an object is, the easier it becomes to predicx dxh d8dar:hv5vtl myfiw76 2;1(mf3t its future position.

In view of the uncertainty principle, why does a baseball seem to have a well-de j0./zrsfzvtz21xz6hn xyt * (fined position and speed whertv2rz /( xxytz* j60fz1sn.zheas an electron does not?

  Would it ever be possible to balance a very sharp needle preciselye 3 xugr ppy;49xiw,3m on its point?yu4;w 3 px9gre3mi,p x Explain.

  A cold thermometer is placed *ri lb*m 0--klyzgj(jobet -::yb+syin a hot bowl of soup. Will the temperature reading +b(ze:j-0-mbyjlsg y*riboyk* :l t-of the thermometer be the same as the temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well you can mk,l71lwrd - 2t,pidc qake any single measurement w-27,c rlptd,1dk i lqof position?

If you knew the position of an obhre6 q )z,w x .-dj qlc3c*hli/ci-1erject precisely, with no uncertainty, how well would you know,h)6er*r cd-l/ iclq.ic1jh e z-xqw3 its momentum?

  When you check the pressure in a tire, doesn't some w,c2aq) ff:glkm2.n(w cjq7t air inevitably escape? Is it possible to avoig fq,2cql(jt2cn mk: w .f7)awd this escape of air altogether? What is the relation to the uncertainty principle?

  It has been said that q4b65ernn, z-i zr:hm the ground-state energy 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 uncertainty principle in its energy form? Explain zezi4b hr5r,n6m: nq-.

Which model of the hydrogen atom, the Bohr model or tjfl 0eoga*t g+,+9 qqxoc9lv6he quantum-mechanical model, predicts thaeof6lq+0tga j9 9 vqg,*colx +t the electron spends more time near the nucleus?

The size of atoms varies by only a factor of tte q r /;p-:0nmzza*lfhree or so, from largest to smallest, yet the number of electrons varies from ;frpzn- *emtaq :lz/0one to over 100. Explain.

Excited hydrogen and exc2lps;oot8dm vh5s pxm /2, c5cited helium atoms both radiate light as they jump down to to s;c2xt 5/h cdvmolpp5,8s2mhe $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there werensf-ynh05 9wavxo(djmi1 .ic2 6bvp; no electron spin but otherwise quantum mechanics were valid? Consider the first 20 elements f15vs2jn m6bh i naco-.;x0w d(vpy9ior so.

  Which of the following electron configurations are not - z xm0msty2w0allowed:
(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 electro52 j 5rdrrcas+n configuration for a uranium atom (careful scrutiny across the periodic table on the irr+2 rja 5dsc5nside back cover will provide useful hints).

In what column of the periodn /5ae1 axwle i3)+socic table would you expect to find the atom with each of the following conewoi + 1csxl3nae5/a)figurations:
(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 similarpjymh a-s) :uf; .3n, aju/thu properties?

Explain why potassium and sodium eohmep2mi q*7 (xhibit similar properties.

The ionization energyzu w-bdv2t2 +c 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 pfcjv6k0p , * ffxqr+d0hoton nature for light? 0 ck6vqx+j0pdrfff *,

Why do we not expect perfect agreement between measured values of X-ray line wakblhex : 4-km9velengths and those calculated using Bohr theory m9xb: hk-k4el?

How would you figure out whicwp+w.-hs 3fj,.wi .k ,haxolb h lines in an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atom to pg(* ;k st)shqdroduce shorter wavelengths thanhss*qk ()dtg; transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ froq f;m/qvcpx:hsw as+*wh;+nti 4k/ n9m ordinary light? How is it the same?

Explain how a 0.0005-W laser beam, 6i fp ej4dzjn 8m482pfphotographed at a distance, can seem much stronger than a 1000-W i 824e6dpfpj4jnm8f z street lamp at the same distance.

  Does the intensity of light from o- pp 0.yf2xb6fomu;aa laser fall off as the inverse square of the distance?.p- oup260; ofxmfayb Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic energy 9w* mq)6umxb prrr (w($0.40 \, \text{eV}$ 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 speed ofv(rpy 3vn,)nr,g9me k $(6.560 \pm 0.012) \times 10^3 \, \text{m/s}$. 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 measyo;evs r-+ *w1 3s k5dcbl:rpsured 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- +r pqv6+ugdm an excited 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 ma 6 ,bl (k4x(ivy/obcw3s u2pq-(4hu6e dsl vqfss 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 er+uueci5x9 9vcjp p1p1 i kqq+f-ix2)nergy of a neutron contained in a typical nucleus of radiu9 ii)pxkic+q-+5urfp c jeqv1p2 u91xs $1.0 \times 10^{-15} \, \text{m}$. [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 prin o5irl.7 -pr**ueje8uxww o, xciple to show that if an electron were present in the nucleus -iwl8*e.jp5,uxwe ou ro7*r x $(r \approx 10^{-15} \, \text{m})$, 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 positioi 6xx) kak;3vj6ggac6n 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 th zo+d7n,mrkb vu 5v;;ye $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whose px ;( )kaeh 3t6cv-pbvgrincipal quantum numberv6( ptx- 3)vac; bgkhe is $n=4$? Write down the quantum numbers for each state.

List the quantum number;7;f fil hl.ap9lo.aos for each electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground state xc yyv72wb: jdx4q 3/qof nitrogen $(Z=7)$.

  Suppose a certain hydrogen5;vah,/ tisp4 i j4d ju7te*st 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 an electr )uqvev6crut,ov qvkx +9f4;5 on 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 hajnib(m88 e1el:a nj pibg35u7qry.6as $m_l=-3$, 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 electmj(jzqpltw 1gbcy5(1cu 7 d0q df+/* erons in a "g" subshell.    electrons

What is the full electk hkwkl n/ a 7;6rtpbn:,rx4-yron configuration 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), (bnw0v(i gky b,3) gold (Au), (c) radium (Ra)? [Hint: see the periodic table insidy(b3w ki,gv n0e the back cover.]

  A hydrogen atom is in thc ga ;g1l;lk7fkv 9ua(e $6s$ 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 thew k9.l66ebe,izd9 mld third electron in lithium using the Bohr theory. [Hint: This electron has ,dlbw9le69zed.m k6i $n=2$ and "sees" a net charge of approximately $+1e$.] The measured value is $5.36 \, \text{eV}$.    eV

Show that the total angular momen r56xi 39svgfj gdz4l65alo z)tum is zero for a filled subshell.

  For each of the following atomic transitions, state whether th0u4 p8hm r wo/cnjehvkq g2lh7c1a.7 :e transition is allowed on/ lq.42c77pmour0kgv e:8chha1 hwjr 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 ieda1ksgl ei67l y d,.*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 ele/6.qa4wdq1dp7s jfo1 ruwq1tp(v h 8fctrons striking the face o6u(r14fw 7vw 1 jppq dhf d/q.sotqa81f 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 tubb-* - pp*h j uk0;fdfwl8/acm5yiro,x e have kyjafph0bou 8*-5/dfwr,l c ;xp*m -i$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelenp -6 ;-yb vmnh7xk2jscgth $\lambda_0$ 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 when 75p.l() plas ,. )8 afuvxcgm6iqkbwta Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for axntbkwwzb r* xr 82a+6h6w.x-n $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelengt5lay rvm:ae3 y4. daa:gza / kx:j2da3h 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 elect5x. -koah 7r54ohqq*p0sdmts rons. The wavelength od t x -o4qr h57aos*5smphk0.qf 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 lo- df, ho(qwg12imj 7retinas 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 lv*:itrdj r k+:btp. rte8 .mr7ab 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 diffrac,blm: 2ye1hs udv 6bb2tion if the beam emerges throubusd mhlyb b2e1 2:,v6gh 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 Hn0qdw4 99 l/aa1*px-nlphau u e-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncezbm:tm +ij54:ss9cw b rtainty for the electron in the ground state mcjb4+m 9:s:it 5wb szof 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.] 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 mome3ckr cpv.ah+.ntum $L$ 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 electro7xpa,or-tb7 xqr 0 ahyvp-cjj-- 1/wsn orbit, estimate the average distance from trb-aw v1-qjxr0h s7-xtcapo- 7/,p y jhe 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 :z mb1 /1kg2 hzn,jbmp/*i9uim ah1ud$95 \, \text{kV}$ 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 im:c,tw*i pn .ys $8.26 \, \text{eV}$.
(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 thbv tv 6ib,h6n6at 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 ofmhjh12idel --v bz9n .l05n+ l4gzu fa 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 kh 78ipj djpq8w/m ,s5 km5lodwkixj ; 4+-gv.different electron states possible for a given value of ji/ 5+,hmwdv mj88ok54kp k jxi-s7p.dg;lq w $n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot throusqon p8sx49 w-gh two narrow slits in a barrier. The n 9pw8 xso-qs4slits 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 bh*fp-l /f316p: fsj4h6 ijd:jfj y vkthe hydrogen atom is given both by the Bohr model and by quantum mechanics. Compare the 61sjfy-j bfl6ji:3p4: d* v jhhkpff/ 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 sphro 2(ja*yx g l,2zls,t -ei:c7n cx.heed 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 contbf9o9 qgs;:;qv1 6xftgkz9f62x yuzjains a line with a wavelength centered at 488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. Estimate the lifetime of the excited st99z62qxbyg6ojvg;fstuqx1f9:kf ;z ate that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated from rest across 550 V. They are then directed at t*/ll1w/ j /fpf c)obndy//ntqwo slits 0.70 mm apart. How far apart will the interference peaks l/1o/* //fcjtqb)pn/ ndf wl ybe on a screen 28 m away? $\Delta y$ =    nm

An electron and a prot /fta0; 5g ols7yywj,ton, 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 of the uncertainty it yj f/stgy7,a ;50olwn their momentum.

  If the principal quantum number n were limited to 2:yc zirot1qy 9 n0l2rthe range from 1 to 6, how many elements would we find in n y2zl: y9o 02i1rctnrqature?   

  If your de Broglie wavelength were 0.50 m, how fast wo9fz:g(5a 7hte wrh+n yuld you be moving if your mass is 75.0 k+nw9hfer y5 a:tz 7hg(g? $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 e lah.kw2zo8f cz. ::znlement shows a series of lines with one out of every four matching a line from the Lyman series of hydrogen. Assuming that the unknown elemez2fkac w:no.8.:lzzh nt 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 a k/san xto94upkug, 81fnc0,b re emitted from the surface of a certain metal when it i9upf ktsoxn8gk/0a1b , 4cnu, s bombarded 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 spz5p)gupi7y1g xm y qh13g/jd 3read 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.]