Compare a matter wavej35wbzh5 s7bz $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory of the silp4 aor6: 8iatom is not compatible with quantum mechanics, particularly the uncertainty prinps io :864alirciple.

Explain why it is that the more massive an/h6 gck(hf ei/s3 nct) object is, the easier it becomes to predict its future posit i3nhte/sf6c/(hgk)c ion.

In view of the uncertainty principle, why does a baseball seem to have t )c3m4h n*kfha well-defined position and speed whereas an electron does nfh)4tcn* kmh 3ot?

  Would it ever be possible to balance a very sharp4 tkq9ae b, umm0q5s+u needle precisely on its point? Expla4s0 b ,k+uemqu m9taq5in.

  A cold thermometer is placed in a hot bowl oqt3v7vkkb d y+50wu j;bke (z8f soup. Will the temperature reading of the thermometer be the same a7vtub +yqjkd kz 0( 5vb;83kwes the temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a lkdnz (n.p+nl9 imit to how well you can make any single measureme+z(nkl pn.9 dnnt of position?

If you knew the posiapn00q:(pl :kcr pr; dtion of an object precisely, with no uncertainty, how well would you know its momentu0kpl:pq( rdrn; p0ac:m?

  When you check the pressure in a tire, doesn't some air inevitably :of.h81 f tiepescape? Is it possible to avoid this escape of air altogether? What is the relation to the :fie1.hpof 8t uncertainty principle?

  It has been said that the ground-state energy in the hydrogezi :zw -c+9m tplx *s;u0v)smzn atom can be precisely known but the excited states have some uncertainty in their values (an "energy width"). Is this consistent with the uncertai lv9p*m wxzziuz t:-+0cs;ms) nty principle in its energy form? Explain.

Which model of the hydrogen atom, the Bohr model or the quantum-mechanicaty6evo uh/3l ptxgf1z)1t p+2l model, predicts that the electron spends more timefetup 23)p1 zg/xtl v61+ytho near the nucleus?

The size of atoms varies by only a factor of threeqk, 81jss os9u or so, from largest to smallest, yet the number of electrons v1 8 9sjqos,kusaries from one to over 100. Explain.

Excited hydrogen and exc1elx jxx4i); lited helium atoms both radiate light as they jump down tjxx)x iel 14;lo the $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there wfplf,o;q6uek u1 4pf.ere no electron spin but otherwise quantum mechanics were valid? Consider the first 20 elemenqufpp1 ef .4lf; o6uk,ts or so.

  Which of the following electrgbl4- ) .asuyjon 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 fo 3kzbg49rtz4tr a uranium atom (careful scrutiny across the periodic table on the insidkgtrz b4t94 3ze back cover will provide useful hints).

In what column of thl*;q0g0m)t p p 4l k.vj:wzxudmqk .a+e periodic table would you expect to find the atom with each of the following configuratiulp0v.x) jmm4q wtq0 *k:gda;zpkl .+ons:
(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 exhinv-b.bs g7i/:fmo i**b 0gtxbbit similar properties?

Explain why potassium and sodium exhibit simi0p9: pcu.yadq i9wm+ilar properties.

The ionization energy for neh1y v.3hp4 hjyon $(Z=10)$ 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 for ligei11: ns2qpmjht? npq11jie s2:m

Why do we not expect perfect agreement between measured values of X-+ybxkv,yt2x 8+az 4jyray line wavelengths and those calcul,x + y8tzav+yk4bj2yxated using Bohr theory?

How would you figure out which lines in an;cpcyet :wpq-pf 6byh 4019o*r k9p ij X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron qb2ol 1)lkd d6mp*y:qssw- 3orpu jf, 9ny- 6ttransitions deep within an atom to produce shorter wavelengths than transitions by outer e*: sslnkrq,qb)pyy -du- 2f3 d6 tjp69o ml1owlectrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinarynygu0a7rr 9a 2 light? How is it the same?

Explain how a 0.0005-W las:2q6d-syd u 7) 8 sxjk2lyfsaher beam, photographed at a distance, can seem much stronger than a 1000-Wh x8d)2 ljqfss-dsy7k2uy6:a street lamp at the same distance.

  Does the intensity of light from a laser falrl uonz)c)1g.l off as the inverse square of the distance? Explaizco1.r ln) u)gn. ----待选择----yesno 

  The neutrons in a parallel beam, ea(,uqb j uys/o -id/ybur1vf00ch 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 traveling26dfza8o vf n2s(rlkavf8m+ 7 with 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 be measured t t*hs2j-7razx0 *tpoto 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 d 6-t21xuf prsof 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 of a muonakt) y2s/ql;iv+qyv2 $(m=105.7 \, \text{MeV/c}^2)$, 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 nucl)0eos .l4nmhdeus ofnd e .l0h4oms) 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 sqz5uf :l8 dtf.tzy/e8r0 js.hhow that if an electron were present in the nuhd8: rzef.zs5yj8t ftl0q /u.cleus $(r \approx 10^{-15} \, \text{m})$, 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 theuws gbzz1ris05 h :u/a w/e:0j 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 ii:omh dxjt2g58+;ig3c1, yi -rn kiidn the $n=6, l=3$ subshell?    elections

How many different staterph +b2mm4 4ras are possible for an electron whose principal quantum numrm2mr+ahb4 p4ber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the gmj um6bt;-:k7 n9z cffround state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground 2(65yzpo czma)ym jvf+s 7o 9ystate of nitrogen $(Z=7)$.

  Suppose a certain hydrogen atom haso o6bl;av9h.+umqoh3 a 3a w-t $l=4$. 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-azt p+hg+ 2ee 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 hr.:pv ocml/j1ko9+cpmb r -)x as $m_l=-3$, 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 i1 mik*v:/q5vwsf ubfmb zvb )5-cb,e. n a "g" subshell.    electrons

What is the full electron configuration in the ground state for elements k :b8x ui)g0qdwith $Z$ equal to (a) 27, (b) 36, (c) 38? [Hint: see the periodic table inside the back cover.]

What is the full electron configuration for njg /iyww-r(d(b7 bt5(a) selenium (Se), (b) gold (Au), (c) radijw- w/b(n gy5ibd 7(rtum (Ra)? [Hint: see the periodic table inside the back cover.]

  A hydrogen atom is in the ( he :xy)qhks/$6s$ 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 usingif0hhmzu y)f7s ) *p5p the Bohr theop5m))si*h z f0fp7 uyhry. [Hint: 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 zeroopjc orbo8 y zo-2gh94-,khw : for a filled subshell.

  For each of the following a0(wfy- ju h3yjtomic transitions, state whether the transition is allowed or forbidden, and if forbidden, what rule is being violated0 w-y (hyufj3j:
(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 infd )rh4jmkex)cb *3(w 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 the72j m.crp6(jko1p r ctsmb5 k) face of5t2jk6p)omrk ( 7jmr1cpc b s. 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 tube3 kj r )pgabm4qzl64+n 7k;joi have4)rzbkj+ikg6 ;op q 4 7nalj3m $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavee .glgzo;,f9 rlength $\lambda_0$ 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 a Co i q *(zc)gbg9,wtzhvhs.dq m , cag61az (jh:+$(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for an 0-: qq9mhu qug$n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelej42ac 80ygwofly y77bngth 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 3u+lacm9 y10cbsdo v+ unknown material is bombarded with electrons. The wavelengb +9+ov 1lsad3cyc0umth 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 qs29a1fzsbhy)( o4m nretinas 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 a power xz -0b a4b2+pehwu1*y7i(zi phsdp)u 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 -cdobtt- wqeg. .ad* e4wn ,2hbeam due to diffraction if the beam emergesedqg2*wbc,t.-.- h andtw 4e o 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-Ne laserx5duv nk2-g0x ?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncertainty fc.y3y+aacqtp(k5n 6l or the electron in the ground st5y aa yck3n (6q.l+ptcate 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 smallest p t vdj13rd:eb ecab4ojs vyv9p4g145y (m1q2aossible 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, estimate the aver p5 *xwhi)w,mgage distance from the nucleugxi 5wp)h*, wms 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 operatha4;a nsa.t5 oes 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 o o+y.t 6zgajdm,v.qlt j5z 82uf 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 to3bup)l j;gd m 4( -ooii4df1xr show 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 different stateb,7l)s cv 72m 65ryx 4yvzuxzds 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 eleo ftrtciu-n in ;:h)(7ctron states possible for a given value of h;-:)rf(ti c nto ui7n$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through tw1ok-o2f8:l4s u e+yufkg5 (gzpvw;;ca ffl, bo narrow slits in a barrier. The slits k,-ks +uzffpgfcb;e( 5l:2gyl wo ;1 4ufoa v8are 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 the 7zbrj/qc:+f yhydrogen atom is given both by the Bohr model and by quantumy7qzfc/j+ :br mechanics. 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 spealx(q wb/d 1(wed 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 centetr p.xu9j-kf4/r/mqx red at 488 nm. Careful measurements show the line is really spread out between /kfxuqm-tr r.jxp/4 9 487 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. Tkgj/h u4 bza(+hey are then directed at two slitsguz/( hb +aj4k 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 proton, each initially at9zex75u sm/edu*9+:c/zgpda u7alvm 5 h8nno 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:9h75/uuos7xdcd5 + gn/ emv*ema azp l8znu9 uncertainty in their momentum.

  If the principal quantum number n were3q pzq+6*hmv gtz94lh w5op;u limited to the range from 1 to 6, how many elements would we fi q+vtwu pg569 3hl*zz ;q4mophnd in nature?   

  If your de Broglie wavelength were 0.50 m, how fast would you be moving if y bk6w:arr2f *7w q)jc)j e0kxz77uz ssour mass is 75.0 kg? zx6 72kk*: cssa ))z77ujwrej bf rw0q$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 elmarz n,81u mf5ement shows a series of lines with one out o,unam85 1 fzrmf 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 element in question. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm are emitted from the .y lktc:)*rmssurface of a certain metal when it is bombarded with high energy radiation. If this photon wa: ty*ml c.krs)velength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive sprea2m ( ,sdqg)ndod 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.]