Compare a matter waveya4ac2kce*zoi m q9 /id0 .ipod+xj84 $\Psi$ 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 compak kuw1,cpf:3m qx1 z9atible with quantum mechanics, particularly the 9cqzuk xa1w:1 fkp3,m uncertainty principle.

Explain why it is that the more massive an object is, the easier7ey ,jlkpf9:i it becomes to predict its future posikfjlpi7y e:9, tion.

In view of the uncert(j pi*yr9e .o2 pqah:yainty principle, why does a baseball seem to have a well-defined position and speed whereas an e*hj y ra(:9e2q.opp iylectron does not?

  Would it ever be possible to balance a very sha5 j2m5/xbyud jrp needle precisely on its point? Expljbd/j m5 uy2x5ain.

  A cold thermometer is placed in a hot bowl of soup. Will the tenwiw-z9pyv3wp2 55b fmperature reading of the thermometer be 55zpf bywwi2p nw v3-9the same as the temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to howt+1ch p;tcq,pn / ehd1i /hg.t well you can make any single measureme 1 h dtp;,ietnchpt./hcq/+1gnt of position?

If you knew the position of an object precisely, with no uncertainty,o:u.aoh,o 2pj how well would y .2ja ophuoo:,ou know its momentum?

  When you check the pressure in a tire, doesn't some air inevitjtljl a61 nx */-hg-elably escape? Is it possible to avl e-ln hgj 61/ljatx*-oid this escape of air altogether? What is the relation to the uncertainty principle?

  It has been said that the ground-state energy in the hydroge xs2f 4irs 4ccrn--ko49v+phd u yy)wdd2*o6dn 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? Explaid)orsv +f-yohprs 4u6wd*ndc i49yxd4 c-2k2n.

Which model of the hydrogen atoml.u v nt/7m+xn, the Bohr model or the quantum-mechanical model, predicts that the electron spen.+7x/unt mvln ds more time near the nucleus?

The size of atoms varies bu -f hy k5yh8.u+tori:y only a factor of three or so, from largest to smallest, yet the number oy thir.8h kf:y+-uou 5f electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate ligha u4ujzd3vfj /j0b3o 3t as they jump down to thzfd ovjjj33 4 au3ub0/e $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if ther4l9g r wnkloiz:(d,llo, d9ul2y-)oze were no electron spin but otherwise quantum mechanics were valid?,l9uo dok2 :rnl9d)4zl-li l,(yozgw Consider the first 20 elements or so.

  Which of the following electron configurations are n)wuyd*ldcjf h 62,j h 8qud9b9ot 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 atom (careful scruti/p:6 xs7wn keiny across the periodic table on the inside back cover will provide useful hik:n6 wspi7e /xnts).

In what column of the periodic table would youpzj 5o4ba lb+4 expect to find the atom with each of t4pob+4aj5 l zbhe 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 properties7z;kai;bz y* n?

Explain why potassium an -l((kaq1g-/k((cyu2l tykyig auw p,d sodium exhibit similar properties.

The ionization energy for neon 1wa2 :tac)gv7*sendu $(Z=10)$ 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 photon nature fp3gkdb rr7a;8 mkc1 z-or light? 31dp 7zka rmcg;-8 bkr

Why do we not expect perfect agreement between measured values of X-ray line1fag)e2mh30e bhqr7o wavelengths and those ca3e)1hb f0ge m qrh7o2alculated using Bohr theory?

How would you figure out which lines in g;vi (x.g(vc 4 -qgco(z+ yooxan X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transit382p/kznh cj yions deep within an atom to produce shorter wavelen j2zn38yc/k hpgths than transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How is it the samejv vz4l*.5d m (0mynixmsf27x ?

Explain how a 0.0005-W laser beam, photographei-02c yr (pv(e2:tkmjnda lbnys:9/dd at a distance, can seem much stronger s9 tc 22jn-y0y(medib( nvp d/:rka l:than a 1000-W street lamp at the same distance.

  Does the intensity of light from a laix:wrs6/o)7;p(zlks7 nc )bls *rdmk ser fall off as the inverse square of the disrskbdmw7(lc i7*;skp/os xl:6 )n r)ztance? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic energ ;+ks.ex( ez4jh e7*/mhv 3ke lx;jbqjy $0.40 \, \text{eV}$ 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 wog:k ;(st k xlxp3t1e9o+imv)ith 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 b i)(h1aeq/ .y/zsj yueus3yc4e 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 excited state of an ato-l9ti em*;tvg;h kgn)m 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 uncertailm7. jru kfkeehw vns :6h4:-7nty in the 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 conta,+zd qddyh,0 gined in a typical nucleus o z,0dhq d,dgy+f radius $1.0 \times 10^{-15} \, \text{m}$. [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 the nu+,vh8gcpf / kocleus c,o /fvp8+khg $(r \approx 10^{-15} \, \text{m})$, 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 p29p7:e*- wg ofqrpvftosition 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 9f)d 8 ;f(ijcehm) lgain the $n=6, l=3$ subshell?    elections

How many different states are possibl),edh3o 0/3w.chfb1 lqgi. ym,y hhcue for an electron whose principal quantum nuhq3b3h fl0 )cci,du/,1m . h.wyohgye mber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in t0m x6./l 5r4jkwqe wkche ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numberlirf j(3ji2lq2sk u+x *))o ths for each electron in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydroge5qxw d s:w,:vy,c7k;mnbe (zbn 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 momentniph:h: ug- h*um 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 hasmidt(9 gg*8 jo $m_l=-3$, 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 "g" se ;qer8z aam7z1)w(v subshell.    electrons

What is the full electrojf 3-rzqbqo* 3n 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)0,ouzlccds. wv+ud 5f1 oae 0/ selenium (Se), (b) gold (Au), (c) radium d0fd.w0 u1,/c+o v uso5alzec (Ra)? [Hint: see the periodic table inside the back cover.]

  A hydrogen atom is in thnvq(d8 wtq l/*o1)mo pe $6s$ 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 chbank70 k11- 0ghk jn.mew4tenergy of the third electron in lithium using the Bohr theory. [Hin 01ka enn1jhkkh07-tc.4g bwmt: This electron 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 zle ) dt7 47ke u x0dnqr1b8dcrax)sk4*ero for a filled subshell.

  For each of the following atomic transitions, state whether the t5 jezwp;p+q:bransition is allowed or forbidden, and if fe5p:+jqw;z bp orbidden, 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 avi:m f5hyt03 +tync4d $6d$ 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 4fh *em((qdzk t.g3so striking the face ofgfokhm43set q(dz (.* 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 tutfk6/o/ zwbgl,*qm 1q)r y0hibe havew,0*gk i6 mhqq /r1/ ztfo)ylb $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelsv wk tt8.j*,n458phl;ep ir oength $\lambda_0$ 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 wavelen , *rveu)neav+oor*v8 gth emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelentg8w hx go)l8(gth for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to wwo6i s1gpz+o3ldzsyv8:* 4p estimate 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 3a;;ky8/ej av de+sqwan unknown material is bombarded with electrons. The wavelength q8a +a jd3swvyke/;e;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 puts out xqi w3 ;9:5doj ggs ;8nqnp,sq$28$-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 i3s98rvx,pe4t1e sg5fffrc1in 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 diffractio.71yvm;jb)u3a o 5(c swyfl pan if the beam emerges through a w ulvyp om) 5;fsacj(a.y173b$3.0$-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 xzillr9 nyt-qaz5n52l(0w o3yn2r)k He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position unl4mxpdn,fp7v- r 3j i8/irx dui59h0j certainty for the electron in the ground state of the hydrogen atom. [Hint: Determine the momentum using the Bohr model of Section 27-12 and assuh7iu3jipx9,di v -8 nfr lr0xd/j54mpme 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-f3 cbiu6rsk-t d (uc0pyp .c3 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 radius3ween mctl68i ::qq w4 of an electron orbit, estimate the average distance from the nucleus for an electron in the innermo e::c6wn 4elq m38iwqtst $(n=1)$ 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 a)k3ch9b4 ddszdr b)8ut $95 \, \text{kV}$ 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 boron0e-du41ut v11dwpj ll 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 wrjc;xsz 4. 2wmfy2(m kx7aych-itten $\sqrt{\frac{1}{\lambda}} = a(Z - b)$, where $b \approx 1$, and evaluate $a$. a =    $\ \text{m}^{-\frac{1}{2}}$

(a) Show that the number of 0 *fjjl 8oms(i7d 1.xv m2glmpdifferent 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 possible for a give4zfrse )62 xstn value of ts)6 es r2fzx4$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with ene38m4pvs9ym j.di.sr argy 45 kV is shot through two narrow slits in a barrier. The slits are a distanceyjsamr. 94di3.psv 8 m $2.0\times10^{-6}\ \text{m}$ 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 anon8lcdpmwc rc(64 8 e6d by quantum mechanics. m8(o6c 84ed6nrccwpl Compare the results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is travelinda,9 +ltdda y3ac7ftw)v. 9gjg 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 li :3f0dnnrp (cene with a wavelength centered at 488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. Estimate thfcd( nn 0:rpe3e lifetime of the excited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerate2t2 gsrej.b 4v,sn w0yd from rest across 550 V. They are then directed at two slitsy2e.s2ng trsb0v ,4 wj 0.70 mm apart. How far apart will the interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a protitq( pzds.1 2s0yogj -on, each initially at rest, are accelerated across the same voltage. 0j-doz s1 ty.iqgs(p 2Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum number n were limited q(f (njdh)u f/ hhz.)rto the range from 1 to 6, how many elements would we find in natuhffjh( n)/uh().zd qrre?   

  If your de Broglie wavelength were 0.50 m, how n5x/gofmf9,i zigc o,.;1abkfast would you be moving if your masi oma9b.;,z5c o/ xfng1gf k,is is 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 of an unknown element shows a sekealrj2 t78 *vries 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 wtv* jel 7ak2r8ith 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 surface of a cer so+oa/j: li5xtain metal when it is bombarded with high energy radiation. If thi/als:i5o j+xos photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive sprevl+j/2jta6zy9 o grq 9ad 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.]