Compare a matter wavn8yz 6qfuh2 d+9f*kyje $\Psi$ 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 wm yis8v / u,gfrm(gb.)ith quantum mechanics, particularly the uncertainusm )mfgg,y. r(i v/b8ty principle.

Explain why it is that theda5uhpv3m *xfjatr*,6v*2 v5 uc cp d) more massive an object is, the easier it becomes to predict its future positrv)hm6dv2cvat *jaup*d5*5cfu , p3x ion.

In view of the uncertainty principle, why does a baseball .mm ,0drxl 7eyseem to have a well-defined7,me .y0dmrxl position and speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle precisely on its pq1zabo *vm wq6gsz9.y1x 5 ge3oint? Expl1 vys95zwgo.6 za3 bg *mxeq1qain.

  A cold thermometer is placed in a hot bowl of soup. Will the 5k 7 xk,/1-afkohz +aar:pqortemperature reading of the thermometer be the same as the temperature of the hot soup before the measurement was made 5kzko+7p af1-:aoxq/r, rahk? Explain.

  Does the uncertainty qayk;2;qgd5lzt3 d 0/ui7 ptg principle set a limit to how well you can make any single measurement of pgup3i5d7 ql;zty q td2g ;ak0/osition?

If you knew the position of an object precisely, with no uncertainty, ha-z4. vu*yv k0q, 019g:lr djymnx mlxow well would you knokxy090u1mrj :,.ll 4nzy-q x* vgdmavw its momentum?

  When you check the pressure in a tire, 8gs8u+3zvj2 ryx qqls i.jk11 doesn't some air inevitably escape? Is it possible to avoid t iq8g+1sxz82vsljr1qu3. jkyhis escape of air altogether? What is the relation to the uncertainty principle?

  It has been said that the ground-state energy in the hydrogen atom +x(p, +bfebbn can be precisely known but the excited states have some uncertainty in the (bfb +npbx,+eir 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 quk mnm4 .xxt w0)t*mlmstx:ayc 8uyx;y 8n--,nantum-mechanical model, predicts that the elect8t a y ;0,-nmx)skxlm umx-xyt4m:nw.* 8 ctnyron spends more time near the nucleus?

The size of atoms varies by only a factor of three or so,2hzwumykr m, ;lxt( k) 1asr*4 from largest to smallest, yet the number of electrons varies from one to over 1002al(*xmr rkzu;,ks 1myt)h w4. Explain.

Excited hydrogen and excited helium atoms both radiate light as they jumpfz*q420 qj qeww/dv)x down to thejeq2 fqw)* 4zdw/v0 qx $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if thr/:- z7m bjwhsb:ji7 d 0lby.rere were no electron spin but otherwise quantum mechanics were valid? Consider /:wzy b07hsb:jdm 7 lri.-jr bthe first 20 elements or so.

  Which of the following electron con5 )s6j-ocwx vgfigurations 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 +neo+2ajg pc20vng tq6hdr,*configuration for a uranium atom (careful scrutiny across the periodic table6r+ pnt,ajodg0qh* gvn2c2e+ on the inside back cover will provide useful hints).

In what column of the periodic table bp9 p.b(*kuet4 1 pj0c59fjnfo js2ay y4avk+would you expect to find the atom with each j 49(c jtjk +o1p02uf9b pab.*vpe4 yyan s5kfof 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 iodincgba8t3-ozzmp t.uy:s, *c r:e exhibit similar properties?

Explain why potassium and sodium exhibit similar properp138qhav+5h g i /uz*lc*bzfe ties.

The ionization energy for nert v7bg-) xmjhr(2kf-on $(Z=10)$ 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 pha)fqk 5lmybbzr2 jw -: sk(,x9oton nature for light? ,kfjbwkry:x5z(a-bsl 2)9 qm

Why do we not expect perfect agreement between measured values6i -0rzy,tg lt of X-ray line wavelengths and those calculated utt z-g,0i6lr ysing Bohr theory?

How would you figure out which lines in an X-ray spectrum c+wqv2 5a9++erq xjb nporrespond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within appm4gd(5-+,tudb0 i fip t+;cs pt5sz n atom to produce shorter wavelengths than transitions by outer smb-pzctg(t,55++ipt0iu4p fd d ps ; electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How is it g37p s-g1kl z 7t3zoerthe same?

Explain how a 0.0005-W laser beam,d;;bblyd e :qbj0w9gilu4,2h1 sr l(k photographed at a distance, can seem much stronger than a 1000-W street lamp at the sar sb:l;;j2uh409 b1e wiylbd,qdkg(lme distance.

  Does the intensity of light from a laser fall off as the inverse square of thclrbyp3y/:d/f o6y n+z8 xe l6e distance? Explx/o6dcf+3yz:y6/y rlbe p 8nlain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic energx-y+u 3l7 fr+ 4ky pcdcl) aecs.0me.ty $0.40 \, \text{eV}$ 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 spes25eijtgyut 3 k*a-- qed 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 accuracy of yj 2t*a x6m lhn4+fuobr8hf;, $1.0 \times 10^{-8} \, \text{m}$, how accurately can its speed be known?
$\Delta v $=    $\times 10^{3}\ \text{m/s}$

  An electron remains in an excited state of xyj(pdcj(zu. 3g y,6x 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 the1sgt096 fc m t i0wbr(*vfv+zxq2s i9m mass 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 nucleup2r / :e*drh) 2h kiqw*s-vkwvs of skpwvw2-r*q vdh/* ) 2ri:eh kradius $1.0 \times 10^{-15} \, \text{m}$. [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 (+/v vgdegoqfm 6.xovo7awlc2+g/y*in the nucl/(o y+oa l 2 w fq.*vexvcgv7/dmgg+o6eus $(r \approx 10^{-15} \, \text{m})$, 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 positionh7q-i..i jwj nj /bls0 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 9fs 5h)lal 8nwau8) hcthe $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whose p1flqv2ucq e- 4rincipal quantum numbe u2qfevlq 41-cr is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers f/7qqk /wdkeb5trwf48 or each electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in thrjs5n u +/xedvnvv7-dn7x; 7ne ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen+gi1gv;dt/gw -xlamz- s1f0b 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 of7wip.0ay*b-bb 4 lth x the 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 hp 0dqhmqj;.j k-,3+ hrceace8as $m_l=-3$, 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 na:e*c(irurp* l :q5s a "g" subshell.    electrons

What is the full electron configur4ht phba c.7eyy9+ xj*ation 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), (b) gold (Auf; 3r6bhqs3+yzax9hq ), (c) radium (Ra)? [Hint: see the periodic table inside the back covex3ysqbfqhzra9+3;6h r.]

  A hydrogen atom is inpl53:ji./hu pyuy,d c 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 ener/b3ik1)jfi, ep72n jh :vajnp gy of the third electron in lithium using the Bohr theory. [Hint: This electron h:)inp i n32 b/,jhfj7 pjkva1eas $n=2$ and "sees" a net charge of approximately $+1e$.] The measured value is $5.36 \, \text{eV}$.    eV

Show that the total angular u9vp ph *uy1ksrkcihc4,s.) 0momentum is zero for a filled subshell.

  For each of the following atomic transitions, state whether the tran4mys kd xfr8,;wky 4*ysition is allowed or forbidden, and ifd8 yxk4m;ky4* , swyrf 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 ihqusegp+;6 t5t(g hb1n 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 electrons striking the fal(t 2a zlic)0wce of()wai2lc0z tl a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrae em99ol3z:q dhlung X-rays emitted from an X-ray tube have zdqom 99:3 eel$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wqo0r 7up)rqgmfmr 6 (-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 wavelengthkp7 /yt 50zbi.r :pvhy emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelenf )-twty.y t)tgth for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimat2xn rva; .f42uix*jij e 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 material399 -hrj)ux/e sov v4(nsrho d is bombarded with electrons. The wavelength of ther9 93jnhr o)v4ev u-odxs(hs/ $K_\alpha$ 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 det tecfb a 5c gp5x/biom6 ;a:pv-f(sm,+ached 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 haqfl y,(b 1,*5rudo- p5 rspyb)4kykapve 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 hxd8 x ctke*0q y*beil ,f0o4(beam emerge*yfl(8bio,4e0ctx0xe *d qkh 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 of the He- go/b,v fa+0x *maenr2Ne laser?$\lambda $ =    nm

Use the uncertainty principy wz++et y0rcs*j0wht0+ot/d le to estimate the position uncertainty for the electron in hy+ro*0tz0/wc 0+swytt+j ed 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 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 smalu1z5e3x; s jx)9p8 pr7kewyc nlest 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,m8v k/ eu d6a67,zeci/4e cmat estimate the average distance from the nucleus for ac6de etak4i/6 vm/,7zamuec8 n 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 a/ss9i:6rrjp 3o7.ax(/ u(c jqlanwj $95 \, \text{kV}$ 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) en0pw0t,a3tgh4vkfx b. ergy 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(Fryhd2/ h7 fuh 99tyc7hnpm5)pig. 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 of3,gqvqt5e8hf4 h3eht 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 different electron states possiblc*ib*yv8 tzrzw z5wkfa))q 28e for a given value of zyb) 5f)8 *t wkva2 8wrzqz*ci$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with lk26wl.bkefq h -u k+9energy 45 kV is shot through two narrow slits in a barrier. The slits are a dk qh92 .u- webkl+lkf6istance $2.0\times10^{-6}\ \text{m}$ 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 model a4u6k t5vv9vqind by quantum mechanics. Compare the5 46ikvu vv9qt results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling kx8r (-l za,egwith 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 488 nm. Caref n0h ree4n-w4rz g(d*oul measurements show the line (-eor*n0wz 4egr dn4h 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. They are then direcm8;7dk4rg 4:s0e.s krki- fzuefair *ted at two slits 0.70 mm apart. How far apart will the interference peaks be on a scdk g ke48.r7 m;:*r4u sffks-ira0izereen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially alon4yf gf;0n3ugr);ly2 djs 5 t rest, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Brogl;s) 2jnfr 3yg;yd 0 gun4lf5olie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantuc,y9yl+(.u jxjkku 9c2*be ngm number n were limited to the range from 1 to 6, how many elements uy9+ xkg9jec* , jc(2nk.ybulwould we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast would) jc*tkj4wv q-s) el4o you be moving if your mass is 75.0 kg?l)cs44j kewt -*vqj)o $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 seriek 8+t,dnamp)js 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 e +8dtm,jpkna )lectron, 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 certain 7r3x ) : uvzug4+4bs(cpf cvefmetal when it is bombarded wip3cfzr uvfs4 : xu)c47egv+(bth 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 yq)d2 anmy9kx+ 6a(v hof 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.]